The structure of fuzzy topological spaces based on WFIalgebras is considered. The notions of WFI-fuzzy topological spaces and WFI-fuzzy continuous mappings are introduced, and several properties are investigated. A relation between WFI-homomorphism and WFI-fuzzy continuous mapping is given.

This paper deals with a new class of sets namely, Tc fuzzy sets in fuzzy topological spaces (via)  sets. Some characterizations and properties of these sets are investigated. Further, we introduce the concept of Tc fuzzy continuous and Tc fuzzy irresolute mappings.

Abstract This paper aims to present the concept of multi-valued mappings in fuzzy cone metric spaces and prove some basic lemmas, a Hausdorff metric, fixed point results for set-valued cone-contraction mappings. We theorem rational type cone-contractions spaces. Our extend improve given literature.

We prove a related fixed point theorem for n mappings which arenot necessarily continuous in n fuzzy metric spaces using an implicit relationone of them is a sequentially compact fuzzy metric space which generalizeresults of Aliouche, et al. [2], Rao et al. [14] and [15].

Motivated by Samet et al. [Nonlinear Anal., 75(4) (2012), 2154-2165], we introduce the notions of $alpha$-$phi$-fuzzy contractive mapping and $beta$-$psi$-fuzzy contractive mapping and prove two theorems which ensure the existence and uniqueness of a fixed point for these two types of mappings. The presented theorems extend, generalize and improve the corresponding results given in the literature.

Introduction A classical question in the theory of functional equations is “when is it true that a mapping, which approximately satisfies a functional equation, must be somehow close to an exact solution of the equation?”. Such a problem, called a stability problem of the functional equation, was formulated by Ulam [1] in 1940. In the next year, Hyers [2] gave a partial solution of Ulam’s probl...

A classical question in the theory of functional equations is “when is it true that a mapping, which approximately satisfies a functional equation, must be somehow close to an exact solution of the equation?” Such a problem, called a stability problem of the functional equation, was formulated by Ulam 1 in 1940. In the next year, Hyers 2 gave a partial solution of Ulam’s problem for the case of...

The present paper studies fuzzy matroids in view of degree. First wegeneralize the notion of $(L,M)$-fuzzy independent structure byintroducing the degree of $M$-fuzzy family of independent $L$-fuzzysets with respect to a mapping from $L^X$ to $M$. Such kind ofdegrees is proved to satisfy some axioms similar to those satisfiedby $(L,M)$-fuzzy independent structure. ...

We introduce the new category VRel(H) consisting of H-fuzzy relation spaces and H-fuzzy mappings between them satisfying a certain condition, where the concept of H-fuzzy mapping is the modification of one of fuzzy mapping introduced by Demirci[6]. And we investigate VRel(H) in the sense of a topological universe and show that VRel(H) is Cartesian closed over Set. Moreover, we construct the cat...

There exists a vast literature about the di erentiabil ity of fuzzy valued mappings see for instance Dubois and Prade Puri and Ralescu Goetschel and Voxman or Kaleva One of the main problems in working with di erentials of fuzzy valued mappings is that the usual class of fuzzy sets of R does not con gure a vectorial space with respect to the sum and the product by a scalar induced by Zadeh s Ex...