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E-raamat: Decision and Game Theory in Management With Intuitionistic Fuzzy Sets

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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.

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From the book reviews:

The main goal of the book under review is to establish theories and methods of both decision and game analysis in management using intuitionistic fuzzy sets (IFS). the presented results are very useful for theoreticians and practitioners of decision-making. (Krzysztof Piasecki, zbMATH, Vol. 1291, 2014)

1 Intuitionistic Fuzzy Set Theories
1(46)
1.1 Introduction
1(1)
1.2 Intuitionistic Fuzzy Sets and Operations
2(12)
1.2.1 Concepts of Intuitionistic Fuzzy Sets and Notations
2(7)
1.2.2 Operations Over Intuitionistic Fuzzy Sets
9(3)
1.2.3 Concepts of Cut Sets for Intuitionistic Fuzzy Sets and Properties
12(2)
1.3 Distances and Similarity Degrees Between Intuitionistic Fuzzy Sets
14(10)
1.3.1 Definition of Similarity Degrees Between Intuitionistic Fuzzy Sets
14(5)
1.3.2 Definition of Distances Between Intuitionistic Fuzzy Sets
19(5)
1.4 Representation Theorems of Intuitionistic Fuzzy Sets
24(4)
1.5 Extension Principles of Intuitionistic Fuzzy Sets and Algebraic Operations
28(7)
1.5.1 Extension Principles of Intuitionistic Fuzzy Sets
28(3)
1.5.2 Algebraic Operations over Intuitionistic Fuzzy Sets
31(4)
1.6 Definitions of Intuitionistic Fuzzy Numbers and Algebraic Operations
35(12)
1.6.1 Trapezoidal Intuitionistic Fuzzy Numbers and Algebraic Operations
36(4)
1.6.2 Triangular Intuitionistic Fuzzy Numbers and Algebraic Operations
40(5)
References
45(2)
2 Intuitionistic Fuzzy Aggregation Operators and Multiattribute Decision-Making Methods with Intuitionistic Fuzzy Sets
47(28)
2.1 Introduction
47(1)
2.2 Intuitionistic Fuzzy Aggregation Operators and Properties
48(14)
2.2.1 The Intuitionistic Fuzzy Weighted Averaging Operator
48(2)
2.2.2 The Intuitionistic Fuzzy Hybrid Weighted Averaging Operator
50(6)
2.2.3 The Intuitionistic Fuzzy Generalized Hybrid Weighted Averaging Operator
56(6)
2.3 The Intuitionistic Fuzzy Generalized Hybrid Weighted Averaging Method of Multiattribute Decision-Making with Intuitionistic Fuzzy Sets
62(13)
2.3.1 Formal Representation of Multiattribute Decision-Making with Intuitionistic Fuzzy Sets
62(1)
2.3.2 Process of the Intuitionistic Fuzzy Generalized Hybrid Weighted Averaging Method for Multiattribute Decision-Making with Intuitionistic Fuzzy Sets and Real Example Analysis
63(10)
References
73(2)
3 Multiattribute Decision-Making Methods with Intuitionistic Fuzzy Sets
75(78)
3.1 Introduction
75(1)
3.2 The Linear Weighted Averaging Method of Multiattribute Decision-Making with Weights and Ratings Expressed by Intuitionistic Fuzzy Sets
76(11)
3.2.1 Linear Weighted Averaging Models of Multiattribute Decision-Making with Intuitionistic Fuzzy Sets
77(1)
3.2.2 Sensitivity Analysis of the Linear Weighted Averaging Method for Multiattribute Decision-Making with Intuitionistic Fuzzy Sets
78(3)
3.2.3 Process of the Linear Weighted Averaging Method for Multiattribute Decision-Making with Intuitionistic Fuzzy Sets and Real Example Analysis
81(6)
3.3 TOPSIS for Multiattribute Decision-Making with Intuitionistic Fuzzy Positive and Negative Ideal-Solutions and Weights Known
87(6)
3.3.1 Principle and Process of TOPSIS
87(2)
3.3.2 TOPSIS Principle of Multiattribute Decision-Making with Intuitionistic Fuzzy Sets and Real Example Analysis
89(4)
3.4 The Optimum Seeking Method of Multiattribute Decision-Making with Intuitionistic Fuzzy Positive and Negative Ideal-Solutions and Weights Known
93(4)
3.4.1 Optimum Seeking Principle of Multiattribute Decision-Making with Intuitionistic Fuzzy Sets
93(2)
3.4.2 Process of the Optimum Seeking Method for Multiattribute Decision-Making with Intuitionistic Fuzzy Sets and Real Example Analysis
