On the greatest solutions to weakly linear systems of fuzzy relation inequalities and equations (Q622073)

The authors study systems of fuzzy relation equations of the form \[ U\circ V_i\leq V_i\circ U \] in which \(U\) is treated as an unknown fuzzy relation and \(V_i\), \(i\in I\), are given fuzzy relations. The dual systems considered here assume the form \(V_i\circ U\leq U\circ V_i\). The composition operator \(\circ\) is a supremum-multiplication one (with the multiplication \(\otimes\) being used to model conjunction). Along with the two classes of fundamental equations, the authors discuss also conjunctions of these equations as well as those of the form \(U\circ V_i= V_i\circ U\). Some applications of these equations to fuzzy automata, concurrency theory, and social network analysis are presented.