Direct and indirect methods for solving two-mode systems of fuzzy relation equations and inequalities

Abstract

The purpose of this paper is to compare two methods for computing the greatest solutions of two-mode systems of FREIs. The first one is the direct method developed recently in [26], and the second one consists in converting the two-mode case into the one-mode case, and computing the greatest solutions of related one-mode systems of FREIs, using algorithms provided in [13, 15]. The conversion is made by means of the well-known method used in social network analysis for transforming two-mode networks into one-mode networks. We prove theoretically interesting result according to which solutions of any two-mode system of FREIs can be derived from solutions of the related one-mode system, and vice versa. However, from the computational point of view, the conversion based method is more memory and time demanding, what favors the direct method.