Topic
Vague set
About: Vague set is a research topic. Over the lifetime, 490 publications have been published within this topic receiving 71075 citations.
Papers published on a yearly basis
Papers
Book•
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1 Aug 1996
TL;DR: A separation theorem for convex fuzzy sets is proved without requiring that the fuzzy sets be disjoint.
Abstract: A fuzzy set is a class of objects with a continuum of grades of membership. Such a set is characterized by a membership (characteristic) function which assigns to each object a grade of membership ranging between zero and one. The notions of inclusion, union, intersection, complement, relation, convexity, etc., are extended to such sets, and various properties of these notions in the context of fuzzy sets are established. In particular, a separation theorem for convex fuzzy sets is proved without requiring that the fuzzy sets be disjoint.
53,228 citations
TL;DR: Various properties are proved, which are connected to the operations and relations over sets, and with modal and topological operators, defined over the set of IFS's.
15,756 citations
Journal Article•
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TL;DR: A vague set is a set of objects, each of which has a grade of membership whose value is a continuous subinterval of according to the inequality of the following type:
Abstract: A vague set is a set of objects, each of which has a grade of membership whose value is a continuous subinterval of
1,787 citations
TL;DR: This paper recapitulates the definition given by Atanassov (1983) of intuitionistic fuzzy sets as well as the definition of vague sets given by Gau and Byehrer (1993) and sees that both definitions coincide.
942 citations
TL;DR: It is shown by examples that the similarity measures proposed by Chen do not fit well in some cases, and a set of modified measures is proposed that turned out to be more reasonable in more general cases than the previous one.
365 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2025 | 1 |
| 2024 | 7 |
| 2023 | 2 |
| 2022 | 11 |
| 2021 | 8 |
| 2020 | 16 |