Search results for """ "Fuzzies""

Book SynopsisWelcome to the MOO and IMPROVED Fuzzy Fuzzy Fuzzy!, a touch, skritch, and tickle novelty book from the one and only Sandra Boynton!Little ones won’t be able to keep their hands off all the interactive, tactile elements in this engaging novelty board book featuring Sandra Boynton’s classic humor and inviting illustrations. Tousle the cow’s fuzzy blue hair! Skritch the puppy’s rough little paw! And check out the cool green shades on that hip piggy! This petting farm playland is always at your fingertips!

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Book Synopsis From the minds of Tom Angleberger, the New York Times bestselling author of the wildly popular Origami Yoda series, and Paul Dellinger, an adult science-fiction writer, comes Fuzzy, a funny middle school story with a memorable robot title character. When Max—Maxine Zelaster—befriends her new robot classmate Fuzzy, part of Vanguard One Middle School’s new Robot Integration Program, she helps him learn everything he needs to know about surviving middle school—the good, the bad, and the really, really, ugly. Little do they know that surviving seventh grade is going to become a true matter of life and death, because Vanguard has an evil presence at its heart: a digital student evaluation system named BARBARA that might be taking its mission to shape the perfect student to extremes! With a strong female main character who will appeal to all readers, Tom Angleberger and Paul Dellinger’s new novel offers readers

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Book SynopsisMore than three decades ago, H. Beam Piper's bestselling science fiction novel Little Fuzzy captivated readers everywhere. Now, all three of Piper's delightful books are available for the first time in one volume: Little Fuzzy, Fuzzy Sapiens and Fuzzies And Other People.

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Book SynopsisMake your own fuzzy stickers featuring your favorite Pokémon!Color in fuzzy stickers featuring some of your favorite Pokémon! Use the included double-tipped pencils in 10 custom colors to color right on top of the fuzzy sticker. It''s that easy! Store your finished stickers in the book, or stick them on your stuff to show off your fandom. Share some with your friends, so they can feel fuzzy, too. Preprinted artwork features Pokémon favorites, including Pikachu, Eevee, Charizard, Gengar, and many more!

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Book SynopsisFrom New York Times bestseller and Hugo Award-winner John Scalzi, comes Fuzzy Nation, an extraordinary retelling of the SF classic Little Fuzzy.They're small. They're fuzzy. They'll change his life.On the planet Zarathustra, Jack Holloway is about to strike it rich. A contractor for intergalactic behemoth ZaraCorp, he’s just discovered a mining seam worth billions. It would make the corporation a fortune, and set Jack up for life. Everyone wins – then he discovers the Fuzzies.Small, intelligent and cat-like, the Fuzzies are the cutest creatures this side of the galaxy. They’ve set up home in Jack’s cabin, and have become best friends with his dog. They’re also standing in the way of ZaraCorp’s profits. For the planet’s resources can only be exploited if it’s free of native sentients. ZaraCorp’s solution: to eliminate the Fuzzies for good. And they’ll permanently silence anyone who interferes – including Jack.Praise for John Scalzi:‘John Scalzi is the most entertaining, accessible writer working in SF today’ – Joe Hill‘Scalzi is one of the slickest writers that SF has ever produced’ – Wall Street Journal

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a huge range and FREE tracked UK delivery on ALL orders.

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Book SynopsisWhat is Vagueness.- Sets and their Properties.- Fuzzy Sets and their Properties.- Extensions of Fuzzy Sets.- Fuzzy Numbers.- Other Fuzzy Constructs.

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Book SynopsisProvides detailed mathematical exposition of the fundamentals of fuzzy set theory, including intuitionistic fuzzy sets This book examines fuzzy and intuitionistic fuzzy mathematics and unifies the latest existing works in literature. It enables readers to fully understand the mathematics of both fuzzy set and intuitionistic fuzzy set so that they can use either one in their applications. Each chapter of Fuzzy Set and Its Extension: The Intuitionistic Fuzzy Set begins with an introduction, theory, and several examples to guide readers along. The first one starts by laying the groundwork of fuzzy/intuitionistic fuzzy sets, fuzzy hedges, and fuzzy relations. The next covers fuzzy numbers and explains Zadeh''s extension principle. Then comes chapters looking at fuzzy operators; fuzzy similarity measures and measures of fuzziness; and fuzzy/intuitionistic fuzzy measures and fuzzy integrals. The book also: discusses the definition and properties of fuzzy measurTable of ContentsPreface xiii Organization of the Book xv 1 Fuzzy/Intuitionistic Fuzzy Set Theory 1 1.1 Introduction to Fuzzy Set 1 1.2 Mathematical Representation of Fuzzy Sets 3 1.3 Membership Function 6 1.4 Fuzzy Relations 10 1.5 Projection 13 1.6 Composition of Fuzzy Relation 14 1.7 Fuzzy Binary Relation 19 1.8 Transitive Closure of Fuzzy Binary Relation 21 1.9 Fuzzy Equivalence Relation 23 1.10 Intuitionistic Fuzzy Set 24 1.11 Construction of Intuitionistic Fuzzy Set 26 1.12 Intuitionistic Fuzzy Relations 29 1.13 Composition of Intuitionistic Fuzzy Relation 31 1.13.1 Composition of IFR Using T-norms and T-conorms 32 1.14 Intuitionistic Fuzzy Binary Relation 34 1.14.1 Reflexive Property 34 1.14.2 Symmetric Property 37 1.14.3 Transitive Property 38 1.15 Summary 39 References 39 2 Playing with Fuzzy/Intuitionistic Fuzzy Numbers 41 2.1 Introduction 41 2.2 Fuzzy Numbers 41 2.3 Fuzzy Intervals 42 2.4 Zadeh’s Extension Principle 43 2.4.1 Extension Principle for Two Variables 44 2.5 Fuzzy Numbers with α-Levels 48 2.6 Operations on Fuzzy Numbers with Intervals 52 2.7 Operations with Fuzzy Numbers based on α-Levels 54 2.8 Operations on Fuzzy Numbers Using Extension Principle 62 2.8.1 Operations 63 2.8.2 Examples on Operations of Fuzzy Numbers Using Extension Principle 64 2.9 L–R Representation of Fuzzy Numbers 66 2.10 Intuitionistic Fuzzy Numbers 73 2.11 Triangular Intuitionistic Fuzzy Number 74 2.12 Operations Using Triangular Intuitionistic Fuzzy Numbers 75 2.13 Trapezoidal Intuitionistic Fuzzy Numbers 77 2.14 Cut Set of Intuitionistic Fuzzy Number 78 2.15 Distances Between Two Intuitionistic Fuzzy Numbers 80 2.16 Summary 80 References 80 3 Similarity Measures and Measures of Fuzziness 83 3.1 Introduction 83 3.2 Distance and Similarity Measures 83 3.2.1 Distance Measure 84 3.2.2 Similarity Measure 84 3.3 Types of Distance Measure Between Fuzzy Sets 84 3.4 Types of Similarity Measures Between Fuzzy Sets 85 3.5 Generalized Fuzzy Number 85 3.6 Similarity Measures Between Two Fuzzy Numbers 88 3.7 Inclusion Measure 94 3.8 Measures of Fuzziness 95 3.8.1 Index of Fuzziness 95 3.8.2 Yager’s Measure 96 3.8.3 Fuzzy Entropy 96 3.9 Intuitionistic Fuzzy Distance and Similarity Measures 98 3.10 Intuitionistic Fuzzy Entropy 105 3.11 Different Types of Intuitionistic Fuzzy Entropies 106 3.12 Summary 107 References 107 4 Fuzzy/Intuitionistic Fuzzy Measures and Fuzzy Integrals 111 4.1 Introduction 111 4.2 Definition of Fuzzy Measure 111 4.3 Fuzzy Measures 112 4.3.1 Sugeno λ-Fuzzy Measure 112 4.3.2 Belief Measure 115 4.3.3 Plausibility Measure 116 4.3.4 Possibility Measure and Necessity Measure 116 4.3.4.1 Possibility Measure 117 4.3.4.2 Necessity Measure 119 4.4 Fuzzy Integrals 121 4.4.1 Sugeno Integral 122 4.4.2 Choquet Integral 125 4.4.3 Sipos Integral 129 4.5 Intuitionistic Fuzzy Integral 130 4.5.1 Intuitionistic Fuzzy Choquet Integral 130 4.6 Summary 131 References 131 5 Operations on Fuzzy/Intuitionistic Fuzzy Sets and Application in Decision Making 133 5.1 Introduction 133 5.2 Fuzzy Operations 133 5.2.1 Fuzzy Union 134 5.2.2 Fuzzy Intersection 134 5.2.3 Fuzzy Complements 134 5.2.4 Algebraic Product 136 5.2.5 Algebraic Sum 137 5.2.6 Simple Difference 137 5.2.7 Bounded Sum 137 5.2.8 Bounded Difference 137 5.2.9 Bounded Product 137 5.3 Fuzzy Other Operators: Fuzzy T-Norms and T-Conorms 138 5.3.1 Definition of T-Norm 138 5.3.2 Definition of T-Conorm 139 5.4 Implication Operator 142 5.5 Aggregation Operator with Application in Decision Making 144 5.5.1 Fuzzy Weighted Averaging Operator (FWA) 144 5.5.2 Fuzzy Ordered Weighted Averaging Operator (FOWA) 145 5.5.3 Fuzzy Generalized Ordered Weighted Averaging Operator (GOWA) 146 5.5.4 Fuzzy Hybrid Averaging Operator (FHA) 146 5.5.5 Fuzzy Quasi-Arithmetic Weighted Averaging Operator 146 5.5.6 Induced Generalized Fuzzy Averaging Operator (IGOWA) 147 5.5.7 Choquet Aggregation Operator 149 5.5.8 Induced Choquet Ordered Aggregation Operator 150 5.6 Intuitionistic Fuzzy Operators 152 5.7 Intuitionistic Fuzzy Aggregation Operator 153 5.7.1 Generalized Intuitionistic Fuzzy Aggregation Operator 153 5.7.2 Generalized Intuitionistic Fuzzy Ordered Weighting Operator (GIFOWA) 155 5.7.3 Generalized Intuitionistic Fuzzy Hybrid Operator 157 5.7.4 Intuitionistic Fuzzy Weighted Geometric Operator (IFWG) 160 5.7.5 Intuitionistic Fuzzy Ordered Weighted Geometric Operator 161 5.7.6 Induced Generalized Intuitionistic Fuzzy Ordered Averaging Operator 161 5.7.7 Intuitionistic Fuzzy Choquet Integral Operator 162 5.7.8 Induced Intuitionistic Fuzzy Choquet Integral Operator 162 5.8 Example on Decision-making Problems 164 5.9 Summary 168 References 168 6 Fuzzy Linear Equations 171 6.1 Introduction 171 6.2 Fuzzy Linear Equation 172 6.2.1 Problem of Finding an Unknown Number 173 6.3 Solving Linear Equation Using Cramer’s Rule 177 6.4 Inverse of a Fuzzy Matrix 182 6.5 Summary 189 References 189 7 Fuzzy Matrices and Determinants 191 7.1 Basic Matrix Theory 191 7.1.1 Matrix Addition 192 7.1.2 Matrix Multiplication 193 7.1.3 Transpose of a Matrix 193 7.2 Fuzzy Matrices 194 7.2.1 Matrix Addition, Multiplication, Max, Min Operations 197 7.2.2 Identity Matrix 202 7.3 Determinant of a Square Fuzzy Matrix 202 7.3.1 Examples of Fuzzy Determinants 203 7.4 Adjoint of a Square Fuzzy Matrix 206 7.4.1 Few Proposition of Adjoint of Fuzzy Matrices 207 7.5 Properties of Reflexive Matrices 212 7.6 Generalized Inverse of a Fuzzy Matrix 215 7.7 Intuitionistic Fuzzy Matrix 216 7.7.1 Identity Matrix 217 7.7.2 Null Matrix 218 7.7.3 Generalized Inverse of Intuitionistic Fuzzy Matrix 218 7.8 Summary 218 References 218 8 Fuzzy Subgroups 221 8.1 Introduction 221 8.2 Theorems of Fuzzy Subgroup 222 8.3 Fuzzy-level Subgroup 226 8.4 Fuzzy Normal Subgroup 228 8.5 Fuzzy Subgroups Using T-norms 229 8.6 Product of Fuzzy Subgroups 231 8.7 Summary 234 References 235 9 Application of Fuzzy/Intuitionistic Fuzzy Set in Image Processing 237 9.1 Introduction 237 9.2 Digital Images 237 9.3 Image Enhancement 238 9.3.1 Fuzzy Enhancement Method 238 9.3.2 Intuitionistic Fuzzy Enhancement Method 239 9.4 Thresholding 240 9.4.1 Intuitionistic Fuzzy Thresholding Method 242 9.4.2 Fuzzy Thresholding Method 244 9.5 Edge Detection 244 9.5.1 Fuzzy Edge-detection Method 245 9.5.2 Intuitionistic Fuzzy Edge Detection 246 9.6 Clustering 248 9.6.1 Fuzzy c Means Clustering (FCM) 248 9.6.2 Intuitionistic Fuzzy Clustering 249 9.6.3 Kernel Clustering 250 9.7 Mathematical Morphology 252 9.7.1 Fuzzy Approach 254 9.7.2 Intuitionistic Fuzzy Approach 254 9.8 Summary 256 References 256 10 Type-2 Fuzzy Set 259 10.1 Introduction 259 10.2 Type-2 Fuzzy Set 260 10.3 Operations on Type-2 Fuzzy Set 263 10.4 Inclusion Measure and Similarity Measure 267 10.4.1 Similarity Measure 268 10.5 Interval Type-2 Fuzzy Set 270 10.6 Application of Interval Type-2 Fuzzy Set in Image Segmentation 271 10.7 Summary 273 References 273 Beyond Your Doubts 275 Index 281

