On the solvability of bipolar max-product fuzzy relation equations with the standard negation
arXiv:2410.07197 · doi:10.1016/j.fss.2020.02.010
Abstract
Bipolar fuzzy relation equations arise when unknown variables together with their logical negations appear simultaneously in fuzzy relation equations. This paper gives a characterization of the solvability of bipolar max product fuzzy (relation) equations with the standard negation. In addition, some properties associated with the existence of the greatest/least solution or maximal/minimal solutions are shown, when these (relation) equations are solvable. Different examples are included in order to clarify the developed theory.