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,...

Interval-valued fuzzy sets are based on the algebra of subintervals of the unit interval [0, 1]. We study valuations as a special type of measures on this algebra. We present a description of all valuations which preserve the standard fuzzy negation and extend the identity on the elements of the form (x, x). Consequences for sublattices are formulated. Keywords— Girard algebra, interval-valued ...

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...

In this paper, a new soft computing group decision method based on the concept of compromise ratio is introduced for determining decision makers (DMs)' weights through the group decision process under uncertainty. In this method, preferences and judgments of the DMs or experts are expressed by linguistic terms for rating the industrial alternatives among selected criteria as well as the relativ...

Multi-criteria decision-making (MCDM) problem is the process of finding the best option from all of the feasible alternatives where all the alternatives can be evaluated according to a number of criteria or attribute. Since human judgments including preferences are often vague and cannot estimate his preference with an exact numerical value. Multi-criteria decision-making problems usually consi...

This paper deals with interval-valued fuzzy sets and I-fuzzy sets, Atanassov's intuitionistic fuzzy sets. They are treated in a systematic way as two, formally equivalent, natural extensions of methods of representing incomplete knowledge about sets. We define and investigate triangular norm-based areas of uncertainty of interval-valued fuzzy sets and I-fuzzy sets, and study some properties of ...

The concept of interval valued fuzzy matrix (IVFM) is one of the recent topics developed for dealing with the uncertainties present in most of our real life situations, the parameterization tool of interval valued fuzzy matrix enhances the flexibility of its applications. Most of our real life problems in medical sciences, engineering, management environment and social sciences often involve da...

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...

Szmidt and Kacprzyk (Lecture Notes in Artificial Intelligence 3070:388– 393, 2004a) introduced a similarity measure, which takes into account not only a pure distance between intuitionistic fuzzy sets but also examines if the compared values are more similar or more dissimilar to each other. By analyzing this similarity measure, we find it somewhat inconvenient in some cases, and thus we develo...

In this paper, (α,β)-interval valued set is studied. The order relation on defined. It shown that complete lattice by giving the definitions of infumum and supremum these sets. Then, negation function sets introduced. 
 With help ,(α,β)-interval intuitionistic fuzzy are fundamental algebraic properties examined. level subsets given. Some propositions examples