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Book SynopsisCelebrate Valentine's Day with Elmo and his friends in this super sweet board book with fuzzy, touchable pages!Elmo wants to know which of his Sesame Street friends sent him a beautiful Valentine's Day card. Children ages 1 to 4 will love touching the fuzzy valentine on every spread! The sturdy board pages will hold up to hours of play as little ones leaf through them, visiting with Elmo, Grover, Cookie Monster, Baby Bear, Bert, and Ernie

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a huge range and FREE tracked UK delivery on ALL orders.

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Book SynopsisMathematical Foundations of Fuzzy Sets Introduce yourself to the foundations of fuzzy logic with this easy-to-use guide Many fields studied are defined by imprecise information or high degrees of uncertainty. When this uncertainty derives from randomness, traditional probabilistic statistical methods are adequate to address it; more everyday forms of vagueness and imprecision, however, require the toolkit associated with ''fuzzy sets'' and ''fuzzy logic''. Engineering and mathematical fields related to artificial intelligence, operations research and decision theory are now strongly driven by fuzzy set theory. Mathematical Foundations of Fuzzy Sets introduces readers to the theoretical background and practical techniques required to apply fuzzy logic to engineering and mathematical problems. It introduces the mathematical foundations of fuzzy sets as well as the current cutting edge of fuzzy-set operations and arithmetic, offering a roundedTable of ContentsPreface ix 1 Mathematical Analysis 1 1.1 Infimum and Supremum 1 1.2 Limit Inferior and Limit Superior 3 1.3 Semi-Continuity 11 1.4 Miscellaneous 19 2 Fuzzy Sets 23 2.1 Membership Functions 23 2.2 𝛼-level Sets 24 2.3 Types of Fuzzy Sets 34 3 Set Operations of Fuzzy Sets 43 3.1 Complement of Fuzzy Sets 43 3.2 Intersection of Fuzzy Sets 44 3.3 Union of Fuzzy Sets 51 3.4 Inductive and Direct Definitions 56 3.5 𝛼-Level Sets of Intersection and Union 61 3.6 Mixed Set Operations 65 4 Generalized Extension Principle 69 4.1 Extension Principle Based on the Euclidean Space 69 4.2 Extension Principle Based on the Product Spaces 75 4.3 Extension Principle Based on the Triangular Norms 84 4.4 Generalized Extension Principle 92 5 Generating Fuzzy Sets 109 5.1 Families of Sets 110 5.2 Nested Families 112 5.3 Generating Fuzzy Sets from Nested Families 119 5.4 Generating Fuzzy Sets Based on the Expression in the Decomposition Theorem 123 5.4.1 The Ordinary Situation 123 5.4.2 Based on One Function 129 Trim Size: 170mm x 244mm Single Column Tight Wu981527 ftoc.tex V1 - 10/14/2022 2:05pm Page vi [1] [1] [1] [1] vi Contents 5.4.3 Based on Two Functions 140 5.5 Generating Fuzzy Intervals 150 5.6 Uniqueness of Construction 160 6 Fuzzification of Crisp Functions 173 6.1 Fuzzification Using the Extension Principle 173 6.2 Fuzzification Using the Expression in the Decomposition Theorem 176 6.2.1 Nested Family Using 𝛼-Level Sets 177 6.2.2 Nested Family Using Endpoints 181 6.2.3 Non-Nested Family Using Endpoints 184 6.3 The Relationships between EP and DT 187 6.3.1 The Equivalences 187 6.3.2 The Fuzziness 191 6.4 Differentiation of Fuzzy Functions 196 6.4.1 Defined on Open Intervals 196 6.4.2 Fuzzification of Differentiable Functions Using the Extension Principle 197 6.4.3 Fuzzification of Differentiable Functions Using the Expression in the Decomposition Theorem 198 6.5 Integrals of Fuzzy Functions 201 6.5.1 Lebesgue Integrals on a Measurable Set 201 6.5.2 Fuzzy Riemann Integrals Using the Expression in the Decomposition Theorem 203 6.5.3 Fuzzy Riemann Integrals Using the Extension Principle 207 7 Arithmetics of Fuzzy Sets 211 7.1 Arithmetics of Fuzzy Sets in ℝ 211 7.1.1 Arithmetics of Fuzzy Intervals 214 7.1.2 Arithmetics Using EP and DT 220 7.1.2.1 Addition of Fuzzy Intervals 220 7.1.2.2 Difference of Fuzzy Intervals 222 7.1.2.3 Multiplication of Fuzzy Intervals 224 7.2 Arithmetics of Fuzzy Vectors 227 7.2.1 Arithmetics Using the Extension Principle 230 7.2.2 Arithmetics Using the Expression in the Decomposition Theorem 230 7.3 Difference of Vectors of Fuzzy Intervals 235 7.3.1 𝛼-Level Sets of 𝐀̃⊖EP 𝐁̃ 235 7.3.2 𝛼-Level Sets of 𝐀̃ ⊖⋄ DT 𝐁̃ 237 7.3.3 𝛼-Level Sets of 𝐀̃ ⊖⋆ DT 𝐁̃ 239 7.3.4 𝛼-Level Sets of 𝐀̃ ⊖† DT 𝐁̃ 241 7.3.5 The Equivalences and Fuzziness 243 7.4 Addition of Vectors of Fuzzy Intervals 244 7.4.1 𝛼-Level Sets of 𝐀̃⊕EP 𝐁̃ 244 7.4.2 𝛼-Level Sets of 𝐀̃⊕DT 𝐁̃ 246 Trim Size: 170mm x 244mm Single Column Tight Wu981527 ftoc.tex V1 - 10/14/2022 2:05pm Page vii [1] [1] [1] [1] Contents vii 7.5 Arithmetic Operations Using Compatibility and Associativity 249 7.5.1 Compatibility 250 7.5.2 Associativity 255 7.5.3 Computational Procedure 264 7.6 Binary Operations 268 7.6.1 First Type of Binary Operation 269 7.6.2 Second Type of Binary Operation 273 7.6.3 Third Type of Binary Operation 274 7.6.4 Existence and Equivalence 277 7.6.5 Equivalent Arithmetic Operations on Fuzzy Sets in ℝ 282 7.6.6 Equivalent Additions of Fuzzy Sets in ℝm 289 7.7 Hausdorff Differences 294 7.7.1 Fair Hausdorff Difference 294 7.7.2 Composite Hausdorff Difference 299 7.7.3 Complete Composite Hausdorff Difference 304 7.8 Applications and Conclusions 312 7.8.1 Gradual Numbers 312 7.8.2 Fuzzy Linear Systems 313 7.8.3 Summary and Conclusion 315 8 Inner Product of Fuzzy Vectors 317 8.1 The First Type of Inner Product 317 8.1.1 Using the Extension Principle 318 8.1.2 Using the Expression in the Decomposition Theorem 322 8.1.2.1 The Inner Product 𝐀̃ ⊛⋄ DT 𝐁̃ 323 8.1.2.2 The Inner Product 𝐀̃ ⊛⋆ DT 𝐁̃ 325 8.1.2.3 The Inner Product 𝐀̃ ⊛† DT 𝐁̃ 327 8.1.3 The Equivalences and Fuzziness 329 8.2 The Second Type of Inner Product 330 8.2.1 Using the Extension Principle 333 8.2.2 Using the Expression in the Decomposition Theorem 335 8.2.3 Comparison of Fuzziness 338 9 Gradual Elements and Gradual Sets 343 9.1 Gradual Elements and Gradual Sets 343 9.2 Fuzzification Using Gradual Numbers 347 9.3 Elements and Subsets of Fuzzy Intervals 348 9.4 Set Operations Using Gradual Elements 351 9.4.1 Complement Set 351 9.4.2 Intersection and Union 353 9.4.3 Associativity 359 9.4.4 Equivalence with the Conventional Situation 363 9.5 Arithmetics Using Gradual Numbers 364 Trim Size: 170mm x 244mm Single Column Tight Wu981527 ftoc.tex V1 - 10/14/2022 2:05pm Page viii [1] [1] [1] [1] viii Contents 10 Duality in Fuzzy Sets 373 10.1 Lower and Upper Level Sets 373 10.2 Dual Fuzzy Sets 376 10.3 Dual Extension Principle 378 10.4 Dual Arithmetics of Fuzzy Sets 380 10.5 Representation Theorem for Dual-Fuzzified Function 385 Bibliography 389 Mathematical Notations 397 Index 401

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Book Synopsis1 Fundamental of Crisp Set Theory.- 2 Fundamental Concepts of Fuzzy Sets.- 3 Generalization of Fuzzy Sets.- 4 Decomposition of a Fuzzy Set and Extension Principle.- 5 Fuzzy Set-Theoretic Operators.- 6 Arithmetic Operations and Fuzzy Mathematics.- 7 Fuzzy Relations.

