Bipolar fuzzy relation equations based on the product T-norm

Abstract

Bipolar fuzzy relation equations are given from the fuzzy relation equations introduced by Sanchez in the 1980s considering a negation operator in the equations. Numerous applications require variables that show a bipolar character such as decision making and revenue management, hence the importance of studying bipolar fuzzy relation equations. According to the literature, bipolar max-min equations have already been studied and a characterization of their solutions, by means of a finite set of maximal and minimal solution pairs, has been provided. This paper will present a first study on bipolar max-product fuzzy relation equations with one equation containing different variables, which includes different interesting properties in order to guarantee both their solvability and the existence of the greatest (least) solution or maximal (minimal) solutions. Moreover, a characterization of the solvability of a particular system of two bipolar max-product fuzzy relation equations is given.