Column stacking approach to resolution of systems of fuzzy relational inequalities - Wang, Shuling; Li, Haitao (Journal of the Franklin Institute, 2019)
This paper investigates several kinds of fuzzy relational inequalities (FRIs) and systems of fuzzy relational inequalities (SFRIs) with the max–min composition, and proposes a column stacking approach. Firstly, the equivalent column stacking forms of the considered FRIs and SFRIs are obtained based on the Boolean Kronecker product of matrices, which converts the resolution of the considered FRIs and SFRIs to the resolution of an FRI with the same form. Secondly, using the semi-tensor product (STP) of matrices, the resolution of FRIs is converted to finding all the parameter set solutions, based on which, the solution set of the considered FRIs and SFRIs is characterized. Finally, a general algorithm is established for the resolution of the considered FRIs and SFRIs.