Generalizations of Rough Sets : Rough sets under similarity, fuzzy and dominance relations

L-valued Fuzzy Rough Sets

In this paper, we take a GL-quantale as the truth value table to study a new rough set model—L-valued fuzzy rough sets. The three key components of this model are: an L-fuzzy set A as the universal set, an L-valued relation of A and an L-fuzzy set of A (a fuzzy subset of fuzzy sets). Then L-valued fuzzy rough sets are completely characterized via both constructive and axiomatic approaches. 

On $L$-double fuzzy rough sets

ur aim of this  paper  is  to introduce the concept of $L$-double fuzzy rough sets in whichboth constructive and axiomatic approaches are used. In constructive approach, a pairof $L$-double fuzzy lower (resp. upper) approximation operators is defined  and the basic properties of them  are studied.From the viewpoint of the axiomatic approach, a set of axioms is constructed to characterize the $L...

Rough Sets, Rough Relations and Rough Functions

Multi-fuzzy rough sets and relations

Pawlak’s Rough set theory was originally proposed as a general mathematical tool for dealing with uncertainty in modeling imperfect knowledge. The purpose of this paper is to introduce the concept of multifuzzy rough sets by combining the multi-fuzzy set and rough set models. Some operations such as Complement, Union, Intersection etc. are defined for multi-fuzzy rough sets and De Morgan’s laws...

Rough Sets and Fuzzy Sets

This issue is dedicated to Professor Lotfi A. Zadeh, the founder of fuzzy set theory, on the occasion of celebrating 50 years of his first publication on fuzzy sets in 1965 [1]. The idea of fuzzy sets has influenced a very large number of researchers all over the world. Since 1965 many thousands of research papers on fuzzy set theory and its applications have been published as well as many thou...