The cut sets, decomposition theorems and representation theorems on intuitionistic fuzzy sets and interval valued fuzzy sets

2010 ◽  
Vol 54 (1) ◽  
pp. 91-110 ◽  
Author(s):  
XueHai Yuan ◽  
HongXing Li ◽  
KaiBiao Sun
Keyword(s):  
Fuzzy Sets ◽  
Intuitionistic Fuzzy Sets ◽  
Representation Theorems ◽  
Intuitionistic Fuzzy ◽  
Decomposition Theorems ◽  
Interval Valued

Interval Cut-Set of Generalized Interval-Valued Intuitionistic Fuzzy Sets

2012 ◽  
Vol 2 (3) ◽  
pp. 35-50 ◽  
Author(s):  
Amal Kumar Adak ◽  
Monoranjan Bhowmik ◽  
Madhumangal Pal
Keyword(s):  
Fuzzy Sets ◽  
Intuitionistic Fuzzy Sets ◽  
Basic Theory ◽  
Intuitionistic Fuzzy ◽  
Different Types ◽  
Cut Set ◽  
Decomposition Theorems ◽  
Interval Valued

In this paper, some different types of interval cut-set of genaralized interval-valued intuitionistic fuzzy sets (GIVIFSs), complement of these cut-sets are introduced. Some properties of those cut-set of GIVIFSs are investigated. Also three decomposition theorems of GIVIFSs are obtained based on the different cut-set of GIVIFSs. These works can also be used in setting up the basic theory of GIVIFSs.

Decomposition Theorem of Generalized Interval-Valued Intuitionistic Fuzzy Sets

2014 ◽  
pp. 174-180
Author(s):  
Amal Kumar Adak ◽  
Monoranjan Bhowmik ◽  
Madhumangal Pal
Keyword(s):  
Fuzzy Sets ◽  
Decomposition Theorem ◽  
Intuitionistic Fuzzy Sets ◽  
Fundamental Theory ◽  
Intuitionistic Fuzzy ◽  
Decomposition Theorems ◽  
Interval Valued

In this chapter, the authors establish decomposition theorems of Generalized Interval-Valued Intuitionistic Fuzzy Sets (GIVIFS) by use of cut sets of generalized interval-valued intuitionistic fuzzy sets. First, new definitions of eight kinds of cut sets generalized interval-valued intuitionistic fuzzy sets are introduced. Second, based on these new cut sets, the decomposition generalized interval-valued intuitionistic fuzzy sets are established. The authors show that each kind of cut sets corresponds to two kinds of decomposition theorems. These results provide a fundamental theory for the research of generalized interval-valued intuitionistic fuzzy sets.

Width-based distance measures on interval-valued intuitionistic fuzzy sets

2021 ◽  
pp. 1-13
Author(s):  
Xi Li ◽  
Chunfeng Suo ◽  
Yongming Li
Keyword(s):  
Pattern Recognition ◽  
Fuzzy Sets ◽  
Medical Diagnosis ◽  
Intuitionistic Fuzzy Sets ◽  
Distance Measures ◽  
Intuitionistic Fuzzy ◽  
Interval Valued ◽  
Dissimilarity Function ◽  
Better Than

An essential topic of interval-valued intuitionistic fuzzy sets(IVIFSs) is distance measures. In this paper, we introduce a new kind of distance measures on IVIFSs. The novelty of our method lies in that we consider the width of intervals so that the uncertainty of outputs is strongly associated with the uncertainty of inputs. In addition, better than the distance measures given by predecessors, we define a new quaternary function on IVIFSs to construct the above-mentioned distance measures, which called interval-valued intuitionistic fuzzy dissimilarity function. Two specific methods for building the quaternary functions are proposed. Moreover, we also analyzed the degradation of the distance measures in this paper, and show that our measures can perfectly cover the measures on a simpler set. Finally, we provide illustrative examples in pattern recognition and medical diagnosis problems to confirm the effectiveness and advantages of the proposed distance measures.

On a Relationship Between Fuzzy Measures and AIFS

2016 ◽  
Vol 24 (06) ◽  
pp. 847-858 ◽  
Author(s):  
VicenÇ Torra ◽  
Yasuo Narukawa ◽  
Ronald R. Yager
Keyword(s):  
Fuzzy Sets ◽  
Intuitionistic Fuzzy Sets ◽  
Fuzzy Measures ◽  
Intuitionistic Fuzzy ◽  
Atanassov Intuitionistic Fuzzy Sets ◽  
Interval Valued

The literature discusses several extensions of fuzzy sets. AIFS, IVFS, HFS, type-2 fuzzy sets are some of them. Interval valued fuzzy sets is one of the extensions where the membership is not a single value but an interval. Atanassov Intuitionistic fuzzy sets, for short AIFS, are defined in terms of two values for each element: membership and non-membership. In this paper we discuss AIFS and their relationship with fuzzy measures. The discussion permits us to define counter AIFS (cIFS) and discretionary AIFS (dIFS). They are extensions of fuzzy sets that are based on fuzzy measures.

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