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E-raamat: Uncertain Fuzzy Preference Relations and Their Applications

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On the basis of fuzzy sets and some of their relevant generalizations, this book systematically presents the fundamental principles and applications of group decision making under different scenarios of preference relations. By using intuitionistic knowledge as the field of discourse, this work investigates by utilizing innovative research means the fundamental principles and methods of group decision making with various different intuitionistic preferences: Mathematical reasoning is employed to study the consistency of group decision making; Methods of fusing information are applied to look at the aggregation of multiple preferences; Techniques of soft computing and optimization are utilized to search for satisfactory decision alternatives. Each chapter follows the following structurally clear format of presentation: literature review, development of basic theory, verification and reasoning of principles , construction of models and computational schemes, and numerical examples, which cover such areas as technology, enterprise competitiveness, selection of airlines, experts decision making in weather-sensitive enterprises, etc. In terms of theoretical principles, this book can be used as a reference for researchers in the areas of management science, information science, systems engineering, operations research, and other relevant fields. It can also be employed as textbook for upper level undergraduate students and graduate students. In terms of applications, this book will be a good companion for all those decision makers in government, business, and technology areas.

This book explores group decision-making in various scenarios of preference relations, studying the consistency of group decision making using mathematical reasoning, probing decision alternatives using soft computing and optimization and more.

Arvustused

From the reviews:

This research monograph is a comprehensive and well-structured treatise on uncertain fuzzy preference relations along with their applications. Each chapter contains illustrative numeric examples demonstrating the main features of the algorithms. The book offers a fully updated, focused material, which will be of significant value to researchers and practitioners in fuzzy decision-making. (Witold Pedrycz, Zentralblatt MATH, Vol. 1263, 2013)

