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We introduce a new class of fuzzy open sets called fuzzy $bigwedge_e$ sets which includes the class of fuzzy $e$-open sets. We also define a weaker form of fuzzy $bigwedge_e$ sets termed as fuzzy locally $bigwedge_e$ sets. By means of these new sets, we present the notions of fuzzy $bigwedge_e$ continuity and fuzzy locally $bigwedge_e$ continuity which are weaker than fuzzy $e$-continuity and f...

In this paper, we define and study fuzzy generalized α-closed sets and r-open sets of a given L-fuzzy topological space and prime element r ∈ P (L) and coprime element α ∈ M(L). The concept of L-fuzzy ropen sets was introduced in [10], and it was proved that all r-open sets for L-fuzzy topological space form a new L-fuzzy topology, which is called stratiform L-fuzzy topology. Making use of the ...

Fuzzy relations are able to model vagueness, in the sense that they provide the degree to which two objects are related to each other. However, they cannot model uncertainty: there is no means to attribute reliability information to the membership degrees. Intuitionistic fuzzy sets, as de1ned by Atanassov (Instuitionistic Fuzzy Sets, Physica-Verlag, Heidelberg, New York, 1999), give us a way to...

<abstract><p>Many real-world decision-making issues frequently involve competing sets of criteria, uncertainty, and inaccurate information. Some these require the involvement a group decision-makers, where it is necessary to reduce various available individual preferences single collective preference. To enhance effectiveness multi-criteria decisions, popular technique that makes pr...

Most of the researches in the domain of fuzzy number comparisons serve the fuzzy number ordering purpose. For making a comparison between two fuzzy numbers, beyond the determination of their order, it is needed to derive the magnitude of their order. In line with this idea, the concept of inequality is no longer crisp however it becomes fuzzy in the sense of representing partial belonging or de...

In this paper we look at two categories, the category F of fuzzy subsets and a quotient category F=M of fuzzy sets. The category F=M is an extension of the category of sets, and the standard constructions in fuzzy set theory arise naturally within this category.

Fuzziness is not a priori an obvious concept and demands some explanation. “Fuzziness” is what Black (NF 1937) calls “vagueness” when he distinguishes it from “generality” and from “ambiguity.” Generalizing refers to the application of a symbol to a multiplicity of objects in the field of reference, ambiguity to the association of a finite number of alternative meanings having the same phonetic...

Orthopairs (pairs of disjoint sets) have points in common with many approaches to managing vaguness/uncertainty such as fuzzy sets, rough soft etc. Indeed, they are successfully employed address partial knowledge, consensus, and borderline cases. One the generalized versions orthopairs is intuitionistic sets which a well-known theory for researchers interested set theory. To extend area applica...

In many applications, multiple correlation and partial correlation for three or more fuzzy sets are very important, but Chiang and Lin (1999, Fuzzy Sets and Systems 102: 221–226) do not solve this problem. Here, we propose a method to calculate the multiple correlation and partial correlation for fuzzy data, by adopting the concepts from the multivariate correlation model. In order to fit into ...