95(2)
3.5 The Linear Programming Method of Multiattribute Decision-Making with Weights and Attribute Ratings Expressed by Intuitionistic Fuzzy Sets
97(12)
3.5.1 Allocation Methods of Hesitancy Degrees
97(2)
3.5.2 Linear Programming Models and Method for Computing Comprehensive Evaluations with Intuitionistic Fuzzy Sets
99(5)
3.5.3 The Relative Closeness Degree Method of Comprehensive Evaluations with Intuitionistic Fuzzy Sets and Real Example Analysis
104(5)
3.6 LINMAP for Multiattribute Decision-Making with an Intuitionistic Fuzzy Positive Ideal-Solution and Weights Unknown
109(14)
3.6.1 Determination Methods of Membership and Nonmembership Degrees of Intuitionistic Fuzzy Sets
110(2)
3.6.2 Consistency and Inconsistency Measure Methods
112(3)
3.6.3 LINMAP Models of Multiattribute Decision-Making with Intuitionistic Fuzzy Sets
115(2)
3.6.4 Process of LINMAP for Multiattribute Decision-Making with Intuitionistic Fuzzy Sets and Real Example Analysis
117(6)
3.7 The Fraction Mathematical Programming Method of Intuitionistic Fuzzy Multiattribute Decision-Making with Intuitionistic Fuzzy Weights Unknown
123(21)
3.7.1 Fraction Mathematical Programming Models for Computing Relative Closeness Degrees with Intuitionistic Fuzzy Sets
124(3)
3.7.2 Inclusion Comparison Probabilities of Relative Closeness Degrees with Intuitionistic Fuzzy Sets and Properties
127(8)
3.7.3 The Determination Method of Optimal Membership Degrees for Inclusion Comparison Probabilities of Relative Closeness Degrees with Intuitionistic Fuzzy Sets
135(4)
3.7.4 Process of the Fraction Mathematical Programming Method for Multiattribute Decision-Making with Intuitionistic Fuzzy Sets and Real Example Analysis
139(5)
3.8 The Linear Programming Method of Intuitionistic Fuzzy Multiattribute Decision-Making with Intuitionistic Fuzzy Weights Unknown
144(9)
3.8.1 Linear Programming Models of Computing Relative Closeness Degrees with Intuitionistic Fuzzy Sets
144(2)
3.8.2 Process of the Linear Programming Method for Multiattribute Decision-Making with Intuitionistic Fuzzy Sets and Real Example Analysis
146(4)
References
150(3)
4 Multiattribute Decision-Making Methods with Interval-Valued Intuitionistic Fuzzy Sets
153(74)
4.1 Introduction
153(1)
4.2 Interval-Valued Intuitionistic Fuzzy Sets and Operations
154(10)
4.3 The Interval-Valued Intuitionistic Fuzzy Generalized Hybrid Weighted Averaging Method of Multiattribute Decision-Making with Interval-Valued Intuitionistic Fuzzy Sets
164(25)
4.3.1 The Interval-Valued Intuitionistic Fuzzy Generalized Hybrid Weighted Averaging Operator
164(14)
4.3.2 Process of the Interval-Valued Intuitionistic Fuzzy Generalized Hybrid Weighted Averaging Method for Multiattribute Decision-Making with Interval-Valued Intuitionistic Fuzzy Sets and Real Example Analysis
178(11)
4.4 The Interval-Valued Intuitionistic Fuzzy Continuous Hybrid Weighted Averaging Operator and Multiattribute Decision-Making Method with Interval-Valued Intuitionistic Fuzzy Sets
189(14)
4.4.1 The Continuous Ordered Weighted Averaging Operator
189(3)
4.4.2 The Interval-Valued Intuitionistic Fuzzy Continuous Hybrid Weighted Averaging Operator
192(7)
4.4.3 Process of the Interval-Valued Intuitionistic Fuzzy Continuous Hybrid Weighted Averaging Method for Multiattribute Decision-Making with Interval-Valued Intuitionistic Fuzzy Sets and Real Example Analysis
199(4)
4.5 TOPSIS-Based Mathematical Programming Methods of Interval-Valued Intuitionistic Fuzzy Multiattribute Decision-Making with Weights Unknown
203(24)
4.5.1 Nonlinear Programming Models for Computing Relative Closeness Degrees with Intuitionistic Fuzzy Sets
204(7)
4.5.2 Variations of Mathematical Programming Models for Computing Relative Closeness Degrees with Intuitionistic Fuzzy Sets
211(5)
4.5.3 Process of TOPSIS-Based Mathematical Programming Methods for Multiattribute Decision-Making with Interval-Valued Intuitionistic Fuzzy Sets and Real Example Analysis
