Fuzzy Logic : An Introductory Course for Engineering Students.

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?.

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.

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Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2024. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.