Obtaining a weaker condition that preserves some inspired topological properties is always desirable. As result, we introduce the concept of infra-fuzzy topology, which subset family degrades fuzzy topology by omitting closedness under arbitrary unions. Fundamental spaces are investigated, including open and closed sets, interior closure operators, boundary set. It not possible to expect latter...

ـــــ In [25], we introduce the notion of r-fuzzy neighborhood filters in smooth topological spaces in sense of Gähler [10], and used it to define and study separation axioms , = , , . Here we continue our study of the axioms of separation in smooth topological spaces. Therefore, we introduce the notion of r-fuzzy neighborhood filter at a set. Then by using this notion we define and study separ...

In 1970, Levine 1 introduced the notion of generalized closed sets in topological spaces as a generalization of closed sets. Since then, many concepts related to generalized closed sets were defined and investigated. In 1997, Balasubramanian and Sundaram 2 introduced the concepts of generalized closed sets in fuzzy setting. Also, they studied various generalizations fuzzy continues mappings. Re...

In this paper, we introduce intuitionistic fuzzy semi pre open (closed) sets and intuitionistic fuzzy semi pre continuous mappings in intuitionistic fuzzy topological spaces in Sostak’s sense. Also we investigate the characteristic properties of these sets and mappings.

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 ...

We explore a notion of fuzzy T -neighbourhood spaces, for any continuous triangular norm T , and we present on this notion a uni6ed treatment. Our theory, on one hand, generalizes the theory of Lowen (Fuzzy Sets and Systems 7 (1982) 65) from T =Min to arbitrary T , which has been the progenitor of this work, and on the other hand it is strongly related to the theory of L-neighbourhoods of H; oh...

In 1965, Zadeh [30] introduced a concept of a fuzzy set as the generalization of a crisp set. Also, in 1971, he introduced a fuzzy relation naturally, as a generalization of a crisp relation in [31]. Nel [27] introduced the notion of a topological universe which implies concrete quasitopos [1]. Every topological universe satisfies all the properties of a topos except one condition on the subobj...

The aim of this paper is to study L-fuzzy uniformizable spaces. A new kind of topological fuzzy remote neighborhood system is defined and used for investigating the relationship between L-fuzzy co-topology and L-fuzzy (quasi-)uniformity. It is showed that this fuzzy remote neighborhood system is different from that in [23] when U is an Lfuzzy quasi-uniformity and they will be coincident when U ...