A Study on m-polar Fuzzy Sets and m-polar Fuzzy Matrix

Fuzzy matrix is a very important topic of fuzzy algebra. In fuzzy matrix, the elements belong to the unit interval [0,1], each element represents the membership value of an element. In this paper, m-polar fuzzy set, m-polar fuzzy relation, m-polar fuzzy matrix is introduced. In m-polar fuzzy matrix, each element is a vector containing m elements and membership values of each elements lie between 0 and 1 including 0 and 1. In m-polar fuzzy matrix, the membership values of rows and columns are crisp, i.e. rows and columns are certain. But, in many real life situations they are also uncertain. So to model these type of uncertain problems, a new type of uncertain problems, a new type of m-polar fuzzy matrix with m-polar fuzzy rows and columns are defined. For these matrices, null, identity, equality, complement, g-m-polar, complete, density are defined. For these matrices, we checked that whether the matrix is balanced, strictly balanced or not.