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.
"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
Inhaltsangabe
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
