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  kn .................................... 108
2.3.4 Metrics on  n and  n .............................. 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 2 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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