  Fuzzy Sets and Fuzzy Decision-Making

1st Edition

CRC Press

288 pages

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Hardback: 9780849389313
pub: 1995-07-03
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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.

Reviews

"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."

From the Foreword

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

References

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

References

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

References

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

References

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

References

Variable Weights Analysis

Defining the Problem

An Empirical Variable Weight Formula

Principles of Variable Weights

References

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

References

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

References

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

References

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

References