in this paper, we establish the theory of fuzzy ideal convergence on completely distributive lattices and give characterizations of some topological notions. we also study fuzzy limit structures and discuss the relationship between fuzzy co-topologies and fuzzy limit structures.

This paper introduces a new approach to topology, based on category theory and universal algebra, and called categorically-algebraic (catalg) topology. It incorporates the most important settings of lattice-valued topology, including poslat topology of S.~E.~Rodabaugh, $(L,M)$-fuzzy topology of T.~Kubiak and A.~v{S}ostak, and $M$-fuzzy topology on $L$-fuzzy sets of C.~Guido. Moreover, its respe...

General topology can be regarded as a special case of fuzzy topology where all membership functions in question take values 0 and 1 only. The usual fuzzy metric spaces, fuzzy Hausdorff topological vector spaces, and Menger probabilistic metric spaces are all the special cases of F-type fuzzy topological spaces. Therefore, one would expect weaker results in the case of fuzzy topology. Recently s...

The purpose of this paper is to introduce and study the concepts of intuitionistic fuzzy perfectly regular weakly generalized continuous mappings and intuitionistic fuzzy perfectly regular weakly generalized open mappings in intuitionistic fuzzy topological space. Some of their properties are explored.

In this paper a method is proposed to compute typical objects for the classes in the scheme of a fuzzy object oriented database. Typical objects are considered as "representatives" of a fuzzy majority of the class instances. The instances of a class are represented in a topological space and the typical object is derived as "closest" to the fuzzy majority of the class instances.

The aim of this paper is to introduce $(L,M)$-fuzzy closurestructure where $L$ and $M$ are strictly two-sided, commutativequantales. Firstly, we define $(L,M)$-fuzzy closure spaces and getsome relations between $(L,M)$-double fuzzy topological spaces and$(L,M)$-fuzzy closure spaces. Then, we introduce initial$(L,M)$-fuzzy closure structures and we prove that the category$(L,M)$-{bf FC} of $(L,M...

Katsaras 1 defined a fuzzy norm on a vector space to construct a fuzzy vector topological structure on the space. Some mathematicians have defined fuzzy norms on a vector space from various points of view 2–4 . In particular, Bag and Samanta 5 , following Cheng and Mordeson 6 , gave an idea of fuzzy norm in such a manner that the corresponding fuzzy metric is of Kramosil and Michálek type 7 . T...

Given a compact and connected metric space (continuum) X, we study topological and dynamical properties of the hyperspace of normal fuzzy sets F1(X) equipped with the Hausdorff, endograph or sendograph metric. Among the many results we show that it is contractible, path connected, locally contractible, locally path connected, locally simply connected and locally connected. For the endograph met...