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Book SynopsisWhy are ignorant people so confident? How do politicians utilize conflation to influence groups? Why do scientists fall for similar mistakes? How is complexity managed? Why does culture effortlessly shape what we can do? This book argues: Because of approximations! Incompleteness pervades our interactions with the world. Its effects on individual and group behaviors can foster creativity or create invisible prisons. We navigate incompleteness with approximations and, too often, end up on the ‘dark side’. This book resembles a tourist’s trip much more than a scientist’s expedition, and is for anyone interested in a broader understanding of an individual’s mental life and how identities, incompletenesses, and social contexts shape it. As we examine approximations and think about their origins and the problems they can create, the reader will encounter glimpses from physics, biology, philosophy of science, management, marketing, politics, systems theory, fuzzy logic, geometry, design and creativity, culture, and neuro-science and more... Fuzzy on the Dark Side is a book about incompleteness, creativity, thinking, identities, and systems. Roughly - it is an approximation of the 'Approximate Thinking' super idea.

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Book Synopsis1. Fuzziness, Cognition and Cybernetics: a historical perspective.- 2. Fuzziness, Cognition and Cybernetics: an outlook on future.- 3. On the Ontology of Vague Predicates: some preliminary remarks.- 4. Aspect of Vagueness and some Epistemological Problems Related to their Formalization.- 5. The question of the presence of vagueness in scientific theories.

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Book SynopsisProvides readers with the foundations of fuzzy mathematics as well as more advanced topics A Modern Introduction to Fuzzy Mathematics provides a concise presentation of fuzzy mathematics., moving from proofs of important results to more advanced topics, like fuzzy algebras, fuzzy graph theory, and fuzzy topologies. The authors take the reader through the development of the field of fuzzy mathematics, starting with the publication in 1965 of Lotfi Asker Zadeh's seminal paper, Fuzzy Sets. The book begins with the basics of fuzzy mathematics before moving on to more complex topics, including: Fuzzy setsFuzzy numbersFuzzy relationsPossibility theoryFuzzy abstract algebraAnd more Perfect for advanced undergraduate students, graduate students, and researchers with an interest in the field of fuzzy mathematics, A Modern Introduction to Fuzzy Mathematics walks through both foundational concepts and cutting-edge, new mathematics in the field.Table of ContentsPreface V Chapter 1 Introduction 1 1.1 What is vagueness? 1 1.2 Vagueness, Ambiguity, Uncertainty,… 4 1.3 Vagueness and Fuzzy Mathematics 5 Chapter 2 Fuzzy Sets and Their Operations 9 2.1 Algebras of Truth Values 9 2.1.1 Posets 9 2.1.2 Lattices 11 2.1.3 Frames 11 2.2 Zadeh’s Fuzzy Sets 12 2.3 α-cuts of Fuzzy Sets 16 2.4 Interval Valued and Type 2 Fuzzy Sets 19 2.5 Triangular Norms and Conorms 21 2.6 L-fuzzy Sets 23 2.7 “Intuitionistic” Fuzzy Sets and Their Extensions 24 2.8 The Extension Principle 28 2.9* Boolean-Valued Sets 30 2.10* Axiomatic Fuzzy Set Theory 32 Chapter 3 Fuzzy Numbers and Their Arithmetic 35 3.1 Fuzzy Numbers 35 3.1.1 Triangular Fuzzy Numbers 36 3.1.2 Trapezoidal Fuzzy Numbers 37 3.1.3 Gaussian Fuzzy Numbers 37 3.1.4 Quadratic Fuzzy Numbers 39 3.1.5 Exponential Fuzzy Numbers 41 3.1.6 LR Fuzzy Numbers 41 3.1.7 Generalized Fuzzy Numbers 42 3.2 Arithmetic of Fuzzy Numbers 43 3.2.1 Interval Arithmetic 43 3.2.2 Interval Arithmetic and α-Cuts 43 3.2.3 Fuzzy Arithmetic and the Extension Principle 44 3.2.4 Fuzzy Arithmetic of Triangular Fuzzy Numbers 45 3.2.5 Fuzzy Arithmetic of Generalized Fuzzy Numbers 45 3.2.6 Comparing Fuzzy Numbers 47 3.3 Linguistic Variables 49 3.4 Fuzzy Equations 50 3.4.1 Solving the Fuzzy Equation 𝐴 ⋅ 𝑋 + 𝐵 = 𝐶 50 3.4.2 Solving the Fuzzy Equation 𝐴 ⋅ 𝑋2 + 𝐵 ⋅ 𝑋 + 𝐶 = 𝐷 53 3.5 Fuzzy Inequalities 55 3.6 Constructing Fuzzy Numbers 55 3.7 Applications of Fuzzy Numbers 57 3.7.1 Simulation of the Human Glucose Metabolism 57 3.7.2 Estimation of an Ongoing Project’s Completion Time 60 Chapter 4 Fuzzy Relations 65 4.1 Crisp Relations 65 4.2 Fuzzy Relations 69 4.3 Cartesian Product, Projections, and Cylindrical Extension 70 4.4 New Fuzzy Relations From Old Ones 72 4.5 Fuzzy Binary Relations on a Set 75 4.6 Fuzzy Orders 80 4.7 Elements of Fuzzy Graph Theory 82 4.7.1 Graphs and Hypergraphs 82 4.7.2 Fuzzy Graphs 83 4.7.3 Fuzzy Hypergraphs 87 4.8* Fuzzy Category Theory 89 4.9* Fuzzy Vectors 96 4.10 Applications 97 Chapter 5 Possibility Theory 101 5.1 Fuzzy Restrictions and Possibility Theory 101 5.2 Possibility and Necessity Measures 103 5.3 Possibility Theory 105 5.4 Possibility Theory and Probability Theory 108 5.5 An Unexpected Application of Possibility Theory 110 Chapter 6 Fuzzy Statistics 117 6.1 Random Variables 117 6.2 Fuzzy Random Variables 120 6.3 Point Estimation 123 6.3.1 The unbiased estimator 124 6.3.2 The consistent estimator 125 6.3.3 The maximum likelihood estimator 126 6.4 Fuzzy Point Estimation 127 6.5 Interval Estimation 128 6.6 Interval Estimation for Fuzzy Data 129 6.7 Hypothesis Testing 131 6.8 Fuzzy Hypothesis Testing 132 6.9 Statistical Regression 134 6.10 Fuzzy Regression 136 Chapter 7 Fuzzy Logics 141 7.1 Mathematical Logic 141 7.2 Many-Valued Logics 146 7.3 On Fuzzy Logics 151 7.4 Hájek’s Basic Many-Valued Logic 152 7.5 Łukasiewicz Fuzzy Logic 155 7.6 Product Fuzzy Logic 157 7.7 Gödel Fuzzy Logic 158 7.8 First Order Fuzzy Logics 160 7.9 Fuzzy Quantifiers 162 7.10 Approximate Reasoning 163 7.11 Application: Fuzzy Expert Systems 166 7.12* A Logic of Vagueness 171 Chapter 8 Fuzzy Computation 173 8.1 Automata, Grammars, and Machines 173 8.2 Fuzzy Languages and Grammars 178 8.3 Fuzzy Automata 181 8.4 Fuzzy Turing Machines 186 8.5 Other Fuzzy Models of Computation 190 Chapter 9 Fuzzy Abstract Algebra 195 9.1 Groups, Rings, and Fields 195 9.2 Fuzzy Groups 199 9.3 Abelian Fuzzy Subgroups 204 9.4 Fuzzy Rings and Fuzzy Fields 206 9.5 Fuzzy Vector Spaces 208 9.6 Fuzzy Normed Spaces 209 9.7 Fuzzy Lie Algebras 210 Chapter 10 Fuzzy Topology 213 10.1 Metric and Topological Spaces 213 10.2 Fuzzy Metric Spaces 218 10.3 Fuzzy Topological Spaces 221 10.4 Fuzzy Product Spaces 224 10.5 Fuzzy Separation 226 10.5.1 Separation 231 10.6 Fuzzy Nets 231 10.7 Fuzzy Compactness 232 10.8 Fuzzy Connectedness 233 10.9 Smooth Fuzzy Topological Spaces 234 10.10 Fuzzy Banach and Fuzzy Hilbert Spaces 235 10.11* Fuzzy Topological Systems 238 Chapter 11 Fuzzy Geometry 243 11.1 Fuzzy Points and Fuzzy Distance 243 11.2 Fuzzy Lines and their Properties 246 11.3 Fuzzy Circles 249 11.4 Regular Fuzzy Polygons 252 11.5 Applications in Theoretical Physics 256 Chapter 12 Fuzzy Calculus 259 12.1 Fuzzy Functions 259 12.2 Integrals of Fuzzy Functions 263 12.3 Derivatives of Fuzzy Functions 266 12.4 Fuzzy Limits of Sequences and Functions 269 12.4.1 Fuzzy Ordinary Differential Equations 272 12.4.2 Fuzzy Partial Differential Equations 277 Appendix A Fuzzy Approximation 283 A.1 Weierstrass and Stone-Weierstrass Approximation Theorems 283 A.2 Weierstrass and Stone-Weierstrass Fuzzy Analogues 284 Appendix B Chaos and Vagueness 287 B.1 Chaos Theory in a Nutshell 287 B.2 Fuzzy Chaos 289 B.3 Fuzzy Fractals 291 Works Cited 293 Subject Index 311 Name Index 323

