Interval-Valued Intuitionistic Fuzzy Matrices

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. Intuitionistic fuzzy matrices (IFMs) introduced first time by Khan, Shyamal and Pal [11]. Several properties on IFMs have been studied in [6]. But, practically it is difficult to measure the membership or non membership value as a point. So, we consider the membership value as an interval and also in the case of non membership values, it is not selected as a point, it can be considered as an interval. Here, we introduce the interval valued intuitionistic fuzzy matrices (IVIFMs) and introduce some basic operators on IVIFMs. The interval-valued intuitionistic fuzzy determinant (IVIFD) is also defined. A real life problem on IVIFM is presented. Interpretation of some of the operators are given with the help of this example.