The aim of this paper is to introduce the concept of fuzzy generalized closed set and study its properties. Secondly the concept of infra L-fuzzy topological space is introduced. Making use of fuzzy -closed sets and fuzzy -generalized closed sets the concept of fuzzy -generalized continuous mapping is introduced. Lastly the concept of fuzzy generalized closed irresolute map in L-fuzzy topologic...

A preliminary analysis of the posbist reliability of typical system structures was provided by Cai et al. [Fuzzy Sets and Systems 42: 145–172 (1991) and Microelectronics and Reliability 35(1): 49–56 (1995)]. In this paper, we provide a detailed analysis of the posbist reliability of k-out-of-n:G system structures. Expressions of the posbist reliability of k-out-of-n:G system is developed. It is...

In this paper, direct proofs of some properties of new classes of fuzzy sets called fuzzy strongly g∗-closed sets and fuzzy g∗∗-closed sets are introduced. Examples are presented showing that some generalizations can not be obtained. MSC: 54A40 • 54A05

We study removable sets for Newtonian Sobolev functions in metric measure spaces satisfying the usual (local) assumptions of a doubling and Poincaré inequality.In particular, when restricted to Euclidean spaces, closed set $E \subset \mathbb{R}^n$ with zero Lebesgue is shown be $W^{1,p}(\mathbb{R}^n \setminus E)$ if only $\mathbb{R}^n E$ supports $p$-Poincaré inequality as space. When $p>1$, th...

A nonzero fuzzy open set () of a fuzzy topological space is said to be fuzzy minimal open (resp. fuzzy maximal open) set if any fuzzy open set which is contained (resp. contains) in is either or itself (resp. either or itself). In this note, a new class of sets called fuzzy minimal open sets and fuzzy maximal open sets in fuzzy topological spaces are introduced and studied which are subclasses ...