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Book SynopsisThis text examines synthetic and dynamical properties of fuzzy control systems in a quantitative manner. It includes fuzzy dynamical systems, controllability and sensitivity analysis and how these affect parameters in membership functions, fuzzification, defuzzification and inferencing.Trade Review"Design and control engineers will value the advanced control techniques, new design and analysis tools presented. Post-graduates...a useful reference." (Engineering Design, July 2000) "...a good read...it boldly tackles the stability issue of fuzzy control systems..." (Measurement and Control, October 2000) "Design and control engineers will value the advanced control techniques and new design and analysis tools presented. Postgraduates studying fuzzy control will find this book a useful reference...." (European Power Electronics & Drives Journal September 2001)Table of ContentsMODELING. Information Granularity in the Analysis and Design of Fuzzy Controllers. Fuzzy Modeling for Predictive Control. Adaptive and Learning Schemes for Fuzzy Modeling. Fuzzy System Identification with General Parameter Radial Basis Function Neural Network. ANALYSIS. Lyapunov Stability Analysis of Fuzzy Dynamic Systems. Passivity and Stability of Fuzzy Control Systems. Frequency Domain Analysis of MIMO Fuzzy Control Systems. Analytical Study of Structure of a Mamdani Fuzzy Controller with Three Input Variables. An Approach to the Analysis of Robust Stability of Fuzzy Control Systems. Fuzzy Control Systems Stability Analysis with Application to Aircraft Systems. SYNTHESIS. Observer-Based Controller Synthesis for Model-Based Fuzzy Systems via Linear Matrix Inequalities. LMI-Based Fuzzy Control: Fuzzy Regulator and Fuzzy Observer Design via LMIs. A Framework for the Synthesis of PDC-Type Takagi-Sugano Fuzzy Control Systems: An LMI Approach. On Adaptive Fuzzy Logic Control on Non-linear Systems--Synthesis and Analysis. Stabilization of Direct Adaptive Fuzzy Control Systems: Two Approaches. Gain Scheduling Based Control of a Class of TSK Systems. Output Tracking Using Fuzzy Neural Networks. Fuzzy Life-Extending Control of Mechanical Systems. Epilogue. Index.

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Book SynopsisThe Journal of Business Market Management (JBM) explores all facets of business-to-business marketing, industrial market management and marketing of business services. That includes the areas of technical and commercial sales management but also industrial supply and business buying behavior. Academics as well as practitioners thinking will be enriched with novel and significant ideas in terms of research approaches and results. Offering a combination of conceptual papers, empirical research analyses, and case study arti-cles the journal represents a valuable knowledge source and contributes to a better understanding of busi-ness market activities.Table of ContentsPräzision ist nicht Wahrheit (Henri Matisse).- Strukturelle und quantifizierbare Vagheit.- 1. Die Elemente der Fuzzy-Theorie.- 1.1. Der Begriff Fuzzy-Menge.- 1.2. Fuzzy-Mengen als Punkte eines Würfels.- 1.3. Operationen mit Fuzzy-Mengen 1.- 1.4. Fuzzy-Untermengen.- 1.5. Trianguläre Normen.- 1.6. Fuzzy-Arithmetik.- 1.7. Zusammenfassung.- 2. Fuzzy-Lukasiewicz-Theorie.- 2.0. Übersicht.- 2.1. Fuzzy-Untermengigkeit als Fuzzy-Subsumption.- 2.2. Ähnlichkeit als Fuzzy-Gleichheit und Vagheit von Fuzzy-Mengen.- 2.3. Vage Ordnungen.- 2.4. Fuzzy-Mikrogeometrie.- 3. Theorie des Möglichen.- 3.0. Übersicht.- 3.1. Die Wahrscheinlichkeit von Fuzzy-Ereignissen.- 3.2. Die Möglichkeit von Fuzzy — Ereignissen.- 3.3. Fuzzy — Zuverlässigkeit.- 3.4. Information als Begriff der Possibilistik.- 4. Fuzzy-Inferenzsysteme.- 4.1. Modellfreiheit von Fuzzy-Inferenzsystemen.- 4.2. Fuzzy-regelnde Systeme.- 4.3. Adaption von Fuzzy-Inferenzsystemen.- Notationen.- Sachwortverzeichnis.

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Book SynopsisThe main focus of this book is on presenting advances in fuzzy statistics, and on proposing a methodology for testing hypotheses in the fuzzy environment based on the estimation of fuzzy confidence intervals, a context in which not only the data but also the hypotheses are considered to be fuzzy. The proposed method for estimating these intervals is based on the likelihood method and employs the bootstrap technique. A new metric generalizing the signed distance measure is also developed. In turn, the book presents two conceptually diverse applications in which defended intervals play a role: one is a novel methodology for evaluating linguistic questionnaires developed at the global and individual levels; the other is an extension of the multi-ways analysis of variance to the space of fuzzy sets. To illustrate these approaches, the book presents several empirical and simulation-based studies with synthetic and real data sets. In closing, it presents a coherent R package called “FuzzySTs” which covers all the previously mentioned concepts with full documentation and selected use cases. Given its scope, the book will be of interest to all researchers whose work involves advanced fuzzy statistical methods.Table of Contents- 1. Introduction. - Part I Theoretical Part. - 2. Fundamental Concepts on Fuzzy Sets. - 3. Fuzzy Rule-Based Systems. - 4. Distances Between Fuzzy Sets. - 5. Fuzzy Random Variables and Fuzzy Distributions. - 6. Fuzzy Statistical Inference. - Conclusion Part I. - Part II Applications. - 7. Evaluation of Linguistic Questionnaire. - 8. Fuzzy Analysis of Variance. - Part III An R Package for Fuzzy Statistical Analysis: A DetailedDescription. - 9. FuzzySTs: Fuzzy Statistical Tools: A Detailed Description. - Conclusion.

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Book SynopsisThis monograph is the r st in Fuzzy Approximation Theory. It contains mostly the author s research work on fuzziness of the last ten years and relies a lot on [10]-[32] and it is a natural outgrowth of them. It belongs to the broader area of Fuzzy Mathematics. Chapters are self-contained and several advanced courses can be taught out of this book. We provide lots of applications but always within the framework of Fuzzy Mathematics. In each chapter is given background and motivations. A c- plete list of references is provided at the end. The topics covered are very diverse. In Chapter 1 we give an extensive basic background on Fuzziness and Fuzzy Real Analysis, as well a complete description of the book. In the following Chapters 2,3 we cover in deep Fuzzy Di?erentiation and Integ- tion Theory, e.g. we present Fuzzy Taylor Formulae. It follows Chapter 4 on Fuzzy Ostrowski Inequalities. Then in Chapters 5, 6 we present results on classical algebraic and trigonometric polynomial Fuzzy Approximation.Table of ContentsABOUT H-FUZZY DIFFERENTIATION.- ON FUZZY TAYLOR FORMULAE.- FUZZY OSTROWSKI INEQUALITIES.- A FUZZY TRIGONOMETRIC APPROXIMATION THEOREM OF WEIERSTRASS-TYPE.- ON BEST APPROXIMATION AND JACKSON-TYPE ESTIMATES BY GENERALIZED FUZZY POLYNOMIALS.- BASIC FUZZY KOROVKIN THEORY.- FUZZY TRIGONOMETRIC KOROVKIN THEORY.- FUZZY GLOBAL SMOOTHNESS PRESERVATION.- FUZZY KOROVKIN THEORY AND INEQUALITIES.- HIGHER ORDER FUZZY KOROVKIN THEORY USING INEQUALITIES.- FUZZY WAVELET LIKE OPERATORS.- ESTIMATES TO DISTANCES BETWEEN FUZZY WAVELET LIKE OPERATORS.- FUZZY APPROXIMATION BY FUZZY CONVOLUTION OPERATORS.- DEGREE OF APPROXIMATION OF FUZZY NEURAL NETWORK OPERATORS, UNIVARIATE CASE.- HIGHER DEGREE OF FUZZY APPROXIMATION BY FUZZY WAVELET TYPE AND NEURAL NETWORK OPERATORS.- FUZZY RANDOM KOROVKIN THEOREMS AND INEQUALITIES.- FUZZY-RANDOM NEURAL NETWORK APPROXIMATION OPERATORS, UNIVARIATE CASE.- -SUMMABILITY AND FUZZY KOROVKIN APPROXIMATION.- -SUMMABILITY AND FUZZY TRIGONOMETRIC KOROVKIN APPROXIMATION.- UNIFORM REAL AND FUZZY ESTIMATES FOR DISTANCES BETWEEN WAVELET TYPE OPERATORS AT REAL AND FUZZY ENVIRONMENT.

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Book SynopsisFoundations of Fuzzy Control: A Practical Approach, 2nd Edition has been significantly revised and updated, with two new chapters on Gain Scheduling Control and Neurofuzzy Modelling. It focuses on the PID (Proportional, Integral, Derivative) type controller which is the most widely used in industry and systematically analyses several fuzzy PID control systems and adaptive control mechanisms. This new edition covers the basics of fuzzy control and builds a solid foundation for the design of fuzzy controllers, by creating links to established linear and nonlinear control theory. Advanced topics are also introduced and in particular, common sense geometry is emphasised. Key features Sets out practical worked through problems, examples and case studies to illustrate each type of control system Accompanied by a website hosting downloadable MATLAB programs Accompanied by an online course on Fuzzy Control which is taught by the author. StTable of ContentsForeword xiii Preface to the Second Edition xv Preface to the First Edition xvii 1Introduction 1 1.1 What Is Fuzzy Control? 1 1.2 Why Fuzzy Control? 2 1.3 Controller Design 3 1.4 Introductory Example: Stopping a Car 3 1.5 Nonlinear Control Systems 9 1.6 Summary 11 1.7 The Autopilot Simulator* 12 1.8 Notes and References* 13 2 Fuzzy Reasoning 17 2.1 Fuzzy Sets 17 2.2 Fuzzy Set Operations 25 2.3 Fuzzy If–Then Rules 33 2.4 Fuzzy Logic 36 2.5 Summary 43 2.6 Theoretical Fuzzy Logic* 43 2.7 Notes and References* 53 3 Fuzzy Control 55 3.1 The Rule Based Controller 56 3.2 The Sugeno Controller 61 3.3 Autopilot Example: Four Rules 64 3.4 Table Based Controller 65 3.5 Linear Fuzzy Controller 68 3.6 Summary 70 3.7 Other Controller Components* 70 3.8 Other Rule Based Controllers* 77 3.9 Analytical Simplification of the Inference* 80 3.10 Notes and References* 84 4 Linear Fuzzy PID Control 85 4.1 Fuzzy P Controller 87 4.2 Fuzzy PD Controller 89 4.3 Fuzzy PD+I Controller 90 4.4 Fuzzy Incremental Controller 92 4.5 Tuning 94 4.6 Simulation Example: Third-Order Process 99 4.7 Autopilot Example: Stable Equilibrium 101 4.8 Summary 103 4.9 Derivative Spikes and Integrator Windup* 104 4.10 PID Loop Shaping* 106 4.11 Notes and References* 109 5 Nonlinear Fuzzy PID Control 111 5.1 Nonlinear Components 111 5.2 Phase Plot 113 5.3 Four Standard Control Surfaces 115 5.4 Fine-Tuning 118 5.5 Example: Unstable Frictionless Vehicle 121 5.6 Example: Nonlinear Valve Compensator 124 5.7 Example: Motor Actuator with Limits 127 5.8 Autopilot Example: Regulating a Mass Load 127 5.9 Summary 130 5.10 Phase Plane Analysis* 130 5.11 Geometric Interpretation of the PD Controller* 134 5.12 Notes and References* 143 6 The Self-Organizing Controller 145 6.1 Model Reference Adaptive Systems 145 6.2 The Original SOC 147 6.3 A Modified SOC 150 6.4 Example with a Long Deadtime 151 6.5 Tuning and Time Lock 155 6.6 Summary 157 6.7 Example: Adaptive Control of a First-Order Process* 157 6.8 Analytical Derivation of the SOC Adaptation Law* 161 6.9 Notes and References* 169 7 Performance and Relative Stability 171 7.1 Reference Model 172 7.2 Performance Measures 177 7.3 PID Tuning from Performance Specifications 180 7.4 Gain Margin and Delay Margin 185 7.5 Test of Four Difficult Processes 186 7.6 The Nyquist Criterion for Stability 188 7.7 Relative Stability of the Standard Control Surfaces 191 7.8 Summary 193 7.9 Describing Functions* 193 7.10 Frequency Responses of the FPD and FPD+I Controllers* 198 7.11 Analytical Derivation of Describing Functions for the Standard Surfaces* 206 7.12 Notes and References* 216 8 Fuzzy Gain Scheduling Control 217 8.1 Point Designs and Interpolation 218 8.2 Fuzzy Gain Scheduling 219 8.3 Fuzzy Compensator Design 221 8.4 Autopilot Example: Stopping on a Hilltop 226 8.5 Summary 228 8.6 Case Study: the FLS Controller* 229 8.7 Notes and References* 235 9 Fuzzy Models 237 9.1 Basis Function Architecture 238 9.2 Handmade Models 240 9.3 Machine-Made Models 249 9.4 Cluster Analysis 253 9.5 Training and Testing 263 9.6 Summary 266 9.7 Neuro-Fuzzy Models* 267 9.8 Notes and References* 275 10 Demonstration Examples 277 10.1 Hot Water Heater 277 10.2 Temperature Control of a Tank Reactor 282 10.3 Idle Speed Control of a Car Engine 287 10.4 Balancing a Ball on a Cart 292 10.5 Dynamic Model of a First-Order Process with a Nonlinearity 301 10.6 Summary 307 10.7 Further State-Space Analysis of the Cart-Ball System* 307 10.8 Notes and References* 314 References 315 Index 319

