Representation of Fuzzy Matrices Based on Reference Function

Fuzzy matrices in the present form do not meet the most important requirement of matrix representatiom in the form of reference function without which no logical result can be expected. In this article, we intend to represent fuzzy matrices in which there would be the use of reference function. Our main purpose is to deal specially with complement of fuzzy matrices and some of its properties when our new definition of complementation of matrices is considered. For doing these the new definition of complementation of fuzzy sets based on reference function plays a very crucial role. Further, a new definition of trace of a fuzzy matrix is introduced in this article which is in accordance with newly defined fuzzy matrices with the help of reference function and thereby efforts have been made to establish some of the properties of trace of fuzzy matrices.