In this paper, the Urysohn, completely Hausdorff and completely regular axioms in $L$-topological spaces are generalized to $L$-fuzzy topological spaces. Each $L$-fuzzy topological space can be regarded to be Urysohn, completely Hausdorff and completely regular tosome degree. Some properties of them are investigated. The relations among them and $T_2$ in $L$-fuzzy topological spaces are discussed.

In this paper, we define the notion of (dual) multi-fuzzy normedspaces and describe some properties of them. We then investigate Ulam-Hyers stability of Jensen's functional equation for mappings from linear spaces into  multi-fuzzy normed spaces. We establish an asymptotic behavior of the Jensen equation in the framework of multi-fuzzy normed spaces.

The present paper introduces the notion of the complete fuzzy norm on a linear space. And, some relations between the fuzzy completeness and ordinary completeness on a linear space is considered, moreover a new form of fuzzy compact spaces, namely b-compact spaces and b-closed spaces are introduced. Some characterizations of their properties are obtained.

In this paper, we introduce a new class of implicit functions and also common property (E.A) in modified intuitionistic fuzzy metric spaces and utilize the same to prove some common fixed point theorems in modified intuitionistic fuzzy metric spaces besides discussing related results and illustrative examples. We are not aware of any paper dealing with such implicit functions in modified intuit...

In this paper, the notion of fuzzy semicompactness degrees isintroduced in $L$-fuzzy topological spaces by means of theimplication operation of $L$. Characterizations of fuzzysemicompactness degrees in $L$-fuzzy topological spaces  areobtained, and some properties of fuzzy semicompactness degrees areresearched.

the aim of the present paper is to define and study (ic)$lm$-fuzzytopological spaces, a generalization of (weakly) induced $lm$-fuzzytopological spaces. we discuss the basic properties of(ic)$lm$-fuzzy topological spaces, and introduce the notions ofinterior (ic)-fication and exterior (ic)-fication of $lm$-fuzzytopologies and prove that {bf iclm-ftop} (the category of(ic)$lm$-fuzzy topological ...

i.p.s. hypergroups are canonical hypergroups such that$[forall(a,x),a+xni x]longrightarrow[a+x=x].$i.p.s. hypergroups were investigated in [1], [2], [3], [4] and it was proved thatif the order is less than 9, they are strongly canonical (see [13]). in this paperwe obtain the sequences of fuzzy sets and of join spaces determined (see [8])by all i.p.s. hypergroups of order seven. for the meaning ...

The aim of this paper is to introduce fuzzy ($e$, almost) $e^{*}$-regular spaces in $check{S}$ostak's fuzzy topological spaces. Using the $r$-fuzzy $e$-closed sets, we define $r$-($r$-$theta$-, $r$-$etheta$-) $e$-cluster points and their properties. Moreover, we investigate the relations among $r$-($r$-$theta$-, $r$-$etheta$-) $e$-cluster points, $r$-fuzzy ($e$, almost) $e^{*}$-regular spaces a...

The purpose of this paper is to introduce and study the concepts of fuzzy $e$-open set, fuzzy $e$-continuity and fuzzy $e$-compactness in intuitionistic fuzzy topological spaces. After giving the fundamental concepts of intuitionistic fuzzy sets and intuitionistic fuzzy topological spaces, we present intuitionistic fuzzy $e$-open sets and intuitionistic fuzzy $e$-continuity and other results re...

K. T. Atanassov, ?Intuitionistic fuzzy sets?, Fuzzy Sets and Systems, 20(1986), 87-96. S. S. Benchalli and Jenifer J. Karnel, ?On fuzzy b open sets in fuzzy topological spaces?, J. Comp. & Math. Sci, 1(2010), 127 – 134. C. L. Chang, ?Fuzzy topological spaces?, J. Math. Anal. Appl, 24(1968), 182-190. D. Coker, ?An introduction to intuitionistic fuzzy topological spaces?, Fuzzy Sets and Systems, ...