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Book SynopsisThis book briefly reviews the basic concepts of type-2 fuzzy systems and then describes the proposed definitions for interval type-3 fuzzy sets and relations, also interval type-3 inference and systems. The use of type-2 fuzzy systems has become widespread in the leading economy sectors, especially in industrial and application areas, such as services, health, defense, and so on. However, recently the use of interval type-3 fuzzy systems has been receiving increasing attention and some successful applications have been developed in the last year. These issues were taken into consideration for this book, as we did realize that there was a need to offer the main theoretical concepts of type-3 fuzzy logic, as well as methods to design, develop and implement the type-3 fuzzy systems. A review of basic concepts and their use in the design and implementation of interval type-3 fuzzy systems, which are relatively new models of uncertainty and imprecision, are presented. The main focus of this work is based on the basic reasons of the need for interval type-3 fuzzy systems in different areas of application. In addition, we describe methods for designing interval type-3 fuzzy systems and illustrate this with some examples and simulations.Table of ContentsChapter 1: Introduction to Interval Type-3 Fuzzy Systems.- Chapter 2: Type-2 Fuzzy Logic Systems.- Chapter 3: Interval Type-3 Fuzzy Sets.- Chapter 4: Interval Type-3 Fuzzy Logic Systems.- Chapter 5: Conclusions of Type-3 Fuzzy Systems.

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Book SynopsisIn one of the most beloved Little Golden Books of all time, Fuzzy Duckling learns to count and explores a busy farm! A perfect gift for your Easter baskets. Early one morning, a small fuzzy duckling goes for a walk around the farm. Who will he meet along the way? Two frisky colts, three baby calves. . . . Little readers everywhere will love following the duckling and counting his new animal friends. Simple words and adorable, classic illustations from the legendary Alice and Martin Provensen make this book as perfect a gift today as it was when it was first published in 1949. Little Golden Books have been loved by children for over 75 years. When they were first published in 1942, high-quality books for children hadn?t been available at a price most people could afford. Little Golden Books changed that! Priced at just 25 cents and sold where people shopped every day, they caused an instant sensation and were soon purchased by the hundreds of thousands. Created by such talented writers as Margaret Wise Brown (author of Goodnight Moon) and Richard Scarry, Little Golden Books have helped millions of children develop a lifelong love of reading. Today, Little Golden Books feature beloved classics such as The Poky Little Puppy and Scuffy the Tugboat, plus new, original stories?the classics of tomorrow?ready to be discovered between their sturdy cardboard covers and gold-foil spines.

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Book SynopsisPresents a systematic treatment of fuzzy fractional differential equations as well as newly developed computational methods to model uncertain physical problems Complete with comprehensive results and solutions, Fuzzy Arbitrary Order System: Fuzzy Fractional Differential Equations and Applications details newly developed methods of fuzzy computational techniquesneeded to model solve uncertainty. Fuzzy differential equations are solved via various analytical andnumerical methodologies, and this book presents their importance for problem solving, prototypeengineering design, and systems testing in uncertain environments. In recent years, modeling of differential equations for arbitrary and fractional order systems has been increasing in its applicability, and as such, the authors feature examples from a variety of disciplines to illustrate the practicality and importance of the methods within physics, applied mathematics, engineering, and chemistry, to nameTable of ContentsPREFACE ix ACKNOWLEDGMENTS xiii 1 Preliminaries of Fuzzy Set Theory 1 Bibliography 7 2 Basics of Fractional and Fuzzy Fractional Differential Equations 9 Bibliography 12 3 Analytical Methods for Fuzzy Fractional Differential Equations (FFDES) 15 3.1 n-Term Linear Fuzzy Fractional Linear Differential Equations 16 3.2 Proposed Methods 18 Bibliography 28 4 Numerical Methods for Fuzzy Fractional Differential Equations 31 4.1 Homotopy Perturbation Method (HPM) 31 4.2 Adomian Decomposition Method (ADM) 35 4.3 Variational Iteration Method (VIM) 37 Bibliography 39 5 Fuzzy Fractional Heat Equations 41 5.1 Arbitrary-Order Heat Equation 41 5.2 Solution of Fuzzy Arbitrary-Order Heat Equations by HPM 41 5.3 Numerical Examples 43 5.4 Numerical Results 45 Bibliography 47 6 Fuzzy Fractional Biomathematical Applications 49 6.1 Fuzzy Arbitrary-Order Predator–Prey Equations 49 6.1.1 Particular Case 51 6.2 Numerical Results of Fuzzy Arbitrary-Order Predator–Prey Equations 54 Bibliography 65 7 Fuzzy Fractional Chemical Problems 67 7.1 Arbitrary-Order Rossler’s Systems 67 7.2 HPM Solution of Uncertain Arbitrary-Order Rossler’s System 68 7.3 Particular Case 71 7.3.1 Special Case 73 7.4 Numerical Results 78 Bibliography 83 8 Fuzzy Fractional Structural Problems 87 8.1 Fuzzy Fractionally Damped Discrete System 88 8.2 Uncertain Response Analysis 90 8.2.1 Uncertain Step Function Response 90 8.2.2 Uncertain Impulse Function Response 93 8.3 Numerical Results 96 8.3.1 Case Studies for Uncertain Step Function Response 97 8.3.2 Case Studies for Uncertain Impulse Function Response 100 8.4 Fuzzy Fractionally Damped Continuous System 101 8.5 Uncertain Response Analysis 110 8.5.1 Unit step Function Response 110 8.5.2 Unit Impulse Function Response 111 8.6 Numerical Results 112 8.6.1 Case Studies for Fuzzy Unit Step Response 114 8.6.2 Case Studies for Fuzzy Unit Impulse Response 115 Bibliography 118 9 Fuzzy Fractional Diffusion Problems 121 9.1 Fuzzy Fractional-Order Diffusion Equation 121 9.1.1 Double-Parametric-Based Solution of Uncertain Fractional-Order Diffusion Equation 123 9.1.2 Solution Bounds for Different External Forces 125 9.2 Numerical Results of Fuzzy Fractional Diffusion Equation 130 Bibliography 139 10 Uncertain Fractional Fornberg–Whitham Equations 141 10.1 Parametric-Based Interval Fractional Fornberg–Whitham Equation 141 10.2 Solution by VIM 143 10.3 Solution Bounds for Different Interval Initial Conditions 145 10.4 Numerical Results 148 Bibliography 152 11 Fuzzy Fractional Vibration Equation of Large Membrane 155 11.1 Double-Parametric-Based Solution of Uncertain Vibration Equation of Large Membrane 156 11.2 Solutions of Fuzzy Vibration Equation of Large Membrane 158 11.3 Case Studies (Solution Bounds for Particular Cases) 160 11.4 Numerical Results for Fuzzy Fractional Vibration Equation for Large Membrane 172 Bibliography 188 12 Fuzzy Fractional Telegraph Equations 191 12.1 Double-Parametric-Based Fuzzy Fractional Telegraph Equations 191 12.2 Solutions of Fuzzy Telegraph Equations Using Homotopy Perturbation Method 194 12.3 Solution Bounds for Particular Cases 195 12.4 Numerical Results for Fuzzy Fractional Telegraph Equations 199 Bibliography 205 13 Fuzzy Fokker–Planck Equation with Space and Time Fractional Derivatives 207 13.1 Fuzzy Fractional Fokker–Planck Equation with Space and Time Fractional Derivatives 207 13.2 Double-Parametric-Based Solution of Uncertain Fractional Fokker–Planck Equation 209 13.2.1 Solution by HPM 209 13.2.2 Solution By ADM 210 13.3 Case Studies Using HPM and ADM 211 13.3.1 Using HPM 211 13.3.2 Using ADM 215 13.4 Numerical Results of Fuzzy Fractional Fokker–Planck Equation 218 Bibliography 220 14 Fuzzy Fractional Bagley–Torvik Equations 223 14.1 Various Types of Fuzzy Fractional Bagley–Torvik Equations 223 14.2 Results and Discussions 231 Bibliography 241 APPENDIX A 243 A.1 Fractionally Damped Spring–Mass System (Problem 1) 243 A.1.1 Response Analysis 246 A.1.2 Analytical Solution Using Fractional Green’s Function 247 A.2 Fractionally Damped Beam (Problem 2) 248 A.2.1 Response Analysis 250 A.2.2 Numerical Results 251 Bibliography 255 INDEX 257

