Fuzzy logic theory and applications Part I and Part II / by Lotfi A. Zadeh (UC Berkeley), Rafik A. Aliev (Azerbaijan State Oil and Industry University, Azerbaijan).

part 1. Fuzzy logic theory 1 -- part 2. Applications and advanced topics of fuzzy logic. Contents
Preface
About the Authors
About the Contributors
Part I Fuzzy Logic Theory
Chapter 1 Fuzzy Sets
1.1 Introduction
1.2 Definitions
1.3 Some Properties of ∪, ∩, and Complementation
1.4 Algebraic Operations on Fuzzy Sets
1.5 Convexity
1.6 Examples on Operations on Fuzzy Sets
1.7 Fuzzy Arithmetic
1.8 Extensions of Fuzzy Sets
1.8.1 Type-2 fuzzy sets and numbers
1.8.2 Intuitionistic fuzzy sets
1.8.3 Rough sets
1.8.4 Neutrosophic set
Chapter 2 Fuzzy Logic
2.1 Introduction
2.2 Fuzzy Logic
2.3 Approximate Reasoning
2.4 Analysis of Different Fuzzy Logics
2.5 Extended Fuzzy Logic
2.5.1 Introduction
2.5.2 f-geometry and f-transformation
Chapter 3 Restriction Concept
3.1 Introduction to Restriction Concept
3.1.1 Computation with restrictions
3.2 Truth and Meaning
3.2.1 Truth qualification: Internal and external truth values
Chapter 4 Fuzzy Probabilities
4.1 Introduction
4.2 The Concept of Fuzzy Probability
Chapter 5 Fuzzy Functions
5.1 Definition of Fuzzy Functions
5.2 Integrability and Differentiability of Fuzzy Functions
Chapter 6 Fuzzy Systems
6.1 Introduction
6.2 System, Aggregate and State
6.3 State Equations for Fuzzy Systems
6.4 Fuzzy Rule-based System
Chapter 7 Z-number Theory
7.1 Introduction
7.2 Computation with Z-numbers
7.2.1 Computation with continuous Z-numbers
7.2.2 Computation with discrete Z-numbers
7.3 Standard Division of Discrete Z-numbers
Chapter 8 Generalized Theory of Uncertainty
8.1 Introduction
8.2 The Concept of NL-Computation
8.3 The Concept of Precisiation
8.4 The Concept of Cointensive Precisiation
8.5 A Key Idea — The Meaning Postulate
8.6 The Concept of a Generalized Constraint
8.7 Principal Modalities of Generalized Constraints
8.8 The Concept of Bimodal Constraint/Distribution
8.9 The Concept of a Group Constraint
8.10 Primary Constraints, Composite Constraints and Standard Constraints
8.11 The Generalized Constraint Language and Standard Constraint Language
8.12 The Concept of Granular Value
8.13 The Concept of Protoform
8.14 The Concept of Generalized-Constraint-Based Computation
8.15 Protoformal Deduction Rules
8.16 Examples of Computation/Deduction
8.16.1 The Robert example
8.16.2 The tall Swedes problem
8.16.3 Tall Swedes and tall Italians
8.16.4 Simplified trip planning
Part II Applications and Advanced Topics of Fuzzy Logic
Chapter 9 Restriction-based Semantics
9.1 Precisiation of Meaning
9.1.1 Canonical form of p: cf (p)
9.2 The Concept of Explanatory Database (ED)
Chapter 10 Granular Computing: Principles and Algorithms
10.1 Introduction
10.2 Information Granularity: Selected Examples
10.2.1 Image processing
10.2.2 Processing and interpretation of time series
10.2.3 Granulation of time
10.2.4 Data summarization
10.3 Formal Platforms of Information Granularity
10.4 Characterization of Information Granules: Coverage and Specificity
10.5 The Design of Information Granules
10.5.1 The principle of justifiable granularity
10.5.2 Augmentations of the principle of justifiable granularity
10.5.2.1 Weighted data
10.5.2.2 Inhibitory data
10.6 Information Granularity as a Design Asset in System Modeling
10.6.1 Granular mappings
10.6.2 Granular aggregation: An enhancement of aggregation operations through allocation of information granularity
10.6.3 Development of granular models of higher type
10.7 Concluding Comments
Chapter 11 Complex Fuzzy Sets and Complex Fuzzy Logic. An Overview of Theory and Applications
11.1 Introduction
11.2 Complex Fuzzy Logic and Set Theory
11.2.1 Complex fuzzy sets
11.2.2 Complex fuzzy logic
11.3 Generalized Complex Fuzzy Logic
11.3.1 Propositional and first-order predicate complex fuzzy logic
11.3.2 Complex fuzzy propositions and inference examples
11.3.3 Complex fuzzy inference example
11.4 Generalized Complex Fuzzy Class Theory
11.4.1 Complex fuzzy classes and connectives examples
11.5 Pure Complex Fuzzy Classes
11.6 Recent Developments in the Theory and Applications of CFL and CFS
11.6.1 Advances in the theoretical foundations of CFL/CFS
11.6.2 Applications of CFL/CFS
11.7 Conclusion
Chapter 12 Introduction to Fuzzy Logic Control
12.1 Introduction
12.2 The Mamdani Fuzzy Controller
12.2.1 Fuzzification module
12.2.2 Fuzzy rules
