Li Decision and Game Theory in Management With Intuitionistic Fuzzy Sets

2014
ISBN: 978-3-642-40712-3
Verlag: Springer
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, Band 308, 444 Seiten, eBook

Reihe: Studies in Fuzziness and Soft Computing

The focus of this book is on establishing theories and methods of both decision and game analysis in management using intuitionistic fuzzy sets. It proposes a series of innovative theories, models and methods such as the representation theorem and extension principle of intuitionistic fuzzy sets, ranking methods of intuitionistic fuzzy numbers, non-linear and linear programming methods for intuitionistic fuzzy multi-attribute decision making and (interval-valued) intuitionistic fuzzy matrix games. These theories and methods form the theory system of intuitionistic fuzzy decision making and games, which is not only remarkably different from those of the traditional, Bayes and/or fuzzy decision theory but can also provide an effective and efficient tool for solving complex management problems. Since there is a certain degree of inherent hesitancy in real-life management, which cannot always be described by the traditional mathematical methods and/or fuzzy set theory, this book offers an effective approach to using the intuitionistic fuzzy set expressed with membership and non-membership functions.

This book is addressed to all those involved in theoretical research and practical applications from a variety of fields/disciplines: decision science, game theory, management science, fuzzy sets, operational research, applied mathematics, systems engineering, industrial engineering, economics, etc.

Zielgruppe

Research

Autoren/Hrsg.

