Solving a class of fuzzy relation inequalities via semi-tensor product

The problem of solving a class of fuzzy relation inequalities (FRIs) is investigated. First, it is shown that if the FRI is solvable, there is a corresponding parameter solution set (briefly, PSS). Then the semi-tensor product of matrices is used to convert the logical inequality into its algebraic form via the vector expression of logical variables. Under this form all the PSS can be obtained. It is proved that all the solutions can be derived from their corresponding PSS. An example is presented to demonstrate the effectiveness of the algorithm provided in this paper.