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ОбложкаAtanassov K.T. Intuitionistic fuzzy sets, measures and integrals / K.T.Atanassov, P.M.Vassilev, R.T.Tsvetkov. - Sofia: Marin Drinov academic publishing house, 2013. - 315 p.: ill. - (Bulgarian academic monographs; 12). - Bibliogr.: p.301-311. - Ind.: p.313-314. - ISBN 978-954-322-709-9
Шифр: (И/И16-А90) 02
 

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Оглавление / 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 Xa,blC,d,e,f 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 fig.1kn .................................... 108
     2.3.4  Metrics on fig.2n and fig.3n .............................. 109
     2.3.5  Examples .......................................... 110
     2.3.6  Distances and similarity measures between
            intuitionistic 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(E) .............. 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 fig.22 and 
            their properties .................................. 153
     2.6.2  Main result for dφ-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
            σ-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

Bibliography .................................................. 300
Index ......................................................... 313

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