Some results on the resolution of fuzzy relation equations (Q1319460)

Let \(R\) be a fuzzy matrix and \textbf{a}, \textbf{b} be fuzzy vectors such that \({\mathbf a}\circ R={\mathbf b}\), where ``\(\circ\)'' denotes the max-min composition. If \(R\) and \textbf{b} are provided, the authors just look for \textbf{a}=\textbf{1} as the greatest solution, \textbf{1} being the unit vector. Another result determines when \textbf{1} is also the unique solution. Three algorithms are given in order to illustrate the theorems. Similar problems were treated by the reviewer and \textit{S. Sessa} in their paper in J. Math. Anal. Appl. 132, No. 1, 39-49 (1988; Zbl 0661.04003)].