In this paper the concept of interval valued intuitionistic fuzzy soft set relations (IVIFSS-relations for short) is proposed. Our relations on interval valued intuitionistic fuzzy soft sets is an extension of the relations on intuitionistic fuzzy soft sets, introduced by Mukherjee and Chakraborty in 2009. The basic properties of the IVIFSS-relations are also presented and discussed. It is seen...

After the introduction of fuzzy set by Zadeh in 1965 [1], there have been a number of generalizations of this fundamental concept. In 1967, Goguen [2] proposed the concept of L-fuzzy set. The idea of interval valued fuzzy set is given by Zadeh in 1975 [3]. Type 2 fuzzy sets were poposed by Zadeh in [4]. Attanasove introduced intuitionistic fuzzy sets in 1986 [5]. Interval valued intuitionistic ...

Interval neutrosophic set (INS) is a generalization of interval valued intuitionistic fuzzy set (IVIFS), whose the membership and non-membership values of elements consist of fuzzy range, while single valued neutrosophic set (SVNS) is regarded as extension of intuitionistic fuzzy set (IFS). In this paper, we extend the hierarchical clustering techniques proposed for IFSs and IVIFSs to SVNSs and...

Rough set theory is one of important tools of soft computing, and rough approximations are the essential elements in rough set models. However, the existing fuzzy rough set model for set-valued data, which is directly constructed based on a kind of similarity relation, fail to explicitly define fuzzy rough approximations. To solve this issue, in this paper, we propose two types of fuzzy rough a...

Interval-valued hesitant fuzzy sets (IVHFS), as a kind of decision information presenting tool which is more complicated and scientific elastic, have an important practical value in multiattribute decision-making. There little research on the uncertainty IVHFS. The existing measure cannot distinguish different IVHFS some contexts. In my opinion, for IVHFS, there should exist two types uncertain...

In this paper, we define the concept of a bipolar fuzzy cosets of a bipolar fuzzy HX subgroup, bipolar anti fuzzy HX subgroup, bipolar fuzzy middle coset of a bipolar fuzzy HX subgroup and bipolar anti fuzzy HX subgroup, conjugate bipolar fuzzy HX subgroup, conjugate bipolar anti fuzzy HX subgroup and discussed some of its properties with the examples. Further we define the level subsets and lo...

In this paper, the notion ofgraph operationsdisjunction and symmetric difference on bipolar fuzzy graphs are defined and it is proved that the new graph is a bipolar graph. Furthermore,the new concepts of bipolar fuzzy graphs calledupperstrong and lower strongbipolar fuzzy graphare introduced and some related </...