Decomposition and Reduction of an Intuitionistic Fuzzy Matrix

Most of the theories of fuzzy matrix have been extended to Intuitionistic fuzzy matrices. We observe that it is possible to decompose any Intuitionistic fuzzy matrix into any composition of fuzzy matrices using modal operators and a new composition operator. Every Fuzzy Matrix is an Intuitionistic Fuzzy Matrix and the converse need not be true. Here using reduction operators we reduce an Intuitionistic fuzzy matrix to Fuzzy Matrix. The relation among the conjunction, disjunction and reduction operators gives an addition law on probability. This relation paves a way for the development of IFM theory with probability theory.