In this paper we look at two categories, the category F of fuzzy subsets and a quotient category F=M of fuzzy sets. The category F=M is an extension of the category of sets, and the standard constructions in fuzzy set theory arise naturally within this category.

lthough fuzzy set theory and  sheaf theory have been developed and studied independently,  ulrich hohle shows that a large part of fuzzy set  theory  is in fact a subfield of sheaf theory. many authors have studied mathematical structures, in particular, algebraic structures, in both  categories of these generalized (multi)sets. using hohle's idea, we show that for a (universal) algebra $a$, th...

In this paper, we formalize the Menger probabilistic normed space as a category in which its objects are the Menger probabilistic normed spaces and its morphisms are fuzzy continuous operators. Then, we show that the category of probabilistic normed spaces is isomorphicly a subcategory of the category of topological vector spaces. So, we can easily apply the results of topological vector spaces...

in this paper, let $l$ be a completeresiduated lattice, and let {bf set} denote the category of setsand mappings, $lf$-{bf pos} denote the category of $lf$-posets and$lf$-monotone mappings, and $lf$-{bf cslat}$(sqcup)$, $lf$-{bfcslat}$(sqcap)$ denote the category of $lf$-completelattices and $lf$-join-preserving mappings and the category of$lf$-complete lattices and $lf$-meet-preserving mapping...

In fairly elementary terms this paper presents how the theory of preordered fuzzy sets, more precisely quantale-valued preorders on quantale-valued fuzzy sets, is established under the guidance of enriched category theory. Motivated by several key results from the theory of quantaloid-enriched categories, this paper develops all needed ingredients purely in order-theoretic languages for the rea...

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 ...