In [Fuzzy Sets and Systems 27 (1988) 385-389], M. Grabiec in- troduced a notion of completeness for fuzzy metric spaces (in the sense of Kramosil and Michalek) that successfully used to obtain a fuzzy version of Ba- nachs contraction principle. According to the classical case, one can expect that a compact fuzzy metric space be complete in Grabiecs sense. We show here that this is not the case,...

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...

it is well known fact that binary relations are generalized mathematical functions. contrary to functions from domain to range, binary relations may assign to each element of domain two or more elements of range. some basic operations on functions such as the inverse and composition are applicable to binary relations as well. depending on the domain or range or both are fuzzy value fuzzy set, i...

This is a summary of our article published in Fuzzy Sets and Systems [1] (JCR Impact Factor 2014: 1.986) to Multi-Conference CAEPIA15 KeyWorks.

Citation classics identify those highly cited papers which are an important reference point in a research field. Identifying citation classics in a research field is one of the main approaches used to conduct a systematic evaluation of research performance. Highly cited articles are interesting due to the potential association between high citation counts and high quality research. The aim of t...

Atanassov (Fuzzy Sets and Systems 20 (1986) 87-96) defined basic operations over the intuitionistic fuzzy sets. Here we shall introduce two operations, subtraction and division, derived from the deconvolution for equations using addition and multiplication operations, respectively. In addition, we shall give some conditions to examine the correctness regarding the defined operations. The remark...

Here are many situations in real applications of decision making where we deal with uncertain conditions.  Due to the different sources of uncertainty,  since its original definition of fuzzy sets in 1965 cite{zadeh1965},  different generalizations and extensions of fuzzy sets have been introduced: Type-2 fuzzy sets cite{6,13}, Intuitionistic fuzzy sets cite{1}, fuzzy multi-sets cite{37} and et...

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...