Li, Deng-Feng

Inhaltsverzeichnis

Chapter 1 Intuitionistic Fuzzy Set Theories1.1 Introduction1.2 Intuitionistic Fuzzy Sets and Operations1.3 Intuitionistic Fuzzy Set Distances and Similarity Degrees1.3.1 Definition of Similarity Degrees between Intuitionistic Fuzzy Sets1.3.2 Definition of Distances between Intuitionistic Fuzzy Sets1.4 Representation Theorem of Intuitionistic Fuzzy Sets1.5 Extension Principle of Intuitionistic Fuzzy Sets and Operations1.5.1 Extension Principle of Intuitionistic Fuzzy Sets1.5.2 Operations over Intuitionistic Fuzzy Sets1.6 Definitions of Intuitionistic Fuzzy Numbers and Algebraic Operations1.6.1 Trapezoidal Intuitionistic Fuzzy Numbers and Algebraic Operations1.6.2 Triangular Intuitionistic Fuzzy Numbers and Algebraic OperationsChapter 2 Intuitionistic Fuzzy Set Aggregation Operators and Multiattribute Decision Making Methods2.1 Introduction2.2 Intuitionistic Fuzzy Set Aggregation Operators and Properties2.2.1 Intuitionistic Fuzzy Set Weighted Aggregation Operators2.2.2 Intuitionistic Fuzzy Set Hybrid Weighted Aggregation Operators2.2.3 Intuitionistic Fuzzy Set Generalized Hybrid Weighted Aggregation Operators2.3 Intuitionistic Fuzzy Set Generalized Hybrid Weighted Aggregation Method for Intuitionistic Fuzzy Set Multiattribute Decision Making2.3.1 Formal Representation of Intuitionistic Fuzzy Set Multiattribute Decision Making Problems2.3.2 Intuitionistic Fuzzy Set Multiattribute Decision Making Process Based on Intuitionistic Fuzzy Set Generalized Hybrid Weighted Aggregation Operators and Real Example AnalysisChapter 3 Intuitionistic Fuzzy Set Multiattribute Decision Making Methods3.1 Introduction3.2 Linear Weighted Average Method for Multiattribute Decision Making with Both Weights and Attribute Ratings Expressed by Intuitionistic Fuzzy Sets3.2.1 Linear Weighted Average Model of Intuitionistic Fuzzy Set Multiattribute Decision Making3.2.2 Sensitivity Analysis of Linear Weighted Average Method for Intuitionistic Fuzzy Set Multiattribute Decision Making3.2.3 Process of Linear Weighted Average Method for Intuitionistic Fuzzy Set Multiattribute Decision Making and Real Example Analysis3.3 TOPSIS for Intuitionistic Fuzzy Set Multiattribute Decision Making with Both Ideal Solutions and Weights Known3.3.1 Basic Principle of TOPSIS3.3.2 Intuitionistic Fuzzy Set TOPSIS Principle and Real Example Analysis3.4 Optimum Seeking Method for Intuitionistic Fuzzy Set Multiattribute Decision Making with Both Ideal Solutions and Weights Known3.4.1 Optimum Seeking Principle for Intuitionistic Fuzzy Set Multiattribute Decision Making3.4.2 Process of Optimum Seeking Method for Intuitionistic Fuzzy Set Multiattribute Decision Making and Real Example Analysis3.5 Linear Programming Method for Multiattribute Decision Making with Both Weights and Attribute Ratings Expressed by Intuitionistic Fuzzy Sets3.5.1 Allocation Method of Hesitancy Degrees3.5.2 Linear Programming Models and Method for Computing Intuitionistic Fuzzy Set Comprehensive Evaluations3.5.3 Relative Closeness Degree Method of Intuitionistic Fuzzy Set Comprehensive Evaluations and Real Example Analysis3.6 LINMAP for Intuitionistic Fuzzy Set Multiattribute Decision Making with Both Ideal Solutions and Weights Unknown3.6.1 Determination Methods of Membership and Nonmembership Degrees of Intuitionistic Fuzzy Sets3.6.2 Consistency and Inconsistency Measure Methods3.6.3 LINMAP Models for Intuitionistic Fuzzy Set Multiattribute Decision Making3.6.4 LINMAP Process for Intuitionistic Fuzzy Set Multiattribute Decision Making and Real Example Analysis3.7 Fraction Mathematical Programming Method for Intuitionistic Fuzzy Set Multiattribute Decision Making with Unknown Weights3.7.1 Fraction Mathematical Programming Model for Computing Intuitionistic Fuzzy Set Relative Closeness Degrees3.7.2 Inclusion Comparison Probability of Intuitionistic Fuzzy Set Relative Closeness Degrees and Properties3.7.3 Determination Method of Optimal Membership Degrees for Inclusion Comparison Probabilities of Intuitionistic Fuzzy Set Relative Closeness Degrees3.7.4 Intuitionistic Fuzzy Set Multiattribute Decision Making Process Based on Fraction Mathematical