Fuzzy relation equations with equality and difference composition operators (Q1102960)

In the usual sup-min-composition for fuzzy relation equations \(A\circ R=B\) (A, B given fuzzy sets) the authors substitute min by an equivalence operator {\S} such that a{\S}b\(=\min (a,b)\) for \(a\neq b\), a{\S}b\(=1\) for \(a=b\). For the corresponding relation equation a solvability criterion is proven and the set of maximal solutions determined. The analogous results are given for a kind of ``dualized'' equations. Unfortunately, the authors give no convincing motivation for choosing those new types of relation equations.