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...

The concept of a fuzzy topology on a fuzzy set was introduced in [Fuzzy Set Syst. 45 (1992) 103]. The aim of this paper is to introduce fuzzy semicontinuity and fuzzy semiseparation axioms in this new situation and validity of some characterization of these concepts have been examined. Also, we define a fuzzy generalized semiopen set and introduce fuzzy separation axioms by using this concept. ...

The sequential $p$-convergence in a fuzzy metric space, in the sense of George and Veeramani, was introduced by D. Mihet as a weaker concept than convergence. Here we introduce a stronger concept called $s$-convergence, and we characterize those fuzzy metric spaces in which convergent sequences are $s$-convergent. In such a case $M$ is called an $s$-fuzzy metric. If $(N_M,ast)$ is a fuzzy metri...

a. csaszar introduced and extensively studied the notion of generalized opensets. following csazar, we introduce a new notion hyperconnected. we study some specicproperties about connected and hyperconnected in generalized topological spaces. finally, wecharacterize the connected component in generalized topological spaces.

Using fuzzy filters in the sense of P. Eklund and W. Gähler [2], it turns out that fuzzy preuniform convergence spaces introduced in [11] form a strong topological universe in which fuzzy topological spaces as well as fuzzy (quasi) uniform spaces can be studied. Thus, better tools such as the existence of natural function spaces, the existence of one-point extensions (and consequently, the here...

Double crises of chaotic oscillators in the presence of fuzzy uncertainty are studied by means of the fuzzy generalized cellmappingmethod.A fuzzy chaotic attractor is characterized by its global topology and membership distribution. A fuzzy crisis implies a simultaneous sudden change both in the topology of the chaotic attractor and in its membership distribution. It happenswhen a fuzzy chaotic...

Keywords: Double fuzzy topology Double neighborhood systems Double fuzzy preproximity Double fuzzy closure space a b s t r a c t In this paper, we introduce the notions of double neighborhood systems and double fuzzy preproximity in double fuzzy topological spaces. We used double neighborhoods to study the initial structure of double fuzzy topological spaces, and the joins between them and the ...

One of the most helpful fuzzy set extensions for dealing with information uncertainties is an n th power root set. In light this, in this paper, we define n,m set, which a new type extension and introduce their relationship n-rung orthopair n,m-rung There symmetry between values membershi...