Programming and Real Example Analysis3.8 Linear Programming Method for Intuitionistic Fuzzy Set Multiattribute Decision Making with Unknown Weights3.8.1 Linear Programming Model for Computing Intuitionistic Fuzzy Set Relative Closeness Degrees3.8.2 Process of Linear Programming Method for Intuitionistic Fuzzy Set Multiattribute Decision Making and Real Example AnalysisChapter 4 Interval-Valued Intuitionistic Fuzzy Set Multiattribute Decision Making Methods4.1 Introduction4.2 Interval-Valued Intuitionistic Fuzzy Sets and Operations4.3 Interval-Valued Intuitionistic Fuzzy Set Generalized Hybrid Weighted Aggregation Method for Interval-Valued Intuitionistic Fuzzy Set Multiattribute Decision Making4.3.1 Interval-Valued Intuitionistic Fuzzy Set Generalized Hybrid Weighted Aggregation Operators4.3.2 Interval-Valued Intuitionistic Fuzzy Set Multiattribute Decision Making Process Based on Interval-Valued Intuitionistic Fuzzy Set Generalized Hybrid Weighted Aggregation Operators and Real Example Analysis4.4 Interval-Valued Intuitionistic Fuzzy Set Continuous Hybrid Weighted Aggregation Operators and Interval-Valued Intuitionistic Fuzzy Set Multiattribute Decision Making Methods4.4.1 Continuous Ordered Weighted Aggregation Operators4.4.2 Interval-Valued Intuitionistic Fuzzy Set Continuous Hybrid Weighted Aggregation Operators4.4.3 Interval-Valued Intuitionistic Fuzzy Set Multiattribute Decision Making Methods Based on Interval-Valued Intuitionistic Fuzzy Set Continuous Hybrid Weighted Aggregation Operators and Real Example Analysis4.5 Mathematical Programming Method for Interval-Valued Intuitionistic Fuzzy Set Multiattribute Decision Making with Unknown Weights4.5.1 Mathematical Programming Model for Computing Intuitionistic Fuzzy Set Relative Closeness Degrees4.5.2 Other Forms of Mathematical Programming Model for Computing Intuitionistic Fuzzy Set Relative Closeness Degrees4.5.3 Mathematical Programming Method for Interval-Valued Intuitionistic Fuzzy Set Multiattribute Decision Making and Real Example AnalysisChapter 5 Multiattribute Decision Making Methods Using Intuitionistic Fuzzy Numbers5.1 Introduction5.2 Ranking Method of Intuitionistic Fuzzy Numbers Based on Weighted Value-Indices and Weighted Ambiguity-Indices5.2.1 Concepts of Value-Indices and Ambiguity-Indices for Intuitionistic Fuzzy Numbers5.2.2 Value-Indices and Ambiguity-Indices for Triangular Intuitionistic Fuzzy Numbers5.2.3 Value-Indices and Ambiguity-Indices for Trapezoidal Intuitionistic Fuzzy Numbers5.2.4 Ranking Method of Intuitionistic Fuzzy Numbers Based on Weighted Value-Indices and Weighted Ambiguity-Indices and Properties5.3 Multiattribute Decision Making Method Based on Weighted Value-Indices and Weighted Ambiguity-Indices Using Intuitionistic Fuzzy Numbers5.3.1 Formal Representation of Multiattribute Decision Making Problems Using Intuitionistic Fuzzy Numbers5.3.2 Multiattribute Decision Making Process Based on Weighted Value-Indices and Weighted Ambiguity-Indices of Intuitionistic Fuzzy Numbers and Real Example AnalysisChapter 6 Intuitionistic Fuzzy Set Multiattribute Group Decision Making Methods6.1 Introduction6.2 TOPSIS for Intuitionistic Fuzzy Set Multiattribute Group Decision Making with Both Ideal Solutions and Weights Known6.2.1 Formal Representation of Multiattribute Group Decision Making Problems with Both Weights and Attribute Ratings Expressed by Intuitionistic Fuzzy Sets6.2.2 TOPSIS Principle for Intuitionistic Fuzzy Set Multiattribute Group Decision Making and Real Example Analysis6.3 LINMAP for Intuitionistic Fuzzy Set Multiattribute Group Decision Making with Both Ideal Solutions and Weights Unknown6.3.1 Intuitionistic Fuzzy Set Multiattribute Group Decision Making Problems6.3.2 Group Consistency and Inconsistency Measure Indices6.3.3 LINMAP Model of Intuitionistic Fuzzy Set Multiattribute Group Decision Making6.3.4 LINMAP Solving Process for Intuitionistic Fuzzy Set Multiattribute Group Decision Making and Real Example Analysis6.3.5 Other Forms of LINMAP Model for Intuitionistic Fuzzy Set Multiattribute Group Decision MakingChapter 7 Intuitionistic Fuzzy Set Matrix Games and Linear or Nonlinear Programming