Solving Fuzzy Relational Equations Via Semitensor Product

The problem of solving max-min fuzzy relational equations is investigated. First, we show that if there is a solution, then there is a corresponding solution within the set of parameters [briefly, the parameter set solution (PSS)]. Then, the semitensor product of matrices is used to convert the logical equations into algebraic equations via the vector expression of logical variables. Under this form, every PSS can be obtained. It is proved that all the solutions can be revealed from their corresponding PSS. Some examples are presented to demonstrate the algorithm to solve fuzzy relational equations.