Fuzzy Logic An Introductory Course for Engineering Students

This book introduces readers to fundamental concepts in fuzzy logic. It describes the necessary theoretical background and a number of basic mathematical models. Moreover, it makes them familiar with fuzzy control, an important topic in the engineering field. The book offers an unconventional introd...

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Bibliographic Details
Main Authors: Trillas, Enric, Eciolaza, Luka
Format: eBook Book
Language:English
Published: Cham Springer Nature 2015
Springer
Springer International Publishing AG
Springer International Publishing
Edition:1
Series:Studies in Fuzziness and Soft Computing
Subjects:
Computational Intelligence
Control and Systems Theory
Engineering
Engineering & allied operations
Fuzzy logic
Symbolic and Algebraic Manipulation
ISBN:3319142038, 9783319142036, 331914202X, 9783319142029
ISSN:1434-9922, 1860-0808
Online Access:Get full text
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Abstract This book introduces readers to fundamental concepts in fuzzy logic. It describes the necessary theoretical background and a number of basic mathematical models. Moreover, it makes them familiar with fuzzy control, an important topic in the engineering field. The book offers an unconventional introductory textbook on fuzzy logic, presenting theory together with examples and not always following the typical mathematical style of theorem-corollaries. Primarily intended to support engineers during their university studies, and to spark their curiosity about fuzzy logic and its applications, the book is also suitable for self-study, providing a valuable resource for engineers and professionals who deal with imprecision and non-random uncertainty in real-world applications.
AbstractList This book introduces readers to fundamental concepts in fuzzy logic. It describes the necessary theoretical background and a number of basic mathematical models. Moreover, it makes them familiar with fuzzy control, an important topic in the engineering field. The book offers an unconventional introductory textbook on fuzzy logic, presenting theory together with examples and not always following the typical mathematical style of theorem-corollaries. Primarily intended to support engineers during their university studies, and to spark their curiosity about fuzzy logic and its applications, the book is also suitable for self-study, providing a valuable resource for engineers and professionals who deal with imprecision and non-random uncertainty in real-world applications.
Author Eciolaza, Luka
Trillas, Enric
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ISSN 1434-9922
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Springer International Publishing AG
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Snippet This book introduces readers to fundamental concepts in fuzzy logic. It describes the necessary theoretical background and a number of basic mathematical...
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SubjectTerms Computational Intelligence
Control and Systems Theory
Engineering
Engineering & allied operations
Fuzzy logic
Symbolic and Algebraic Manipulation
Subtitle An Introductory Course for Engineering Students
TableOfContents 4.3 Which Relevant Properties Do Have a Fuzzy Binary Relation? -- 4.4 The Concept of T-State -- 4.5 Fuzzy relations and α-cuts -- 5 T-Preorders and T-Indistinguishabilities -- 5.1 Which Is the Aim of This Section? -- 5.2 The Characterization of T-Preorders -- 5.3 The Characterization of T-Indistinguishabilities -- 6 Fuzzy Arithmetic -- 6.1 Introduction -- 6.2 Fuzzy Numbers -- 6.2.1 Operations with Fuzzy Numbers -- 6.2.2 Operations with Triangular Fuzzy Numbers -- 6.2.3 Note -- 6.3 A Note on the Lattice of Fuzzy Numbers -- 6.3.1 Example -- 6.4 A Note on Fuzzy Quantifiers -- 6.4.1 Quantified Fuzzy Statements -- 7 Fuzzy Measures -- 7.1 Introduction -- 7.2 The Concept of a Measure -- 7.3 Types of Measures -- 7.4 λ-Measures -- 7.5 Measures of Possibility and Necessity -- 7.6 Examples -- 7.7 Probability, Possibility and Necessity -- 7.8 Probability of Fuzzy Sets -- 8 An Introduction to Fuzzy Control -- 8.1 Introduction -- 8.1.1 Note -- 8.2 Revising Conditional and Implications in Fuzzy Control -- 8.2.1 Inference from Imprecise Rules -- 8.2.2 Takagi-Sugeno of Order 1 -- 8.3 Control of Nonlinear Systems -- 8.3.1 State-Space Representation -- 8.3.2 Takagi-Sugeno Models for Control of Nonlinear Systems -- 8.3.3 Stability Analysis -- 8.3.4 Parallel Distributed Compensation -- 8.3.5 Piecewise Bilinear Model -- 8.3.6 Vertex Placement Principle -- Bibliography
Intro -- Preface -- Contents -- 1 On the Roots of Fuzzy Sets -- 1.1 A Genesis of Fuzzy Sets -- 1.1.1 L-Degree -- 1.1.2 Fuzzy Sets -- 1.2 Opposite, Negate, and Middle -- 1.2.1 Antonyms -- 1.2.2 Negations -- 1.2.3 Antonyms and Negations -- 1.2.4 Medium Term -- 1.3 AND/OR -- 1.3.1 AND -- 1.3.2 OR -- 1.4 Qualified, Modified, and Constrained Predicates -- 1.4.1 Qualified Predicates -- 1.4.2 Linguistic Modifiers -- 1.4.3 Constrained Predicates -- 1.4.4 Group Meaning -- 1.4.5 Synonims -- 1.5 Linguistic Variables -- 1.5.1 Fuzzy Partition -- 1.6 A Note on Lattices -- 1.6.1 Examples -- 2 Algebras of Fuzzy Sets -- 2.1 Introduction -- 2.1.1 Cartesian Product -- 2.1.2 Extension Principle -- 2.1.3 Preservation of the Classical Case -- 2.1.4 Resolution -- 2.2 The Concept of an `Algebra of Fuzzy Sets' -- 2.2.1 Introduction -- 2.2.2 Algebras of Fuzzy Sets -- 2.2.3 Non-contradiction and Excluded-Middle -- 2.2.4 Decomposable Algebras -- 2.2.5 Standard Algebras of Fuzzy Sets -- 2.2.6 Strong Negations -- 2.2.7 Continuous T-Norms and T-Conorms -- 2.2.8 Laws of Fuzzy Sets -- 2.2.9 Examples -- 2.3 On Aggregating Imprecise Information -- 2.3.1 Aggregation Functions -- 2.3.2 Ordered Weighted Means -- 2.3.3 More on Aggregations -- 2.3.4 Examples -- 3 Reasoning and Fuzzy Logic -- 3.1 What Does It Mean ``Logic''? -- 3.1.1 Logic and Consequence Operators -- 3.1.2 Conjecturing -- 3.2 Reasoning with Conditionals: Representation -- 3.2.1 What is a Conditional? -- 3.2.2 The Case of Boolean Algebras -- 3.2.3 Fuzzy Conditionals -- 3.3 Short Note on Other Modes of Reasoning -- 3.4 Inference with Fuzzy Rules -- 3.4.1 Finite Case -- 3.4.2 Inference with Several Rules -- 3.4.3 Examples -- 3.5 Deffuzification -- 3.6 Rules and Conjectures -- 3.7 Two Final Examples -- 4 Fuzzy Relations -- 4.1 What Is a Fuzzy Relation? -- 4.2 How to Compose Fuzzy Relations?
Title Fuzzy Logic
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