12.2.3 Fuzzy inference mechanism and defuzzification
12.3 Design of Fuzzy Controllers
12.3.1 Selection of membership functions
12.3.2 Rule-base
12.3.3 Implementation
12.4 Multiple-Output, Single-Input (MISO) Mamdani Fuzzy Controllers
12.5 Takagi-Sugeno (TS) Fuzzy Controllers
12.6 Fuzzy Control Versus Conventional Control
12.6.1 Advantages of fuzzy control
12.6.2 Disadvantages of fuzzy control
12.7 Applicability of Fuzzy Control
Chapter 13 Fuzzy Decision-Making
13.1 Introduction
13.2 Definitions
13.3 Decision Model
13.4 Examples
13.4.1 Zadeh’s two boxes problem
13.4.2 Investment problem
Chapter 14 Selected Interpretability Aspects of Fuzzy Systems for Classification
14.1 Introduction
14.1.1 Attempts at systematizing solutions for interpretability of fuzzy systems
14.1.2 Solutions proposed in this chapter
14.2 Description of a Fuzzy System for Classification
14.2.1 Rule base
14.2.2 Defuzzification process
14.2.3 Aggregation and inference operators
14.3 A Hybrid Genetic-Imperialist Algorithm for Automatic Selection of Structure and Parameters of a Fuzzy System
14.3.1 Encoding of potential solutions
14.3.2 Evaluation of potential solutions
14.3.3 Processing of potential solutions
14.4 Interpretability Criteria of a Fuzzy System for Classification
14.4.1 Complexity evaluation criterion
14.4.2 Fuzzy sets readability evaluation criterion
14.4.2.1 Criterion for assessing similarity of fuzzy sets width
14.4.3 Fuzzy rules readability evaluation criteria
14.4.3.1 Criterion for assessing fuzzy rules activity
14.4.4 Criterion for assessing the readability of weights values in the fuzzy rule base
14.4.5 Criterion for assessing the readability of aggregation and inference operators
14.4.6 Criterion for assessing the defuzzification mechanism
14.5 Simulations
Chapter 15 Fuzzy Reinforcement Learning
15.1 The GARIC Architecture
15.2 The ACFRL Algorithm
15.3 Fuzzy Q-Learning to Solve Fuzzy Dynamic Programming
Chapter 16 Adaptive Neuro-Fuzzy Inference Systems (ANFISs)
16.1 Introduction
16.2 ANFIS Architecture
16.3 Hybrid Learning Algorithm
16.4 Learning Methods That Cross-Fertilize ANFIS and RBFN
16.5 ANFIS as a Universal Approximator
16.5.1 Stone-Weierstrass theorem
16.5.2 Algebraic closure — Multiplicative
16.6 Simulation Examples
16.6.1 Practical considerations
16.6.2 Example 1: Modeling a two-input sinc function
16.6.3 Example 2: Modeling a three-input nonlinear function
16.6.4 Example 3: Online identification in control systems
16.6.5 Example 4: Predicting chaotic time series
16.6.6 Example 5: Dimensionality reduction for ANFIS
16.7 Extensions and Advanced Topics
Chapter 17 Fuzzy Expert Systems
17.1 Introduction
17.2 Fuzzy Expert Systems Using Bayes-Shortliffe Approach
17.2.1 Structure of the system
17.2.2 Knowledge representation
17.2.3 Inference
17.3 Examples
17.3.1 The expert system for scheduling of oil-refinery production
17.3.2 Fuzzy hypotheses generating and accounting systems
17.3.3 Forecasting of conflicts
Chapter 18 Application of Logistic Regression Analysis to Fuzzy Cognitive Maps
18.1 Introduction
18.2 Fuzzy Cognitive Maps
18.3 Logistic and Multinomial Logistic Regression Analysis
18.4 Application Examples
18.4.1 The city-health model
18.4.2 The liquid tank model
18.5 Conclusions
Chapter 19 Fuzzy Logic in Medicine
19.1 Introduction
19.2 Fuzzy Signal Processing-Trans-Skull Brain Imaging
19.2.1 Characteristics with respect to echo shape, λf
19.2.2 Characteristics with respect to magnitude of echo amplitude, λa
19.2.3 Characteristic value with respect to location, λth
19.3 Health Checkup Data Analysis
Bibliography
Index

Nowadays, voluminous textbooks and monographs in fuzzy logic are devoted only to separate or some combination of separate facets of fuzzy logic. There is a lack of a single book that presents a comprehensive and self-contained theory of fuzzy logic and its applications.Written by world renowned authors, Lofti Zadeh, also known as the Father of Fuzzy Logic, and Rafik Aliev, who are pioneers in fuzzy logic and fuzzy sets, this unique compendium includes all the principal facets of fuzzy logic such as logical, fuzzy-set-theoretic, epistemic and relational. Theoretical problems are prominently illustrated and illuminated by numerous carefully worked-out and thought-through examples.This invaluable volume will be a useful reference guide for academics, practitioners, graduates and undergraduates in fuzzy logic and its applications.