Categorical foundations, fuzzy topology, fuzzy measures, and mathematical applications of fuzzy sets

1991 ◽  
Vol 42 (1) ◽  
pp. 1-2
Author(s):  
Erich Peter Klement
Keyword(s):  
Fuzzy Sets ◽  
Fuzzy Topology ◽  
Fuzzy Measures ◽  
Mathematical Applications

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.

Some results on fuzzy topology on fuzzy sets

1993 ◽  
Vol 56 (3) ◽  
pp. 331-336 ◽  
Author(s):  
A.K. Chaudhuri ◽  
P. Das
Keyword(s):  
Fuzzy Sets ◽  
Fuzzy Topology

Fuzzy Dynamic Groups

2012 ◽  
pp. 41-60 ◽  
Author(s):  
José-Domingo Mora
Keyword(s):  
Fuzzy Sets ◽  
Group Size ◽  
Cognitive Processing ◽  
Statistical Models ◽  
Fuzzy Measures ◽  
Individual Consumption ◽  
Group Size And Composition

Television audiences have been shown to be a mixture of lone individuals and groups of viewers, with groups contributing at least 50% of total ratings. Viewing with others also makes the experience more enjoyable and has important effects on cognitive processing of programs and advertisements. A major problem for researchers and managers is that groups of viewers are dynamic entities difficult to define or measure. This study frames groups of television viewers as fuzzy sets and presents fuzzy measures of group size and composition. The effects of these characteristics on individual consumption of television are assessed using statistical models, which incorporate the arithmetic forms of the proposed measures.

scholarly journals Multi-argument fuzzy measures on lattices of fuzzy sets

2013 ◽  
Vol 53 ◽  
pp. 27-39 ◽  
Author(s):  
Elena E. Castiñeira ◽  
Tomasa Calvo ◽  
Susana Cubillo
Keyword(s):  
Fuzzy Sets ◽  
Fuzzy Measures

A Similarity Measure between Fuzzy Sets

2012 ◽  
Vol 229-231 ◽  
pp. 2663-2666
Author(s):  
Gao Zheng
Keyword(s):  
Fuzzy Logic ◽  
Fuzzy Sets ◽  
Similarity Measure ◽  
Fuzzy Measures ◽  
Axiomatic Definition ◽  
Computation Formula ◽  
Fuzzy Logic Theory

The similarity measure is one of the most useful fuzzy measures in fuzzy logic theory. In this paper, we propose a new similarity measure between fuzzy sets. As a preparation, we first choose an axiomatic definition for the similarity measure. Then, according to the chosen axiomatic definition, we propose a new computation formula. Finally, we give two examples to validate its performance. The results show that the new similarity measure is rational for fuzzy sets.

Suitable interval-valued intuitionistic fuzzy topological spaces

2021 ◽  
pp. 1-11
Author(s):  
O.R. Sayed ◽  
N.H. Sayed ◽  
Gui-Xiu Chen
Keyword(s):  
Fuzzy Sets ◽  
Intuitionistic Fuzzy Sets ◽  
Topological Spaces ◽  
Fuzzy Topology ◽  
Intuitionistic Fuzzy ◽  
Set Operations ◽  
The Family ◽  
Fuzzy Topological Spaces ◽  
Interval Valued

In the present paper, a characterization of the intuitionistic fuzzy sets, the interval-valued intuitionistic fuzzy sets and their set-operations are given. By making use of these characterizations, the relationships between the interval-valued intuitionistic fuzzy topology and four fuzzy topologies associated to it are studied. For this reason, some subclasses of the family of interval-valued intuitionistic fuzzy topologies on a set which we call pre-suitable and suitable are introduced. Furthermore, the concepts of homeomorphism functions and compactness in the framework of interval-valued intuitionistic fuzzy topological spaces are introduced and studied.

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