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Book SynopsisFuzzy set theory deals with sets or categories whose boundaries are blurry or, in other words, fuzzy. This book presents an accessible introduction to fuzzy set theory, focusing on its applicability to the social sciences. Unlike most books on this topic, Fuzzy Set Theory: Applications in the Social Sciences provides a systematic, yet practical guide for researchers wishing to combine fuzzy set theory with standard statistical techniques and model-testing. Key Features: Addresses Basic Concepts: Fuzzy set theory is an analytic framework for handling concepts that are simultaneously categorical and dimensional. Starting with a rationale for fuzzy sets, this book introduces readers with an elementary knowledge of statistics to the necessary concepts and techniques of fuzzy set theory and fuzzy logic. Introduces Novel Ways of Analyses: Researchers are shown alternative methods to conventional models, especially for testing Trade Review"I think that the book is a simple and accessible introduction to the theory of fuzzy sets and it includes many examples, formulae, figures, and tables which illustrate its contents. The presentation of the book and the academic content are very careful, which make for pleasant reading." -- Marinano Ruiz EspejoTable of ContentsSeries Editor’s Introduction Acknowledgments 1. Introduction 2. An Overview of Fuzzy Set Mathematics 2.1 Set Theory 2.2 Why Fuzzy Sets? 2.3 The Membership Function 2.4 Operations of Fuzzy Set Theory 2.5 Fuzzy Numbers and Fuzzy Variables 2.6 Graphical Representations of Fuzzy Sets 3. Measuring Membership 3.1 Introduction 3.2 Methods for Constructing Membership Functions 3.3 Measurement Properties Required for Fuzzy Sets 3.4 Measurement Properties of Membership Functions 3.5 Uncertainty Estimates in Membership Assignment 4. Internal Structure and Properties of a Fuzzy Set 4.1 Cardinality: The Size of a Fuzzy Set 4.2 Probability Distributions for Fuzzy Sets 4.3 Defining and Measuring Fuzziness 5. Simple Relations Between Fuzzy Sets 5.1 Intersection, Union, and Inclusion 5.2 Detecting and Evaluating Fuzzy Inclusion 5.3 Quantifying and Modeling Inclusion: Ordinal Membership Scales 5.4 Quantified and Comparable Membership Scales 6. Multivariate Fuzzy Set Relations 6.1 Compound Set Indexes 6.2 Multiset Relations: Comorbidity, Covariation, and Co-Occurrence 6.3 Multiple and Partial Intersection and Inclusion 7. Concluding Remarks References Index About the Authors

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Book SynopsisFUZZY COMPUTING IN DATA SCIENCE This book comprehensively explains how to use various fuzzy-based models to solve real-time industrial challenges. The book provides information about fundamental aspects of the field and explores the myriad applications of fuzzy logic techniques and methods. It presents basic conceptual considerations and case studies of applications of fuzzy computation. It covers the fundamental concepts and techniques for system modeling, information processing, intelligent system design, decision analysis, statistical analysis, pattern recognition, automated learning, system control, and identification. The book also discusses the combination of fuzzy computation techniques with other computational intelligence approaches such as neural and evolutionary computation. Audience Researchers and students in computer science, artificial intelligence, machine learning, big data analytics, and information and communication technology.Table of ContentsPreface xvii Acknowledgement xxi 1 Band Reduction of HSI Segmentation Using FCM 1 V. Saravana Kumar, S. Anantha Sivaprakasam, E.R. Naganathan, Sunil Bhutada and M. Kavitha 1.1 Introduction 2 1.2 Existing Method 3 1.2.1 K-Means Clustering Method 3 1.2.2 Fuzzy C-Means 3 1.2.3 Davies Bouldin Index 4 1.2.4 Data Set Description of HSI 4 1.3 Proposed Method 5 1.3.1 Hyperspectral Image Segmentation Using Enhanced Estimation of Centroid 5 1.3.2 Band Reduction Using K-Means Algorithm 6 1.3.3 Band Reduction Using Fuzzy C-Means 7 1.4 Experimental Results 8 1.4.1 DB Index Graph 8 1.4.2 K-Means–Based PSC (EEOC) 9 1.4.3 Fuzzy C-Means–Based PSC (EEOC) 10 1.5 Analysis of Results 12 1.6 Conclusions 16 References 17 2 A Fuzzy Approach to Face Mask Detection 21 Vatsal Mishra, Tavish Awasthi, Subham Kashyap, Minerva Brahma, Monideepa Roy and Sujoy Datta 2.1 Introduction 22 2.2 Existing Work 23 2.3 The Proposed Framework 26 2.4 Set-Up and Libraries Used 26 2.5 Implementation 27 2.6 Results and Analysis 29 2.7 Conclusion and Future Work 33 References 34 3 Application of Fuzzy Logic to the Healthcare Industry 37 Biswajeet Sahu, Lokanath Sarangi, Abhinadita Ghosh and Hemanta Kumar Palo 3.1 Introduction 38 3.2 Background 41 3.3 Fuzzy Logic 42 3.4 Fuzzy Logic in Healthcare 45 3.5 Conclusions 49 References 50 4 A Bibliometric Approach and Systematic Exploration of Global Research Activity on Fuzzy Logic in Scopus Database 55 Sugyanta Priyadarshini and Nisrutha Dulla 4.1 Introduction 56 4.2 Data Extraction and Interpretation 58 4.3 Results and Discussion 59 4.3.1 Per Year Publication and Citation Count 59 4.3.2 Prominent Affiliations Contributing Toward Fuzzy Logic 60 4.3.3 Top Journals Emerging in Fuzzy Logic in Major Subject Areas 61 4.3.4 Major Contributing Countries Toward Fuzzy Research Articles 63 4.3.5 Prominent Authors Contribution Toward the Fuzzy Logic Analysis 66 4.3.6 Coauthorship of Authors 67 4.3.7 Cocitation Analysis of Cited Authors 68 4.3.8 Cooccurrence of Author Keywords 68 4.4 Bibliographic Coupling of Documents, Sources, Authors, and Countries 70 4.4.1 Bibliographic Coupling of Documents 70 4.4.2 Bibliographic Coupling of Sources 71 4.4.3 Bibliographic Coupling of Authors 72 4.4.4 Bibliographic Coupling of Countries 73 4.5 Conclusion 74 References 76 5 Fuzzy Decision Making in Predictive Analytics and Resource Scheduling 79 Rekha A. Kulkarni, Suhas H. Patil and Bithika Bishesh 5.1 Introduction 80 5.2 History of Fuzzy Logic and Its Applications 81 5.3 Approximate Reasoning 82 5.4 Fuzzy Sets vs Classical Sets 83 5.5 Fuzzy Inference System 84 5.5.1 Characteristics of FIS 85 5.5.2 Working of FIS 85 5.5.3 Methods of FIS 86 5.6 Fuzzy Decision Trees 86 5.6.1 Characteristics of Decision Trees 87 5.6.2 Construction of Fuzzy Decision Trees 87 5.7 Fuzzy Logic as Applied to Resource Scheduling in a Cloud Environment 88 5.8 Conclusion 90 References 91 6 Application of Fuzzy Logic and Machine Learning Concept in Sales Data Forecasting Decision Analytics Using ARIMA Model 93 S. Mala and V. Umadevi 6.1 Introduction 94 6.1.1 Aim and Scope 94 6.1.2 R-Tool 94 6.1.3 Application of Fuzzy Logic 94 6.1.4 Dataset 95 6.2 Model Study 96 6.2.1 Introduction to Machine Learning Method 96 6.2.2 Time Series Analysis 96 6.2.3 Components of a Time Series 97 6.2.4 Concepts of Stationary 99 6.2.5 Model Parsimony 100 6.3 Methodology 100 6.3.1 Exploratory Data Analysis 100 6.3.1.1 Seed Types—Analysis 101 6.3.1.2 Comparison of Location and Seeds 101 6.3.1.3 Comparison of Season (Month) and Seeds 103 6.3.2 Forecasting 103 6.3.2.1 Auto Regressive Integrated Moving Average (ARIMA) 103 6.3.2.2 Data Visualization 106 6.3.2.3 Implementation Model 108 6.4 Result Analysis 108 6.5 Conclusion 110 References 110 7 Modified m-Polar Fuzzy Set ELECTRE-I Approach 113 Madan Jagtap, Prasad Karande and Pravin Patil 7.1 Introduction 114 7.1.1 Objectives 114 7.2 Implementation of m-Polar Fuzzy ELECTRE-I Integrated Shannon’s Entropy Weight Calculations 115 7.2.1 The m-Polar Fuzzy ELECTRE-I Integrated Shannon’s Entropy Weight Calculation Method 115 7.3 Application to Industrial Problems 118 7.3.1 Cutting Fluid Selection Problem 118 7.3.2 Results Obtained From m-Polar Fuzzy ELECTRE-I for Cutting Fluid Selection Problem 122 7.3.3 FMS Selection Problem 125 7.3.4 Results Obtained From m-Polar Fuzzy ELECTRE-I for FMS Selection 130 7.4 Conclusions 143 References 143 8 Fuzzy Decision Making: Concept and Models 147 Bithika Bishesh 8.1 Introduction 148 8.2 Classical Set 149 8.3 Fuzzy Set 150 8.4 Properties of Fuzzy Set 151 8.5 Types of Decision Making 153 8.5.1 Individual Decision Making 153 8.5.2 Multiperson Decision Making 157 8.5.3 Multistage Decision Making 158 8.5.4 Multicriteria Decision Making 160 8.6 Methods of Multiattribute Decision Making (MADM) 162 8.6.1 Weighted Sum Method (WSM) 162 8.6.2 Weighted Product Method (WPM) 162 8.6.3 Weighted Aggregates Sum Product Assessment (WASPAS) 163 8.6.4 Technique for Order Preference by Similarity to Ideal Solutions (TOPSIS) 166 8.7 Applications of Fuzzy Logic 167 8.8 Conclusion 169 References 169 9 Use of Fuzzy Logic for Psychological Support to Migrant Workers of Southern Odisha (India) 173 Sanjaya Kumar Sahoo and Sukanta Chandra Swain 9.1 Introduction 174 9.2 Objectives and Methodology 175 9.2.1 Objectives 175 9.2.2 Methodology 176 9.3 Effect of COVID-19 on the Psychology and Emotion of Repatriated Migrants 176 9.3.1 Psychological Variables Identified 176 9.3.2 Fuzzy Logic for Solace to Migrants 176 9.4 Findings 178 9.5 Way Out for Strengthening the Psychological Strength of the Migrant Workers through Technological Aid 178 9.6 Conclusion 179 References 180 10 Fuzzy-Based Edge AI Approach: Smart Transformation of Healthcare for a Better Tomorrow 181 B. RaviKrishna, Sirisha Potluri, J. Rethna Virgil Jeny, Guna Sekhar Sajja and Katta Subba Rao 10.1 Significance of Machine Learning in Healthcare 182 10.2 Cloud-Based Artificial Intelligent Secure Models 183 10.3 Applications and Usage of Machine Learning in Healthcare 183 10.3.1 Detecting Diseases and Diagnosis 183 10.3.2 Drug Detection and Manufacturing 183 10.3.3 Medical Imaging Analysis and Diagnosis 184 10.3.4 Personalized/Adapted Medicine 185 10.3.5 Behavioral Modification 185 10.3.6 Maintenance of Smart Health Data 185 10.3.7 Clinical Trial and Study 185 10.3.8 Crowdsourced Information Discovery 185 10.3.9 Enhanced Radiotherapy 186 10.3.10 Outbreak/Epidemic Prediction 186 10.4 Edge AI: For Smart Transformation of Healthcare 186 10.4.1 Role of Edge in Reshaping Healthcare 186 10.4.2 How AI Powers the Edge 187 10.5 Edge AI-Modernizing Human Machine Interface 188 10.5.1 Rural Medicine 188 10.5.2 Autonomous Monitoring of Hospital Rooms—A Case Study 188 10.6 Significance of Fuzzy in Healthcare 189 10.6.1 Fuzzy Logic—Outline 189 10.6.2 Fuzzy Logic-Based Smart Healthcare 190 10.6.3 Medical Diagnosis Using Fuzzy Logic for Decision Support Systems 191 10.6.4 Applications of Fuzzy Logic in Healthcare 193 10.7 Conclusion and Discussions 193 References 194 11 Video Conferencing (VC) Software Selection Using Fuzzy TOPSIS 197 Rekha Gupta 11.1 Introduction 197 11.2 Video Conferencing Software and Its Major Features 199 11.2.1 Video Conferencing/Meeting Software (VC/MS) for Higher Education Institutes 199 11.3 Fuzzy TOPSIS 203 11.3.1 Extension of TOPSIS Algorithm: Fuzzy TOPSIS 203 11.4 Sample Numerical Illustration 207 11.5 Conclusions 213 References 213 12 Estimation of Nonperforming Assets of Indian Commercial Banks Using Fuzzy AHP and Goal Programming 215 Kandarp Vidyasagar and Rajiv Kr. Dwivedi 12.1 Introduction 216 12.1.1 Basic Concepts of Fuzzy AHP and Goal Programming 217 12.2 Research Model 221 12.2.1 Average Growth Rate Calculation 227 12.3 Result and Discussion 233 12.4 Conclusion 234 References 234 13 Evaluation of Ergonomic Design for the Visual Display Terminal Operator at Static Work Under FMCDM Environment 237 Bipradas Bairagi 13.1 Introduction 238 13.2 Proposed Algorithm 240 13.3 An Illustrative Example on Ergonomic Design Evaluation 245 13.4 Conclusions 249 References 249 14 Optimization of Energy Generated from Ocean Wave Energy Using Fuzzy Logic 253 S. B. Goyal, Pradeep Bedi, Jugnesh Kumar and Prasenjit Chatterjee 14.1 Introduction 254 14.2 Control Approach in Wave Energy Systems 255 14.3 Related Work 257 14.4 Mathematical Modeling for Energy Conversion from Ocean Waves 259 14.5 Proposed Methodology 260 14.5.1 Wave Parameters 261 14.5.2 Fuzzy-Optimizer 262 14.6 Conclusion 264 References 264 15 The m-Polar Fuzzy TOPSIS Method for NTM Selection 267 Madan Jagtap and Prasad Karande 15.1 Introduction 268 15.2 Literature Review 268 15.3 Methodology 270 15.3.1 Steps of the mFS TOPSIS 270 15.4 Case Study 272 15.4.1 Effect of Analytical Hierarchy Process (AHP) Weight Calculation on the mFS TOPSIS Method 273 15.4.2 Effect of Shannon’s Entropy Weight Calculation on the m-Polar Fuzzy Set TOPSIS Method 277 15.5 Results and Discussions 281 15.5.1 Result Validation 281 15.6 Conclusions and Future Scope 283 References 284 16 Comparative Analysis on Material Handling Device Selection Using Hybrid FMCDM Methodology 287 Bipradas Bairagi 16.1 Introduction 288 16.2 MCDM Techniques 289 16.2.1 Fahp 289 16.2.2 Entropy Method as Weights (Influence) Evaluation Technique 290 16.3 The Proposed Hybrid and Super Hybrid FMCDM Approaches 291 16.3.1 Topsis 291 16.3.2 FMOORA Method 292 16.3.3 FVIKOR 292 16.3.4 Fuzzy Grey Theory (FGT) 293 16.3.5 COPRAS –G 293 16.3.6 Super Hybrid Algorithm 294 16.4 Illustrative Example 295 16.5 Results and Discussions 298 16.5.1 FTOPSIS 298 16.5.2 FMOORA 298 16.5.3 FVIKRA 298 16.5.4 Fuzzy Grey Theory (FGT) 299 16.5.5 COPRAS-G 299 16.5.6 Super Hybrid Approach (SHA) 299 16.6 Conclusions 302 References 302 17 Fuzzy MCDM on CCPM for Decision Making: A Case Study 305 Bimal K. Jena, Biswajit Das, Amarendra Baral and Sushanta Tripathy 17.1 Introduction 306 17.2 Literature Review 307 17.3 Objective of Research 308 17.4 Cluster Analysis 308 17.4.1 Hierarchical Clustering 309 17.4.2 Partitional Clustering 309 17.5 Clustering 310 17.6 Methodology 314 17.7 TOPSIS Method 316 17.8 Fuzzy TOPSIS Method 318 17.9 Conclusion 325 17.10 Scope of Future Study 326 References 326 Index 329