216(8)
References
224(3)
5 Multiattribute Decision-Making Methods with Intuitionistic Fuzzy Numbers
227(26)
5.1 Introduction
227(1)
5.2 The Weighted Value and Ambiguity-Based Ranking Method of Intuitionistic Fuzzy Numbers
227(18)
5.2.1 Concepts of Values and Ambiguities for Intuitionistic Fuzzy Numbers
227(4)
5.2.2 Values and Ambiguities of Triangular Intuitionistic Fuzzy Numbers
231(2)
5.2.3 Values and Ambiguities of Trapezoidal Intuitionistic Fuzzy Numbers
233(3)
5.2.4 Weighted Values and Ambiguities and Ranking Method of Intuitionistic Fuzzy Numbers
236(5)
5.2.5 Properties of the Weighted Value and Ambiguity-Based Ranking Method of Intuitionistic Fuzzy Numbers
241(4)
5.3 The Weighted Value and Ambiguity-Based Multiattribute Decision-Making Method with Intuitionistic Fuzzy Numbers
245(8)
5.3.1 Formal Representation of Multiattribute Decision-Making with Intuitionistic Fuzzy Numbers
245(1)
5.3.2 Process of the Weighted Value and Ambiguity-Based Multiattribute Decision-Making Method with Intuitionistic Fuzzy Numbers and Real Example Analysis
246(6)
References
252(1)
6 Multiattribute Group Decision-Making Methods with Intuitionistic Fuzzy Sets
253(38)
6.1 Introduction
253(1)
6.2 TOPSIS for Multiattribute Group Decision-Making with Intuitionistic Fuzzy Positive and Negative Ideal-Solutions and Weights Known
254(9)
6.2.1 Formal Representation of Multiattribute Group Decision-Making with Attribute Ratings and Weights Expressed by Intuitionistic Fuzzy Sets
254(1)
6.2.2 TOPSIS Principle of Multiattribute Group Decision-Making with Intuitionistic Fuzzy Sets and Real Example Analysis
255(8)
6.3 LINMAP for Multiattribute Group Decision-Making with an Intuitionistic Fuzzy Positive Ideal-Solution and Weights Unknown
263(28)
6.3.1 Multiattribute Group Decision-Making Problems with Intuitionistic Fuzzy Sets
263(3)
6.3.2 Group Consistency and Inconsistency Measure Indices
266(3)
6.3.3 LINMAP Models of Multiattribute Group Decision-Making with Intuitionistic Fuzzy Sets
269(4)
6.3.4 Process of LINMAP for Multiattribute Group Decision-Making with Intuitionistic Fuzzy Sets and Real Example Analysis
273(13)
6.3.5 Variations of LINMAP Models for Multiattribute Group Decision-Making with Intuitionistic Fuzzy Sets
286(3)
References
289(2)
7 Matrix Games with Payoffs of Intuitionistic Fuzzy Sets and Linear and Nonlinear Programming Methods
291(30)
7.1 Introduction
291(1)
7.2 Formal Representation of Matrix Games with Intuitionistic Fuzzy Sets and Solutions' Concepts
292(6)
7.3 Existence of Solutions of Matrix Games with Payoffs of Intuitionistic Fuzzy Sets and Auxiliary Mathematical Programming Models
298(16)
7.4 Linear and Nonlinear Programming Methods of Matrix Games with Payoffs of Intuitionistic Fuzzy Sets and Real Example Analysis
314(7)
7.4.1 Nonlinear Programming Models of Matrix Games with Payoffs of Intuitionistic Fuzzy Sets
314(2)
7.4.2 Process of Linear and Nonlinear Programming Methods for Matrix Games with Payoffs of Intuitionistic Fuzzy Sets
316(4)
References
320(1)
8 Matrix Games with Payoffs of Interval-Valued Intuitionistic Fuzzy Sets and Linear and Nonlinear Programming Methods
321(40)
8.1 Introduction
321(1)
8.2 Formal Representation of Matrix Games with Payoffs of Interval-Valued Intuitionistic Fuzzy Sets and Solutions' Concepts
322(9)
8.3 Multiobjective Programming Models of Matrix Games with Payoffs of Interval-Valued Intuitionistic Fuzzy Sets and Properties of Solutions
331(22)
8.3.1 Concepts of Interval-Valued Objective Optimization and Transformation Forms
331(1)
8.3.2 Multiobjective Programming Models of Matrix Games with Payoffs of Interval-Valued Intuitionistic Fuzzy Sets and Transformation Forms
332(12)
8.3.3 Relations Between Solutions of Matrix Games with Payoffs of Interval-Valued Intuitionistic Fuzzy Sets and Noninferior Solutions of Corresponding Multiobjective Programming
344(9)
