In this paper we introduce the concentration and dilation operators on interval valued intuitionistic fuzzy soft sets of root type which is a generalization of fuzzy set, intuitionistic fuzzy set, interval valued intuitionistic fuzzy set and intuitionistic fuzzy set of root type and establish some properties of these operators. We define Hamming distance between two interval valued intuitionist...

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...

a new approach to define the similarity measure betweeninterval-valued fuzzy sets is presented. the proposed approach isbased on a weighted measure in which the normalized similaritiesbetween lower functions and also between upper functions arecombined by a weight parameter. the properties of this similaritymeasure are investigated. it is shown that, the proposed measurehas some advantages in c...

A new accuracy function for the theory of interval-valued intuitionistic fuzzy set, which overcomes some difficulties arising in the existing methods for determining rank of interval-valued intuitionistic fuzzy numbers, is proposed by taking into account the hesitancy degree of interval-valued intuitionistic fuzzy sets. By comparing it with several proposed accuracy functions, the necessity and...

The evaluation is an important approach to promote the development of the E-Government. Since the rapid development of E-Government in the world, the E-Government performance evaluation has become a hot issue in the academia. In this paper, we develop a new evaluation method for the development of the E-Government based on the interval-valued intuitionistic fuzzy set which is a powerful techniq...

We establish relationships between the set of trapezoidal intuitionistic fuzzy numbers and the set of interval-valued trapezoidal fuzzy numbers and, on the other hand, between the set of triangular intuitionistic fuzzy numbers and the set of triangular fuzzy numbers. Based on these main results of the paper, the methods or procedures elaborated for interval-valued trapezoidal or triangular fuzz...

Molodtsov first proposed the soft set theory, which can be used as a general mathematical tool for dealing with fuzzy and uncertain information. As a generalization of soft set, interval-valued intuitionistic fuzzy soft set is another soft set structure,it is a combination of an interval-valued intuitionistic fuzzy set and a soft set. The objective of this paper is to study the decision making ...

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...

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...