Methods7.1 Introduction7.2 Formal Representation of Intuitionistic Fuzzy Set Matrix Games and Concepts of Solutions7.3 Existence and Properties of Solutions of Intuitionistic Fuzzy Set Matrix Games and Auxiliary Programming Models7.4 Linear or Nonlinear Programming Methods of Intuitionistic Fuzzy Set Matrix Games and Real Example Analysis7.4.1 Nonlinear Programming Models of Intuitionistic Fuzzy Set Matrix Games7.4.2 Linear or Nonlinear Programming Solving Process of Intuitionistic Fuzzy Set Matrix Games and Real Example AnalysisChapter 8 Interval-Valued Intuitionistic Fuzzy Set Matrix Games and Linear or Nonlinear Programming Methods8.1 Introduction8.2 Formal Representation of Interval-Valued Intuitionistic Fuzzy Set Matrix Games and Concepts of Solutions8.3 Multiobjective Programming Models of Interval-Valued Intuitionistic Fuzzy Set Matrix Games and Properties of Solutions8.3.1 Concepts of Interval-Valued Objective Function Optimization and Transformation Forms8.3.2 Multiobjective Programming Models of Interval-Valued Intuitionistic Fuzzy Set Matrix Games and Transformation Forms8.3.3 Relations between Solutions of Interval-Valued Intuitionistic Fuzzy Set Matrix Games and Noninferior Solutions of Corresponding Multiobjective Programming8.4 Linear or Nonlinear Programming Methods of Interval-Valued Intuitionistic Fuzzy Set Matrix Games and Real Example Analysis8.4.1 Nonlinear Programming Models of Interval-Valued Intuitionistic Fuzzy Set Matrix Games8.4.2 Linear or Nonlinear Programming Solving Process for Interval-Valued Intuitionistic Fuzzy Set Matrix Games and Real Example AnalysisChapter 9 Matrix Games with Payoffs of Intuitionistic Fuzzy Numbers and Solution Methods9.1 Introduction9.2 Formal Representation of Matrix Games with Payoffs of Intuitionistic Fuzzy Numbers and Concepts of Solutions9.3 Cut-Set Based Method of Matrix Games with Payoffs of Intuitionistic Fuzzy Numbers9.3.1 Mathematical Programming Models of Matrix Games Based on Cut-Sets of Intuitionistic Fuzzy Numbers9.3.2 Cut-Set Based Solving Process for Matrix Games with Payoffs of Intuitionistic Fuzzy Numbers and Real Example Analysis9.4 Solving Method Based on Weighted Mean-Areas of Membership and Nonmembership Degrees for Matrix Games with Payoffs of Intuitionistic Fuzzy Numbers9.4.1 Weighted Mean-Areas of Membership and Nonmembership Degrees for Intuitionistic Fuzzy Numbers9.4.2 Mathematical Programming Models of Matrix Games Based on Weighted Mean-Areas of Membership and Nonmembership Degrees for Intuitionistic Fuzzy Numbers9.4.3 Solving Process Based on Weighted Mean-Areas of Membership and Nonmembership Degrees for Matrix Games with Payoffs of Intuitionistic Fuzzy Numbers and Real Example Analysis9.5 Lexicographic Method of Matrix Games with Payoffs of Intuitionistic Fuzzy Numbers Based on Weighted Value-Indices and Weighted Ambiguity-Indices9.5.1 Multiobjective Programming Models of Matrix Games Based on Weighted Value-Indices and Weighted Ambiguity-Indices of Intuitionistic Fuzzy Numbers9.5.2 Lexicographic Solving Process for Matrix Games with Payoffs of Intuitionistic Fuzzy Numbers and Real Example Analysis

Über Autor(innen)

Deng-Feng Li was born in 1965. He received both his B.Sc. and M.Sc. degrees in Applied Mathematics from the National University of Defense Technology, Changsha, China, in 1987 and 1990, respectively, and completed his Ph.D. in System Science and Optimization at the Dalian University of Technology, Dalian, China, in 1995. From 2003 to 2004, he was a visiting scholar at the School of Management, University of Manchester Institute of Science and Technology, UK.
He is currently a “Minjiang Scholar” Distinguished Professor and an Assistant Dean of the School of Management, Fuzhou University, China. He has published more than 200 international journal papers and four monographs and is the coauthor of one monograph and three textbooks. His current research interests include fuzzy decision analysis, group decision-making, fuzzy game theory, fuzzy sets and system analysis, fuzzy optimization and differential games in economic management. He has been recognized with eighteen scientific achievement awards.