Many authors have developed lots of entropies and similarity measures for interval-valued intuitionistic fuzzy sets(IvIFSs). In this paper, we first review some famous entropies for IvIFSs. Then, a new entropy for IvIFSs based on intuitionism and fuzziness is proposed and proved to satisfy the axiomatic requirements given by Liu and Zhang. Furthermore, a new class of similarity measure for IvIF...

This paper proposes an improved score function for the effective ranking order of interval-valued intuitionistic fuzzy sets (IVIFSs) and an interval-valued intuitionistic fuzzy TOPSIS method based on the score function to solve multicriteria decision-making problems in which all the preference information provided by decision-makers is expressed as interval-valued intuitionistic fuzzy decision ...

As a generalization of fuzzy sets and intuitionistic fuzzy sets, neutrosophic sets have been developed to represent uncertain, imprecise, incomplete, and inconsistent information existing in the real world. And interval neutrosophic sets (INSs) have been proposed exactly to address issues with a set of numbers in the real unit interval, not just a specific number. However, there are fewer relia...

In the present paper, a new entropy of order and type on Interval-Valued Intutionistic Fuzzy Sets (IVIFSs) along with their proofs of validity is proposed. It has been proved that the proposed entropy has monotonic decreasing behavior with respect to and . Further, a new algorithm for multiple attribute decision making method (MADM) has been provided using the benefit attributes and cost attrib...

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...

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...

The relationship between the intuitionistic fuzzy sets and the algebraic hyperstructures is described in this paper. The concept of the quasi-coincidence of an intuitionistic fuzzy interval valued with an interval-valued intuitionistic fuzzy set is introduced and this is a natural generalization of the quasi-coincidence of an intuitionistic fuzzy point in intuitionistic fuzzy sets. By using thi...

it is firstly proved that the multi-input-single-output (miso) fuzzy systems based on interval-valued $r$- and $s$-implications can approximate any continuous function defined on a compact set to arbitrary accuracy.  a formula to compute the lower upper bounds on the number  of interval-valued fuzzy sets needed to achieve a pre-specified approximation  accuracy for an arbitrary multivariate con...

In the present paper, a new entropy of order α and type β on Interval-Valued Intutionistic Fuzzy Sets (IVIFSs) along with their proofs of validity is proposed. It has been proved that the proposed entropy has monotonic decreasing behavior with respect to α and β. Further, a new algorithm for multiple attribute decision making method (MADM) has been provided using the benefit attributes and cost...

In this paper we develop a measure for calculating the association coe±cient between Atanassov's intuitionistic fuzzy sets (A-IFSs), and show its desirable axiomatic properties. Then we present an algorithm for clustering A-IFSs. The algorithm ̄rst utilizes the association coe±cient of A-IFSs to construct an association matrix, and then calculates the -cutting matrix of the association matrix no...