The definition of hesitant interval-valued intuitionistic fuzzy sets (HIVIFSs) is developed based on interval-valued intuitionistic fuzzy sets (IVIFSs) and hesitant fuzzy sets (HFSs). Then, some operations on HIVIFSs are introduced in detail, and their properties are further discussed. In addition, some hesitant interval-valued intuitionistic fuzzy number aggregation operators based on t-conorm...

The objective of image fusion for medical images is to combine multiple images obtained from various sources into a single image suitable for better diagnosis. Most of the state-of-the-art image fusing technique is based on nonfuzzy sets, and the fused image so obtained lags with complementary information. Intuitionistic fuzzy sets (IFS) are determined to be more suitable for civilian, and medi...

In this paper, we research the relationship between entropy and similarity of interval valued intuitionistic fuzzy sets in detail and prove eight theorems that entropy and similarity of interval valued intuitionistic fuzzy sets can be transformed to each other based on their axiomatic definitions. Finally, we propose some formulaes to calculate entropy and similarity of interval valued intuitio...

The notion of interval-valued intuitionistic fuzzy sets was first introduced by Atanassov and Gargov in 1989 as a generalization of both interval-valued fuzzy sets and intuitionistic fuzzy sets. In this paper we first apply the concept of interval-valued intuitionistic fuzzy sets to K-algebras. Then we introduce the notion of interval-valued intuitionistic fuzzy ideals (IIFIs, in short) of K-al...

Hesitancy is the most common problem in decision making, for which hesitant fuzzy set can be considered as a useful tool allowing several possible degrees of membership of an element to a set. Recently, another suitable means were defined by Zhiming Zhang [1], called interval valued intuitionistic hesitant fuzzy sets, dealing with uncertainty and vagueness, and which is more powerful than the h...

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...

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 ...

Inspired by the idea of multiplicative intuitionistic preference relation (Xia MM et al. Preference relations based on intuitionistic multiplicative information, IEEE Transactions on Fuzzy Systems, 2013, 21(1): 113-133), in this paper, a new preference relation called the interval-valued multiplicative intuitionistic preference relation is developed. It is analyzed the basic operations for inte...

On the basis of the concept of the interval valued intuitionistic fuzzy sets introduced by K. Atanassov, the notion of interval valued intuitionistic fuzzy subsemimodule of a semimodule with respect to t-norm T and s-norm S is given and the characteristic properties are described. The homomorphic image and inverse image are investigated. In particular, by the help of the congruence relations on...