Fuzzy Galois connections on fuzzy sets

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 readership of fuzzy set theorists, with particular attention paid to fuzzy Galois connections between preordered fuzzy sets.Comment: 30 pages, final versio

An adjustable method for data ranking based on fuzzy soft sets

This work deals with an adjustable approach for ranking objects based on fuzzy soft models. We first generate two preorder relations, thus, two equivalence relations based on the fuzzy soft topology. Then, a method for data ranking is designed according to these binary relations. The connection between Separation axioms and such data ranking method is also studied. Finally, an example is provided to illustrate this method for problem of data ranking

Lower Approximations by Fuzzy Consequence Operators

Peer ReviewedPostprint (author's final draft

Existence of Order-Preserving Functions for Nontotal Fuzzy Preference Relations under Decisiveness

Looking at decisiveness as crucial, we discuss the existence of an order-preserving function for the nontotal crisp preference relation naturally associated to a nontotal fuzzy preference relation. We further present conditions for the existence of an upper semicontinuous order-preserving function for a fuzzy binary relation on a crisp topological space