Decision and game theory in management with intuitionistic fuzzy sets
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Bibliographic Information
Decision and game theory in management with intuitionistic fuzzy sets
（Studies in fuzziness and soft computing, 308）
Springer, c2014
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Includes bibliographical references
Description and Table of Contents
Description
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.
Table of Contents
Chapter 1 Intuitionistic Fuzzy Set Theories
1.1 Introduction
1.2 Intuitionistic Fuzzy Sets and Operations
1.3 Intuitionistic Fuzzy Set Distances and Similarity Degrees
1.3.1 Definition of Similarity Degrees between Intuitionistic Fuzzy Sets
1.3.2 Definition of Distances between Intuitionistic Fuzzy Sets
1.4 Representation Theorem of Intuitionistic Fuzzy Sets
1.5 Extension Principle of Intuitionistic Fuzzy Sets and Operations
1.5.1 Extension Principle of Intuitionistic Fuzzy Sets
1.5.2 Operations over Intuitionistic Fuzzy Sets
1.6 Definitions of Intuitionistic Fuzzy Numbers and Algebraic Operations
1.6.1 Trapezoidal Intuitionistic Fuzzy Numbers and Algebraic Operations
1.6.2 Triangular Intuitionistic Fuzzy Numbers and Algebraic Operations
Chapter 2 Intuitionistic Fuzzy Set Aggregation Operators and Multiattribute Decision Making Methods
2.1 Introduction
2.2 Intuitionistic Fuzzy Set Aggregation Operators and Properties
2.2.1 Intuitionistic Fuzzy Set Weighted Aggregation Operators
2.2.2 Intuitionistic Fuzzy Set Hybrid Weighted Aggregation Operators
2.2.3 Intuitionistic Fuzzy Set Generalized Hybrid Weighted Aggregation Operators
2.3 Intuitionistic Fuzzy Set Generalized Hybrid Weighted Aggregation Method for Intuitionistic Fuzzy Set Multiattribute Decision Making
2.3.1 Formal Representation of Intuitionistic Fuzzy Set Multiattribute Decision Making Problems
2.3.2 Intuitionistic Fuzzy Set Multiattribute Decision Making Process Based on Intuitionistic Fuzzy Set Generalized Hybrid Weighted Aggregation Operators and Real Example Analysis
Chapter 3 Intuitionistic Fuzzy Set Multiattribute Decision Making Methods
3.1 Introduction
3.2 Linear Weighted Average Method for Multiattribute Decision Making with Both Weights and Attribute Ratings Expressed by Intuitionistic Fuzzy Sets
3.2.1 Linear Weighted Average Model of Intuitionistic Fuzzy Set Multiattribute Decision Making
3.2.2 Sensitivity Analysis of Linear Weighted Average Method for Intuitionistic Fuzzy Set Multiattribute Decision Making
3.2.3 Process of Linear Weighted Average Method for Intuitionistic Fuzzy Set Multiattribute Decision Making and Real Example Analysis
3.3 TOPSIS for Intuitionistic Fuzzy Set Multiattribute Decision Making with Both Ideal Solutions and Weights Known
3.3.1 Basic Principle of TOPSIS
3.3.2 Intuitionistic Fuzzy Set TOPSIS Principle and Real Example Analysis
3.4 Optimum Seeking Method for Intuitionistic Fuzzy Set Multiattribute Decision Making with Both Ideal Solutions and Weights Known
3.4.1 Optimum Seeking Principle for Intuitionistic Fuzzy Set Multiattribute Decision Making
3.4.2 Process of Optimum Seeking Method for Intuitionistic Fuzzy Set Multiattribute Decision Making and Real Example Analysis
3.5 Linear Programming Method for Multiattribute Decision Making with Both Weights and Attribute Ratings Expressed by Intuitionistic Fuzzy Sets
3.5.1 Allocation Method of Hesitancy Degrees
3.5.2 Linear Programming Models and Method for Computing Intuitionistic Fuzzy Set Comprehensive Evaluations
3.5.3 Relative Closeness Degree Method of Intuitionistic Fuzzy Set Comprehensive Evaluations and Real Example Analysis
3.6 LINMAP for Intuitionistic Fuzzy Set Multiattribute Decision Making with Both Ideal Solutions and Weights Unknown
3.6.1 Determination Methods of Membership and Nonmembership Degrees of Intuitionistic Fuzzy Sets
3.6.2 Consistency and Inconsistency Measure Methods
3.6.3 LINMAP Models for Intuitionistic Fuzzy Set Multiattribute Decision Making
3.6.4 LINMAP Process for Intuitionistic Fuzzy Set Multiattribute Decision Making and Real Example Analysis
