Fuzzy Sets and Fuzzy Decision-Making  book cover
1st Edition

Fuzzy Sets and Fuzzy Decision-Making

ISBN 9780849389313
Published July 3, 1995 by CRC Press
288 Pages

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Book Description

The increasing number of applications of fuzzy mathematics has generated interest in widely ranging fields, from engineering and medicine to the humanities and management sciences. Fuzzy Sets and Fuzzy Decision-Making provides an introduction to fuzzy set theory and lays the foundation of fuzzy mathematics and its applications to decision-making. New concepts are simplified with the use of figures and diagrams, and methods are discussed in terms of their direct applications in obtaining solutions to real problems, particularly to decision-related problems.
The first chapter presents the current state of knowledge of fuzzy set theory, using pan-Venn-diagrams to illustrate mathematical concepts. The second chapter clearly describes the theory of factor spaces, on which fuzzy decision-making is based. The remainder of the book is devoted to the methods, applications, techniques, and examples of this fuzzy decision-making, and includes methods for determining membership functions and for treating multifactorial and variable weights analyses.

Table of Contents

The Basics of Fuzzy Set Theory
Fuzzy Phenomena and Fuzzy Concepts
Naive Thoughts of Fuzzy Sets
Definition of Fuzzy Sets
Basic Operations of Fuzzy Sets
The Resolution Theorem
A Representation Theorem
Extension Principles
Factor Spaces
What are "Factors"?
The State Space of Factors
Relations and Operations Between Factors
Axiomatic Definition of Factor Spaces
Describing Concepts in a Factor Space
The Basics of Fuzzy Decision-Making
Feedback Extension and Its Applications
Feedback Ranks and Degrees of Coincidence
Equivalence Between Sufficient Factors and Coincident Factors
How to Improve the Precision of a Feedback Extension
Representation of the Intention of a Concept
Basic Forms of Fuzzy Decision-Making
Limitations of the Weighted Average Formula
Determination of Membership Functions
A General Method for Determining Membership Functions
The Three-Phase Method
The Incremental Method
The Multiphase Fuzzy Statistical Method
The Method of Comparisons
The Absolute Comparison Method
The Set-Valued Statistical Iteration Method
Ordering by Precedence Relations
The Relative Comparison Method and the Mean Pair-Wise Comparison Method
Multifactorial Analysis
Background of the Problem
Multifactorial Functions
Axiomatic Definition of Additive Standard Multifactorial Functions
Properties of ASMm-funcs
Generations of ASMm-funcs
Applications of ASMm-funcs in Fuzzy Decision-Making
A General Model of Multifactorial Decision-Making
Variable Weights Analysis
Defining the Problem
An Empirical Variable Weight Formula
Principles of Variable Weights
Multifactorial Decision-Making with Multiple Objectives
Background and Models
Multifactorial Evaluation
The Multifactorial Evaluation Approach to the Classification of Quality
Incomplete Multifactorial Evaluation
Multi-Level Multifactorial Evaluation
An Application of Multifactorial Evaluation in Textile Engineering
Set-Valued Statistics and Degree Analysis
Fuzzy Statistics and Random Sets
The Falling Shadow of Random Sets
Set-Valued Statistics
Degree Analysis
Random and Set-Valued Experiments
A Mathematical Model for Employee Evaluation
Refinements of Fuzzy Operators
The Axiomatic Structure of Zadeh's Operators
Common Fuzzy Operators
Generalized Fuzzy Operators
The Strength of Fuzzy Operators "AND" and "OR"
Fuzzy Operators Based on the Falling Shadow Theory
Multifactorial Decision Based on Theory of Evidence
A Brief Introduction to Theory of Evidence
Composition of Belief Measures
Multifactorial Evaluation Based on the Theory of Evidence
Two Special Types of Composition Functions
The Maximum Principle for Multiple Object Evaluations

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"Must reading for anyone interested in acquiring a thorough understanding of fuzzy logic, its role in soft computing, and its application to control and related fields."
-Lotfi A. Zadeh
From the Foreword