Decomposition and resolution of min-implication fuzzy relation equations based on S-implications (Q703395)

An S-implication (strong implication) \(\Theta : [0,1]^2 \to[0,1]\) is a binary operation defined as \(\Theta(a,b)= s(h(a),b)\) for all \(a,b\in[0,1]\), where \(s: [0,1]^2 \to[0,1]\) is a triangular conorm and \(h: [0,1]\to[0,1]\) is a negation. The authors study fuzzy relation equations of type min-\(\Theta\) by characterizing the whole set of solutions in the finite case. Indeed they find the minimum solution and the maximal ones. Some suitable numerical examples are given.