3.7 Fraction Mathematical Programming Method for Intuitionistic Fuzzy Set Multiattribute Decision Making with Unknown Weights
3.7.1 Fraction Mathematical Programming Model for Computing Intuitionistic Fuzzy Set Relative Closeness Degrees
3.7.2 Inclusion Comparison Probability of Intuitionistic Fuzzy Set Relative Closeness Degrees and Properties
3.7.3 Determination Method of Optimal Membership Degrees for Inclusion Comparison Probabilities of Intuitionistic Fuzzy Set Relative Closeness Degrees
3.7.4 Intuitionistic Fuzzy Set Multiattribute Decision Making Process Based on Fraction Mathematical Programming and Real Example Analysis
3.8 Linear Programming Method for Intuitionistic Fuzzy Set Multiattribute Decision Making with Unknown Weights
3.8.1 Linear Programming Model for Computing Intuitionistic Fuzzy Set Relative Closeness Degrees
3.8.2 Process of Linear Programming Method for Intuitionistic Fuzzy Set Multiattribute Decision Making and Real Example Analysis
Chapter 4 Interval-Valued Intuitionistic Fuzzy Set Multiattribute Decision Making Methods
4.1 Introduction
4.2 Interval-Valued Intuitionistic Fuzzy Sets and Operations
4.3 Interval-Valued Intuitionistic Fuzzy Set Generalized Hybrid Weighted Aggregation Method for Interval-Valued Intuitionistic Fuzzy Set Multiattribute Decision Making
4.3.1 Interval-Valued Intuitionistic Fuzzy Set Generalized Hybrid Weighted Aggregation Operators
4.3.2 Interval-Valued Intuitionistic Fuzzy Set Multiattribute Decision Making Process Based on Interval-Valued Intuitionistic Fuzzy Set Generalized Hybrid Weighted Aggregation Operators and Real Example Analysis
4.4 Interval-Valued Intuitionistic Fuzzy Set Continuous Hybrid Weighted Aggregation Operators and Interval-Valued Intuitionistic Fuzzy Set Multiattribute Decision Making Methods
4.4.1 Continuous Ordered Weighted Aggregation Operators
4.4.2 Interval-Valued Intuitionistic Fuzzy Set Continuous Hybrid Weighted Aggregation Operators
4.4.3 Interval-Valued Intuitionistic Fuzzy Set Multiattribute Decision Making Methods Based on Interval-Valued Intuitionistic Fuzzy Set Continuous Hybrid Weighted Aggregation Operators and Real Example Analysis
4.5 Mathematical Programming Method for Interval-Valued Intuitionistic Fuzzy Set Multiattribute Decision Making with Unknown Weights
4.5.1 Mathematical Programming Model for Computing Intuitionistic Fuzzy Set Relative Closeness Degrees
4.5.2 Other Forms of Mathematical Programming Model for Computing Intuitionistic Fuzzy Set Relative Closeness Degrees
4.5.3 Mathematical Programming Method for Interval-Valued Intuitionistic Fuzzy Set Multiattribute Decision Making and Real Example Analysis
Chapter 5 Multiattribute Decision Making Methods Using Intuitionistic Fuzzy Numbers
5.1 Introduction
5.2 Ranking Method of Intuitionistic Fuzzy Numbers Based on Weighted Value-Indices and Weighted Ambiguity-Indices
5.2.1 Concepts of Value-Indices and Ambiguity-Indices for Intuitionistic Fuzzy Numbers
5.2.2 Value-Indices and Ambiguity-Indices for Triangular Intuitionistic Fuzzy Numbers
5.2.3 Value-Indices and Ambiguity-Indices for Trapezoidal Intuitionistic Fuzzy Numbers
5.2.4 Ranking Method of Intuitionistic Fuzzy Numbers Based on Weighted Value-Indices and Weighted Ambiguity-Indices and Properties
5.3 Multiattribute Decision Making Method Based on Weighted Value-Indices and Weighted Ambiguity-Indices Using Intuitionistic Fuzzy Numbers
5.3.1 Formal Representation of Multiattribute Decision Making Problems Using Intuitionistic Fuzzy Numbers
5.3.2 Multiattribute Decision Making Process Based on Weighted Value-Indices and Weighted Ambiguity-Indices of Intuitionistic Fuzzy Numbers and Real Example Analysis
Chapter 6 Intuitionistic Fuzzy Set Multiattribute Group Decision Making Methods
6.1 Introduction
6.2 TOPSIS for Intuitionistic Fuzzy Set Multiattribute Group Decision Making with Both Ideal Solutions and Weights Known
6.2.1 Formal Representation of Multiattribute Group Decision Making Problems with Both Weights and Attribute Ratings Expressed by Intuitionistic Fuzzy Sets
