Rough set theory can be generalized by induced topology through equivalence relations. Motivated the work of generalization rough via topology, concept and properties $ \tau-\mathfrak{K} $-fuzzy open (closed) sets are proposed. Considering sets, we have obtained lower upper approximations also proved their properties. represented as $-open \alpha level sets. The fuzzy on basis binary relation c...

Abstract Convexity is a deeply studied concept since it very useful in many fields of mathematics, like optimization. When we deal with imprecision, the convexity required as well and some important applications can be found fuzzy optimization, particular sets. In this paper have extended notion for interval-valued sets order to able cover wider area imprecision. We show its interesting propert...

Many applications of fuzzy set theory require defuzzification and ranking approaches based on alpha level sets because exact membership functions may not always be available. In this article, we have assumed that exact membership functions can be approximated using piecewise linear functions based on alpha level sets and derived two analytical formulas to meet such a requirement. The two formul...

In this paper, we introduce the sets of bounded, convergent and null series and the set of sequences of bounded variation of fuzzy numbers with the level sets. We investigate the relationships between these sets and their classical forms and give some properties including definitions, lemmas and various kind of fuzzy metric spaces. Furthermore, we study some of their properties like completenes...