The notion of the interval-valued intuitionistic fuzzy set (IVIFS) is a generalization of that of the Atanassov’s intuitionistic fuzzy set. The fundamental characteristic of IVIFS is that the values of its membership function and non-membership function are intervals rather than exact numbers. There are various averaging operators defined for IVIFSs. These operators are not monotone with respec...

This study is to propose a new approach for medical diagnosis using the distance between interval-valued intuitionistic fuzzy sets. For this purpose, we developed an interview chart with interval fuzzy degrees based on the relation between symptoms and diseases (three types of headache), and utilized the interval-valued intuitionistic fuzzy weighted arithmetic average operator to aggregate fuzz...

Due to the increasing competition of globalization, selection of the most appropriate supplier is one of the key factors for asupply chain management’s success. Due to conflicting evaluations and insufficient information about the criteria, Intuitionisticfuzzy sets (IFSs) considered as animpressive tool and utilized to specify the relative importance of the criteria. The aim of this paper is to...

The entropy of intuitionistic fuzzy sets is used to indicate the degree of fuzziness of an interval-valued intuitionistic fuzzy set(IvIFS). In this paper, we deal with the entropies of IvIFS. Firstlt, we propose a family of entropies on IvIFS with a parameter λ ∈ [0, 1], which generalize two entropy measures defined independently by Zhang and Wei, for IvIFS, and then we prove that the new entro...

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...

Matrices play important roles in various areas in science and engineering. The classical matrix theory can not solve the problems involving various types of uncertainties. That type of problems are solved by using fuzzy matrix [14]. Later much works have been done by many researchers. Fuzzy matrix deals with only membership values. These matrices can not deal non membership values. Intuitionist...

In this paper, we propose a method to calculate the correlation coefficient of generalized intuitionistic fuzzy sets by means of "centroid". The value which obtained from this method tell us the strength of relationship between the generalized intuitionistic fuzzy sets [11] and the whether the generalized intuitionistic fuzzy sets are positively or negatively related. This method looks better t...

In this paper, associated with dominance relation, lattice theory and intuitionistic fuzzy sets theory, the lattice-valued information systems with interval-valued intuitionistic fuzzy decision are proposed and some of its properties are investigated carefully. And, an approach to knowledge reduction based on discernibility matrix in consistent latticevalued information systems with interval-va...