6.2.2 TOPSIS Principle for Intuitionistic Fuzzy Set Multiattribute Group Decision Making and Real Example Analysis
6.3 LINMAP for Intuitionistic Fuzzy Set Multiattribute Group Decision Making with Both Ideal Solutions and Weights Unknown
6.3.1 Intuitionistic Fuzzy Set Multiattribute Group Decision Making Problems
6.3.2 Group Consistency and Inconsistency Measure Indices
6.3.3 LINMAP Model of Intuitionistic Fuzzy Set Multiattribute Group Decision Making
6.3.4 LINMAP Solving Process for Intuitionistic Fuzzy Set Multiattribute Group Decision Making and Real Example Analysis
6.3.5 Other Forms of LINMAP Model for Intuitionistic Fuzzy Set Multiattribute Group Decision Making
Chapter 7 Intuitionistic Fuzzy Set Matrix Games and Linear or Nonlinear Programming Methods
7.1 Introduction
7.2 Formal Representation of Intuitionistic Fuzzy Set Matrix Games and Concepts of Solutions
7.3 Existence and Properties of Solutions of Intuitionistic Fuzzy Set Matrix Games and Auxiliary Programming Models
7.4 Linear or Nonlinear Programming Methods of Intuitionistic Fuzzy Set Matrix Games and Real Example Analysis
7.4.1 Nonlinear Programming Models of Intuitionistic Fuzzy Set Matrix Games
7.4.2 Linear or Nonlinear Programming Solving Process of Intuitionistic Fuzzy Set Matrix Games and Real Example Analysis
Chapter 8 Interval-Valued Intuitionistic Fuzzy Set Matrix Games and Linear or Nonlinear Programming Methods
8.1 Introduction
8.2 Formal Representation of Interval-Valued Intuitionistic Fuzzy Set Matrix Games and Concepts of Solutions
8.3 Multiobjective Programming Models of Interval-Valued Intuitionistic Fuzzy Set Matrix Games and Properties of Solutions
8.3.1 Concepts of Interval-Valued Objective Function Optimization and Transformation Forms
8.3.2 Multiobjective Programming Models of Interval-Valued Intuitionistic Fuzzy Set Matrix Games and Transformation Forms
8.3.3 Relations between Solutions of Interval-Valued Intuitionistic Fuzzy Set Matrix Games and Noninferior Solutions of Corresponding Multiobjective Programming
8.4 Linear or Nonlinear Programming Methods of Interval-Valued Intuitionistic Fuzzy Set Matrix Games and Real Example Analysis
8.4.1 Nonlinear Programming Models of Interval-Valued Intuitionistic Fuzzy Set Matrix Games
8.4.2 Linear or Nonlinear Programming Solving Process for Interval-Valued Intuitionistic Fuzzy Set Matrix Games and Real Example Analysis
Chapter 9 Matrix Games with Payoffs of Intuitionistic Fuzzy Numbers and Solution Methods
9.1 Introduction
9.2 Formal Representation of Matrix Games with Payoffs of Intuitionistic Fuzzy Numbers and Concepts of Solutions
9.3 Cut-Set Based Method of Matrix Games with Payoffs of Intuitionistic Fuzzy Numbers
9.3.1 Mathematical Programming Models of Matrix Games Based on Cut-Sets of Intuitionistic Fuzzy Numbers
9.3.2 Cut-Set Based Solving Process for Matrix Games with Payoffs of Intuitionistic Fuzzy Numbers and Real Example Analysis
9.4 Solving Method Based on Weighted Mean-Areas of Membership and Nonmembership Degrees for Matrix Games with Payoffs of Intuitionistic Fuzzy Numbers
9.4.1 Weighted Mean-Areas of Membership and Nonmembership Degrees for Intuitionistic Fuzzy Numbers
9.4.2 Mathematical Programming Models of Matrix Games Based on Weighted Mean-Areas of Membership and Nonmembership Degrees for Intuitionistic Fuzzy Numbers
9.4.3 Solving Process Based on Weighted Mean-Areas of Membership and Nonmembership Degrees for Matrix Games with Payoffs of Intuitionistic Fuzzy Numbers and Real Example Analysis
9.5 Lexicographic Method of Matrix Games with Payoffs of Intuitionistic Fuzzy Numbers Based on Weighted Value-Indices and Weighted Ambiguity-Indices
9.5.1 Multiobjective Programming Models of Matrix Games Based on Weighted Value-Indices and Weighted Ambiguity-Indices of Intuitionistic Fuzzy Numbers
9.5.2 Lexicographic Solving Process for Matrix Games with Payoffs of Intuitionistic Fuzzy Numbers and Real Example Analysis
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