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Book SynopsisUncertainty Vagueness and Impreciseness.- Intelligent Systems.- Fuzzy Sets and Extensions.-Intuitionistic Fuzzy Sets.- Decomposed Fuzzy Sets.

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Book SynopsisIntroduction.- Part 1: Type-1 Fuzzy Sets and Systems.- Short Primers on Type-1 Fuzzy Sets and Fuzzy Logic.- Type-1 Fuzzy Logic Systems.- Part 2: Type-2 Fuzzy Sets.- Sources of Uncertainty.- Type-2 Fuzzy Sets.- Operations on and Properties OF Type-2 Fuzzy Sets.- Type-2 Relations and Compositions.- Centroid of a Type-2 Fuzzy Set: Type-Reduction.- Part 3: Type-2 Fuzzy Logic Systems.- Mamdani Interval Type-2 Fuzzy Logic Systems (IT2 FLSS).- TSK Interval Type-2 Fuzzy Logic Systems.- General Type-2 Fuzzy Logic Systems (GT2 FLSS).- Conclusion.

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Book SynopsisFuzzy set theory is a mathematical structure for representing uncertainty. Modern intelligent systems must combine knowledge based on techniques for gathering and processing information with methods of approximate reasoning. This enables an intelligent system to better emulate human decision-making in uncertain environments.Table of ContentsGetting Started. Fuzzy Set Theory. Possibility/Probability Consistency Principle. Knowledge Representation. Imprecision and Fuzzy Logic. Knowledge Processing. Knowledge in FEST. Inference Engine. The Fuzzy Inference Engine. Fuzzy Inference in FEST. References. Index.

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Book SynopsisA funny, sinister and thought-provoking comic thriller from the multimillion-copy selling author of Holes. If you go down to the woods today ... Well, every child knows NOT to, don't they? Tamaya is on a scholarship to the prestigious Woodridge Academy and every day she and seventh-grader Marshall walk to school together. They never go through the woods. When they arrive at school they stop talking to each other because Marshall can't be seen to be friends with a little kid like Tamaya. Especially not with Chad around. Chadthebully, who makes Marshall's life utterly miserable. But today, hoping to avoid Chad, Marshall and Tamaya decide to go through the woods ... And what is waiting there for them is strange, sinister and entirely unexpected. The town is about to be turned upside down by the mysterious Fuzzy Mud ...Trade Review...a fast-paced and exciting story of bravery, friendships, and science gone wacky * BookTrust *An exciting story of school life, friends, and bullies that becomes a quick meditation on the promise and dangers of modern science * Kirkus *Sachar blends elements of mystery, suspense, and school-day life into a taut environmental cautionary tale about the insatiable hunger for energy sources and the cost of not doing the right thing * Publishers Weekly *But most of all, it's a great story, skillfully told. Readers will relate to Tamaya and Marshall straightaway and race through a tense plot for the denouement. It's quite a slim volume, Fuzzy Mud, but it packs a punch * The Bookbag *There’s no doubt that Louis Sachar, the Newbery Medal-winning author of Holes, knows how to draw in his readers. His latest book, Fuzzy Mud, reads like a middle school version of Contagion - it’s a thriller that will have readers quickly turning its pages * BookPage *Grounded in well-rounded central characters, this compelling novel holds as much suspense as fuel for discussion * Booklist *

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a huge range and FREE tracked UK delivery on ALL orders.

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a huge range and FREE tracked UK delivery on ALL orders.

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Book Synopsis

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a huge range and FREE tracked UK delivery on ALL orders.

