Comment on “Bipolar fuzzy relation equations systems based on the product t-norm”

This note provides counterexamples to illustrate that Theorem 4 which is proposed by Cornejo, Lobo and Medina [M. E. Cornejo, D. Lobo, J. Medina, Bipolar fuzzy relation equations systems based on the product t-norm. Mathematical Methods in the Applied Sciences. 2019,42(17):5779-5793] is incorrect. The incorrect of Theorem 4 is due to the inaccuracy of the definition of feasible pair. Then we present the correction of the definition of feasible pair to the contention.

Covering Problem for Solutions of Max-Archimedean Bipolar Fuzzy Relation Equations

This paper discusses the resolution of max-Archimedean bipolar fuzzy relation equations. In the literature, many methods have been proposed based on 0-1 integer programming problem or reduction methods for the optimization with bipolar fuzzy relation equations. A new concept based on the idea of covering and the notions of leading, non-leading variables are introduced in the present paper for finding the solutions of max-Archimedean bipolar fuzzy relation equations. It is shown that the problem of finding the complete solution set of the system of max-Archimedean bipolar fuzzy relation equations is equivalent to solving a covering problem and the solutions of such equations correspond to irredundant coverings of the covering problem. The proposed method is illustrated with some examples.