8.4 Linear and Nonlinear Programming Methods of Matrix Games with Payoffs of Interval-Valued Intuitionistic Fuzzy Sets and Real Example Analysis
353(8)
8.4.1 Nonlinear Programming Models of Matrix Games with Payoffs of Interval-Valued Intuitionistic Fuzzy Sets
353(2)
8.4.2 Process of Linear and Nonlinear Programming Methods for Matrix Games with Payoffs of Interval-Valued Intuitionistic Fuzzy Sets
355(4)
References
359(2)
9 Matrix Games with Payoffs of Trapezoidal Intuitionistic Fuzzy Numbers and Solution Methods
361(42)
9.1 Introduction
361(1)
9.2 Formal Representation of Matrix Games with Payoffs of Trapezoidal Intuitionistic Fuzzy Numbers and Solutions' Concepts
362(2)
9.3 The Cut-Set-Based Method of Matrix Games with Payoffs of Trapezoidal Intuitionistic Fuzzy Numbers
364(14)
9.3.1 Cut-Set-Based Mathematical Programming Models of Matrix Games with Payoffs of Trapezoidal Intuitionistic Fuzzy Numbers
365(9)
9.3.2 Process of the Cut-Set-Based Method for Matrix Games with Payoffs of Trapezoidal Intuitionistic Fuzzy Numbers and Real Example Analysis
374(4)
9.4 The Weighted Mean-Area-Based Method of Matrix Games with Payoffs of Trapezoidal Intuitionistic Fuzzy Numbers
378(12)
9.4.1 Weighted Mean-Areas of Trapezoidal Intuitionistic Fuzzy Numbers with Respect to Membership and Nonmembership Functions
378(6)
9.4.2 Weighted Mean-Area-Based Mathematical Programming Models of Matrix Games with Payoffs of Trapezoidal Intuitionistic Fuzzy Numbers
384(4)
9.4.3 Process of the Weighted Mean-Area-Based Method for Matrix Games with Payoffs of Trapezoidal Intuitionistic Fuzzy Numbers and Real Example Analysis
388(2)
9.5 The Weighted Value and Ambiguity-Based Lexicographic Method of Matrix Games with Payoffs of Trapezoidal Intuitionistic Fuzzy Numbers
390(13)
9.5.1 Weighted Value and Ambiguity-Based Multiobjective Programming Models of Matrix Games with Payoffs of Trapezoidal Intuitionistic Fuzzy Numbers
390(4)
9.5.2 Process of the Weighted Value and Ambiguity-Based Lexicographic Method for Matrix Games with Payoffs of Trapezoidal Intuitionistic Fuzzy Numbers and Real Example Analysis
394(8)
References
402(1)
10 Matrix Games with Goals of Intuitionistic Fuzzy Sets and Linear Programming Method
403(22)
10.1 Introduction
403(1)
10.2 Formal Representation of Matrix Games with Goals of Intuitionistic Fuzzy Sets and Solutions' Concepts
404(2)
10.2.1 Concepts and Representation of Goals with Intuitionistic Fuzzy Sets
404(1)
10.2.2 Concepts of Solutions of Matrix Games with Goals of Intuitionistic Fuzzy Sets
405(1)
10.3 Auxiliary Linear Programming Models of Matrix Games with Goals of Intuitionistic Fuzzy Sets
406(15)
10.3.1 Linear Forms of Goals with Intuitionistic Fuzzy Sets
406(5)
10.3.2 Linear Programming Models of Matrix Games with Goals of Intuitionistic Fuzzy Sets and Properties
411(10)
10.4 Process of the Linear Programming Method for Matrix Games with Goals of Intuitionistic Fuzzy Sets and Real Example Analysis
421(4)
References
424(1)
11 Bi-matrix Games with Payoffs of Intuitionistic Fuzzy Sets and Bilinear Programming Method
425(22)
11.1 Introduction
425(1)
11.2 The Defuzzification Ranking Method of Intuitionistic Fuzzy Sets and Bi-matrix Games
426(6)
11.2.1 The Defuzzification Function of Intuitionistic Fuzzy Sets and Properties
426(3)
11.2.2 Bi-matrix Games and Auxiliary Bilinear Programming Models
429(3)
11.3 Bi-matrix Games with Payoffs of Intuitionistic Fuzzy Sets and Bilinear Programming Models
432(7)
11.3.1 Concepts of Solutions of Bi-matrix Games with Payoffs of Intuitionistic Fuzzy Set
432(4)
11.3.2 Auxiliary Bilinear Programming Models of Bi-matrix Games with Payoffs of Intuitionistic Fuzzy Sets
436(3)
11.4 Process of the Bilinear Programming Method for Bi-matrix Games with Payoffs of Intuitionistic Fuzzy Sets and Real Example Analysis
439(8)
References
445(2)
Biography 447
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.
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