Comparison of Interval-valued fuzzy sets, Intuitionistic fuzzy sets, and bipolar-valued fuzzy sets

INTERVAL-VALUED INTUITIONISTIC FUZZY SETS AND SIMILARITY MEASURE

In this paper, the problem of measuring the degree of inclusion and similarity measure for two   interval-valued intuitionistic  fuzzy sets is considered. We propose inclusion and similarity measure by using  order on interval-valued intuitionistic fuzzy sets connected with lexicographical order. Moreover, some properties of inclusion and similarity measure and some correlation, between them an...

Distances between interval-valued intuitionistic fuzzy sets

We give a geometrical interpretation of the interval-valued fuzzy set (IVFS). Based on the geometrical background, we propose new distance measures between IVFSs and compare these measures with distance measures proposed by Burillo and Bustince (1996) and Grzegorzewski (2004), respectively. Furthermore, we extend three methods for measuring distances between IVFSs to interval-valued intuitionis...

Soft interval-valued intuitionistic fuzzy rough Sets

Soft set theory, fuzzy set theory and rough set theory are all mathematical tools for dealing with uncertainties and are closely related. Feng et al. introduced the notions of rough soft set, soft rough set and soft rough fuzzy set by combining fuzzy set, rough set and soft set all together. This paper is devoted to the discussions of the combinations of intervalvalued intuitionistic fuzzy set,...

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. 

Intuitionistic fuzzy sets and interval-valued fuzzy sets: a critical comparison