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Intuitionistec fuzzy sets measures and integrals –atanassov vasilev tsvetkov 2013

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Описание

Contents

Preface 9

Chapter 1. On the concept of intuitionistic fuzzy sets 11

1.1. Definition of the concept of intuitionistic fuzzy set 11

1.2. Basic operations and relations over IFSs 13

1.3. IF implications and negations over IFSs 16

1.4. Definitions and properties of some

new IF subtractions 22

1.5. Geometrical interpretations of an IFS 24

1.6. On IF-interpretation of interval data 29

1.7. “Necessity” and “possibility” operators 30

1.8. Topological operators over IFSs 33

1.9. Extended topological operators 36

1.10. Weight-center operator over an IFS 40

1.11. Other extended topological operators over an IFS 41

1.12. On the first group of the extended modal

operators over IFSs 44

1.13. Operator Xatb;C;d;ej over IFSs 58

1.14. Partial extension of the extended modal

operators over IFSs 60

1.15. IFSs of certain level 62

1.16. Level type of operators over IFSs 66

1.17. Other types of modal operators over IFSs 70

1.18. Cartesian products over IFSs 80

1.19. Index matrix 84

1.20. Intuitionistic fuzzy relations 90

Chapter 2. Norms, distances, similarity measures

and applications 95

2.1. Standard IF-norms 95

2.2. Cantor’s IF-norms 100

2.3. Metrics and another point of view

on the notion intuitionistic fuzzy sets 101

2.3.1. Metrics, norms and subnorms 101

2.3.2. On a way for introducing metric in Cartesian product

of metric spaces 105

2.3.3. Metrics on 108

2.3.4. Metrics on Rn and Cn 109

2.3.5. Examples 110

2.3.6. Distances and similarity measures between

mtuitionistic fuzzy sets 111

2.3.7. Distances and pseudodistances over IFS(E') 112

2.3.8. Lebesgue integrals on finite sets 114

2.3.9. Distances between continuous IFSs 128

2.3.10. A modified Pompeiu-Hausdorff distance between

intuitionistic fuzzy sets 131

2.4. Similarity measures, induced by distances and pseudodistances

over IFS(E) 137

2.4.1. Generating new distances over IFS(JF) 140

2.4.2. Generating uncountably many similarity measures over

IFS(E) ” ' 144

2.5. A new distance on intuitionistic fuzzy sets 145

2.6. Metric introduction of IFS 148

2.6.1. Conforming, absolute conforming norms on M2 and their

properties 153

2.6.2. Alain result for dtp-IFS(E) 162

2.7. Application to the reassessment of expert

evaluation in the case of intuitionistic fuzzines 176

2.8. On introducing similar operators 184

2.9. Intuitionistic fuzzy histograms 192

Chapter 3. Intuitionistic fuzzy integrals 199

3.1. Intuitionistic fuzzy integrals

generated from extended Sugeno

and Choquet integrals 199

3.1.1. Basic ideas of generalized measure theory 199

3.1.2. Some properties of the extended Sugeno integrals 200

3.1.3. Intuitionistic fuzzy integrals and various

integral topological operators 208

3.1.4. Extended Choquet integral 216

3.1.5. Monotone measures defined

on intuitionistic fuzzy cr-algebras 225

3.1.6. Intuitionistic fuzzy Choquet integrals on finite sets 231

3.2. Some new relations between intuitionistic fuzzy sets 235

3.3. Repeated Choquet integral 243

3.3.1. The double repeated Choquet integral on finite sets 279

3.3.2. Intuitionistic fuzzy integrals

generated by Choquet integral 281

3.3.3. Intuitionistic fuzzy numbers 290