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Book SynopsisFUZZY LOGIC APPLICATIONS IN COMPUTER SCIENCE AND MATHEMATICSTICS The prime objective of developing this book is to provide meticulous details about the basic and advanced concepts of fuzzy logic and its all-around applications to different fields of mathematics and engineering. The basic steps of fuzzy inference systems starting from the core foundation of the fuzzy concepts are presented in this book. The fuzzy theory is a mathematical concept and, at the same time, it is applied to many versatile engineering fields and research domains related to computer science. The fuzzy system offers some knowledge about uncertainty and is also related to the theory of probability. A fuzzy logic-based model acts as the classifier for many different types of data belonging to several classes. Covered in this book are topics such as the fundamental concepts of mathematics, fuzzy logic concepts, probability and possibility theories, and evolutionary computing to some extent. TTable of ContentsPreface xiii 1 Decision Making Using Fuzzy Logic Using Multicriteria 1Panem Charanarur, Srinivasa Rao Gundu and J.Vijaylaxmi 1.1 Introduction 2 1.2 Fuzzy Logic 5 1.3 Decision Making 6 1.4 Literature Review 7 1.5 Conclusion 10 2 Application of Fuzzy Logic in the Context of Risk Management 13Sudipta Adhikary and Kaushik Banerjee 2.1 Introduction 13 2.2 Objectives of Risk Management 14 2.3 Improved Risk Estimation 15 2.4 Threat at Quantification Matrix 17 2.5 Fundamental Definitions 18 2.6 Fuzzy Logic 19 2.7 Risk Related to Fuzzy Matrix 20 2.8 Conclusion 26 3 Use of Fuzzy Logic for Controlling Greenhouse Environment: Study Through the Lens of Web Monitoring 29Kaushik Banerjee and Sudipta Adhikary 3.1 Introduction 29 3.2 Design (Hardware) 30 3.3 Programming Arduino Mega Board 31 3.4 Implementation of a Prototype 34 3.5 Results 35 3.6 Conclusion 37 4 Fuzzy Logics and Marketing Decisions 41Mohammed Majeed 4.1 Introduction 41 4.2 Literature 42 4.3 Conclusion 46 4.4 Further Studies 47 5 A Method for Ranking Fuzzy Numbers Based on Their Value, Ambiguity, Fuzziness, and Vagueness 51Sunayana Saikia and Rituparna Chutia 5.1 Introduction 51 5.2 Preliminaries 54 5.3 The Designed Method 56 5.4 Validate the Reasonableness of the Suggested Ranking Algorithm 68 5.5 Comparative Analysis and Numerical Examples 75 5.6 Application 87 5.7 Conclusions 94 6 Evacuation of Attributes to Translucent TNSET in Mathematics Using Rough Topology 99Kala Raja Mohan, R. Narmada Devi, Nagadevi Bala Nagaram, Sathish Kumar Kumaravel and Regan Murugesan 6.1 Introduction 99 6.2 Basic Concepts of Rough Topology 100 6.3 Algorithm 102 6.4 Information System 102 6.5 Working Procedure 104 6.6 Conclusion 104 7 Design of Type-2 Fuzzy Controller for Hybrid Multi-Area Power System 107Susmit Chakraborty, Arindam Mondal and Soumen Biswas 7.1 Introduction 108 7.2 Plant Model 108 7.3 Controller Design 109 7.4 Levenberg-Marquardt Algorithm 115 7.5 Optimization of Controller Parameters Using CASO Algorithm 116 7.6 Result and Analysis 116 7.7 Conclusion 121 8 Alzheimer's Detection and Classification Using Fine-Tuned Convolutional Neural Network 125Anooja Ali, Sarvamangala D. R., Meenakshi Sundaram A. and Rashmi C. 8.1 Introduction 125 8.2 Literature Review 129 8.3 Methodology 133 8.3.1 Dataset 134 8.3.2 Pre-Processing 134 8.4 Implementation and Results 134 8.5 Conclusion 138 9 Design of Fuzzy Logic-Based Smart Cars Using Scilab 143Josiga S., Maheswari R. and Subbulakshmi T. 9.1 Introduction 143 9.2 Literature Survey 145 9.3 Proposed Fuzzy Inference System for Smart Cars 149 9.4 Implementation Details and Results 155 9.5 Conclusion and Future Work 156 10 Financial Planning and Decision Making for Students Using Fuzzy Logic 159G. Surya Deepan and T. Subbulakshmi 10.1 Introduction 159 10.2 Literature Review 161 10.3 System Architecture 163 10.4 Conclusion and Future Scope 169 11 A Novel Fuzzy Logic (FL) Algorithm for the Automatic Detection of Oral Cancer 173M. Praveena Kiruba bai and G. Arumugam 11.1 Introduction 173 11.2 Image Enhancement 174 11.3 Gabor Transform 175 11.4 Image Transformation 175 11.5 Adaptive Networks: Architecture 176 11.6 Results and Discussions 177 11.7 Conclusion 177 12 A Study on Decision Making of Difficulties Faced by Indian Workers Abroad by Using Rough Topology 179Nagadevi Bala Nagaram, R. Narmada Devi , Kala Raja Mohan, Regan Murugesan and Sathish Kumar Kumaravel 12.1 Introduction 179 12.2 Fundamental Idea of Rough Topology 182 12.3 Algorithm 183 12.4 Information System 183 12.5 Working Procedure 185 12.6 Conclusion 185 13 Case Study on Fuzzy Logic: Fuzzy Logic-Based PID Controller to Tune the DC Motor Speed 187Devendra Kumar Somwanshi 13.1 Introduction 188 13.2 Literature Review 190 13.3 Design of Fuzzy-Based PID Controller 196 13.4 Experimental Work and Results Analysis 205 13.5 Conclusion and Future Scope 207 14 Application of Intuitionistic Fuzzy Network Using Efficient Domination 213A. Meenakshi, J. Senbagamalar and A. Kannan 14.1 Introduction 213 14.2 Efficient Domination in Intuitionistic Fuzzy Graph (IFG) 215 14.3 Main Frame Work 217 14.4 Secret Key 219 14.5 Illustration 224 14.6 Conclusion 231 15 Analysis of Parameters Related to Malaria with Comparative Study on Fuzzy Cognitive Maps and Neutrosophic Cognitive Maps 233Regan Murugesan, Sathish Kumar Kumaravel, Kala Raja Mohan, Narmada Devi Rathinam and Suresh Rasappan 15.1 Introduction 233 15.2 Parameters of Malaria 235 15.3 Fuzzy Cognitive Map 235 15.4 Neutrosophic Cognitive Map 240 15.5 Comparison and Discussion 246 15.6 Conclusion 247 16 Applications of Fuzzy Cognitive Maps and Neutrosophic Cognitive Maps on Analysis of Dengue Fever 249Sathish Kumar Kumaravel, Regan Murugesan, Nagadevi Bala Nagaram, Suresh Rasappan and G. Yamini 16.1 Introduction 249 16.2 Parameters of Dengue 251 16.3 Fuzzy Cognitive Maps 251 16.4 Neutrosophic Cognitive Map 257 16.5 Comparison and Discussion 263 16.6 Conclusion 264 17 A Comprehensive Review and Analysis of the Plethora of Branches of Medical Science and Bioinformatics Based on Fuzzy Logic 267Partha Sarker and Siddhartha Roy 17.1 Introduction 267 17.2 Previous Work 271 17.3 Fuzzy Logic in Medical Fields and Bioinformatics 271 17.4 Review of Published Work and In-Depth Analysis 273 17.5 Conclusion 273 References 277 Index 279

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Book SynopsisSolving Fuzzy Linear Equations.- Graphs, Fuzzy Graphs and Intuitionistic Fuzzy Graphs.- Fuzzy Measures, Possibility and Necessity.- Compositional Rule of Inference.- Fuzzy Topological Spaces.- Fuzzy Subgroups and Fuzzy Normal Subgroups.- Application of Fuzzy Mathematics in Other Disciplines.

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Book SynopsisOffering a new perspective on a growing field, the text explores the many hardware implications of fuzzy logic based circuits. As use of AI increases, so the VLSI area of circuits is becoming a growth subject. The text surveys fuzzy set theory before moving on to cover a range of nonstandard solutions for fuzzy logic VLSI circuits. An overview of future trends is included plus practical examples from the authors'' research which will enhance the reader''s understanding of the topic. This is the first book on hardware aspects of fuzzy systems which offers a mixture of classical work and the authors'' new perspective.Table of ContentsFuzzy Sets in Approximate Reasoning: A Personal View. FUZZY LOGIC CONTROL. Fuzzy Logic Control: A systematic Design and Performance Assessment Methodology. On the Compatibility of Fuzzy Control and Conventional Control Techniques. On the Crisp-Type Fuzzy Controller: Behaviour Analysis and Improvement. FUZZY LOGIC HARDWARE IMPLEMENTATIONS. Design Considerations of Digital Fuzzy Logic Controllers. Parallel Algorithm for Fuzzy Logic Controller. Fuzzy Flip-Flop. Design Automation of Fuzzy Logic Circuits. HYBRID SYSTEMS AND APPLICATIONS. Neuro-Fuzzy Systems: Hybrid Configurations. A Fuzzy Logic Approach to Handwriting Recognition. Index.

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Book SynopsisThere are many situations in science and engineering where complex output data from a given system is used to formulate a model of how that system operates, or to simulate its response to different inputs. Applications include control, decision theory, and the emerging fields of bioinformatics.Trade Review"To cope with real world uncertainties and provide a philosophical and practical guide...several methodologies are presented..." (SciTech Book News, Vol. 25, No. 4, December 2001) "...certainly a book that should be in the library of any institution where research and advanced study in fuzzy systems are carried out." (Choice, Vol. 39, No. 7, March 2002) "...well organized, easy to read, and self-contained.... I would recommend it to anyone interested in self-study of the basic ideas of fuzzy systems..." (International Journal of General Systems, Vol. 31, No. 6, 2002)Table of ContentsPreface. Acknowledgments. Introduction. System Analysis. Uncertainty Techniques. Learning from Data: System Identification. Propositions as Subsets of the Data Space. Fuzzy Systems and Identification. Random-Set Modelling and Identification. Certain Uncertainty. Fuzzy Inference Engines. Fuzzy Classification. Fuzzy Control. Fuzzy Mathematics. Summary. Appendices. Index.

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Book SynopsisChapter 1. A Bibliometric and Trend Analysis on Impact of Fuzzy Logic in Industry 4.0.- Chapter 2. Analyzing the industry 5. adoption barriers in the pharmaceutical sector using an integrated Fuzzy MCDM methodology: A case study application for Turkey.- Chapter 3. Fuzzy Analysis of Ground Humidity Sensor Readings on a Crop Area Managed Using IoT-Technology.- Chapter 4. Intelligent Illumination: Fuzzy Logic Applications in IoT Driven Lighting Solutions.- Chapter 5. Fuzzy Logic and Cybersecurity: An Intelligent Shield in the Digital Age.- Chapter 6. A Text Mining Procedure for Recognizing the Awareness of Industry 4.0 and digitalization perceptions in Construction Industry.- Chapter 7. Additive Manufacturing: Fuzzy Logic Strategies In The Manufacturing Of The Future.- Chapter 8. Share of Local Assortments in Revenue for a Large Scale National Food Retailer : Assessment of Long and Short Time Series Patterns.- C

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Book SynopsisThis book aims to contribute to the discussion about the implications of fuzzy logic, neural networks, digital era, and other intelligent techniques on organizations. This book will be very useful for academic researchers and postgraduate students aiming to introduce themselves to the field of quantitative techniques for overcoming uncertain environments and developing models to make decisions. Developments in other theories and socioeconomic and computational changes have shed light on the importance of fuzzy applications in social sciences. The treatment of uncertainty in the economic and business analysis is fundamental and requires instruments compatible with the uncertain environment of economics and business, because most of the traditional models have been overtaken by this reality when trying to make decisions with uncertain information. In the face of information technology, digitization, and uncertainty, organizations confront new opportunities and challenges. In order to take advantage of these opportunities and overcome current and future challenges, it is needed to understand the evolution of these phenomenon.Table of ContentsWavelet entropy and complexity analysis of cryptocurrencies dynamics.- The Use of Fuzzy Decoupled Net Present Value in pepper production.- The effect of energy prices on Mexican households’ consumption.- How to Cope with Complexity in Decision-Making: an Application of Fuzzy Qualitative Comparative Analysis in the Triage Process.- ESG risk disclosure and earning timelines in the Mexican capital market using fuzzy logic regression.- The Digital Taxation Adoption and its Impact on Income Tax in Mexico (2010-2020).

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