A new algorithm for decomposition problem of binary fuzzy relations

This paper deals with the decomposition problem of a binary fuzzy relation defined in the Cartesian product of finite spaces. First, a necessary and sufficient condition on the solvability of the problem is shown. Then logical equations are converted into algebraic equations via semi-tensor product (STP) approach, based on which all solutions of the decomposition problem can be obtained. Finally, an illustrative example is shown to demonstrate effectiveness of the derived algorithm.