1 Introduction
1(4)
1.1 The Connotation of Uncertainty
1(1)
1.2 The Research Scope of Uncertain Judgment Knowledge
2(1)
1.3 A Historical Evolution of Uncertainty Fuzzy Sets Theory
2(1)
1.4 Research Contents of Uncertain Preference Relations
3(2)
2 Relevant Theories of Reciprocal Preference and Fuzzy Preference Relations
5(14)
2.1 Preference Relations and Their Scales
5(3)
2.2 Properties of Preference Relations
8(3)
2.2.1 Properties of MPRs
8(1)
2.2.2 Properties of Fuzzy Preference Relations (FPRs)
9(2)
2.3 Priority Method of Fuzzy Preference Relations with Incomplete Information
11(7)
2.3.1 A Least Square Model for Collective Preference Relations with Incomplete Information
12(5)
2.3.2 Numerical Example
17(1)
2.4 Conclusions
18(1)
3 Complementary Preference Relations of Interval Fuzzy Numbers
19(26)
3.1 Basic Concepts
19(2)
3.2 Properties and Priorities of IFNCPRs with Additive Consistency
21(6)
3.2.1 Properties of IFNCPRs with Additive Consistency
21(4)
3.2.2 A Numerical Example
25(2)
3.3 Properties and Priorities of IFNCPRs with Multiplicative Consistency
27(7)
3.3.1 Properties of IFNCPRs with Multiplicative Consistency
27(5)
3.3.2 Priorities of IFNCPRs with Multiplicative Consistency
32(1)
3.3.3 A Numerical Example
33(1)
3.4 Group Decision Making Based on Complementary Judgment Matrices of Incomplete Interval Fuzzy Numbers
34(5)
3.4.1 Least Squares Priority Model of Complementary Preference Relations of Incomplete Interval Fuzzy Numbers
34(4)
3.4.2 A Numerical Example
38(1)
3.5 Logarithmic Least Squares Priority Model of Collective IFNCPRs
39(5)
3.5.1 Logarithmic Least Squares Priority Model of Collective IFNCPRs
39(3)
3.5.2 A Numerical Example
42(2)
3.6 Conclusions
44(1)
4 Complementary Preference Relations of Triangular Fuzzy Numbers
45(30)
4.1 Basic Concepts
46(1)
4.2 Properties and Priority of Additively Consistent Complementary Preference Relations of Triangular Fuzzy Numbers
47(10)
4.2.1 A Comparative Method of Two Triangular Fuzzy Numbers
47(1)
4.2.2 Additively Consistent Complementary Preference Relations of Triangular Fuzzy Numbers
48(6)
4.2.3 Aggregations of Complementary Preference Relations of Triangular Fuzzy Numbers
54(2)
4.2.4 A Numerical Example
56(1)
4.3 Properties and Priority of Multiplicatively Consistent Complementary Preference Relations of Triangular Fuzzy Numbers
57(9)
4.3.1 Properties of Multiplicatively Consistent Complementary Preference Relations of Triangular Fuzzy Numbers
57(7)
4.3.2 Priorities of TFNCPRs with Multiplicative Consistency
64(1)
4.3.3 A Numerical Example
65(1)
4.4 Group Decision Making Based on TFNCPRs
66(8)
4.4.1 Least Squares Priority Model of Incomplete TFNCPRs
66(6)
4.4.2 A Numerical Example
72(2)
4.5 Conclusions
74(1)
5 Two-Tuple Linguistic Preference Relations
75(18)
5.1 The Basic Concept of 2-Tuple Linguistic Term Set
76(3)
5.2 Two-Tuple Linguistic Preference Relations
79(6)
5.3 Relationship between FPRs and 2-Tuple LPRs
85(3)
5.4 A Numerical Example
88(2)
5.5 Conclusions
90(3)
6 Preference Relations of Trapezoidal Fuzzy Numbers
93(10)
6.1 Relationship between Preference Relations of Trapezoidal Fuzzy Numbers and 2-Tuple LPRs
93(5)
6.2 Aggregation of Preference Relations of Trapezoidal Fuzzy Numbers
98(2)
6.3 A Numerical Example
100(2)
6.4 Conclusions
102(1)
7 Group Decision Making for Different Fuzzy Preference Relations
103(18)
7.1 Group Decision Making Based on 2-Tuple Linguistic LPRs with Different Fuzzy Preferences
103(12)
7.1.1 Definitions
103(2)
7.1.2 Relationship between Uncertainty Preference Relations and 2-Tuple LPRs
105(7)
7.1.3 Aggregation of Different Preference Relations
112(1)
7.1.4 A Numerical Example
113(2)
7.2 Group Decision Making for Different Preference Relations
115(5)
7.2.1 Steps for Aggregating Different Fuzzy Preference Relations
115(2)
7.2.2 A Numerical Example
117(3)
7.3 Conclusions
120(1)
8 Intuitionistic Fuzzy Preference Relations
121(74)
8.1 Basic Concepts
122(2)
8.1.1 Intuitionistic Fuzzy Sets
122(1)
8.1.2 Comparison of Intuitionistic Fuzzy Values
123(1)
8.2 Intuitionistic Fuzzy Preference Relations
124(3)
8.2.1 Intuitionistic Fuzzy Preference Relations
124(1)
8.2.2 Relationship between IFPRs and the IFNCPRs
125(2)
8.3 Additive Consistency of IFPRs
127(11)
8.3.1 Additive Consistency of IFPRs
127(7)
8.3.2 Numerical Examples
134(4)
8.4 Multiplicatively Consistent IFPRs
138(6)
8.5 Least Squared Priority Models of IFPRs
144(7)
8.5.1 Priority Model of Consistent IFPRs
144(3)
8.5.2 Priority Model of Multiplicatively Consistent IFPRs
147(1)
8.5.3 Priority Model of Inconsistent IFPRs
147(2)
8.5.4 Priority Algorithm of IFPRs
149(1)
8.5.5 Numerical Examples
149(2)
8.6 Goal Programming Priority Model of IFPRs
151(8)
8.6.1 Normalization of Intervals
151(1)
8.6.2 Goal Programming Priority Model of Inconsistent IFPRs
152(1)
8.6.3 Goal Programming Priority of Collectively Inconsistent IFPRs
153(3)
8.6.4 Numerical Examples
156(3)
8.7 Optimal Priority Models of Additively Consistent IFPRs
159(16)
8.7.1 Additively Consistent IFPRs
160(2)
8.7.2 Priority of Collective Additively Consistent IFPRs
162(2)
8.7.3 The Priority of an Individual Inconsistent IFPR
164(2)
8.7.4 Priority of Collective Inconsistent IFPRs
166(1)
8.7.5 Numerical Examples
167(6)
8.7.6 IFPR Models Applied to Select Meteorologically-Sensitive Industries
173(2)
8.8 Optimization Models of Incomplete IFPRs
175(4)
8.8.1 Optimization Models of Incomplete IFPRs
175(2)
8.8.2 A Numerical Example
177(2)
8.9 Group Decision Making Model Based on IFPRs
179(8)
8.9.1 Operation Laws of Intuitionistic Fuzzy Values
179(1)
8.9.2 Group Decision Making Model of IFPRs
180(5)
8.9.3 A Numerical Example
185(2)
8.10 Consensus Measures of Group IFPRs
187(4)
8.10.1 Consensus Measure of IFPRs
187(3)
8.10.2 A Numerical Example
190(1)
8.11 Conclusion
191(4)
References 195(10)
Index 205