### On A Weak Commutativity Condition Of Mappings In Fixed Point Considerations

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A maximal disjoint subset S of an MV-algebra A is a basis iff {x in A : x ≤ a} is a linearly ordered subset of A for all a in S. Let Spec A be the set of the prime ideals of A with the usual spectral topology. A decomposition Spec A = U T U X is said to be orthogonal iff each T is compact open and S = {a} is a maximal disjoint subset. We prove that this decomposition is unrefinable (i.e. no T = Theta ∩ Y with Theta open, Theta ∩ Y = emptyset, int Y = emptyset) iff S is a basis. Many results are...

This paper follows a companion paper (Stochastica 8 (1984), 99-145) in which we gave the state of the art of the theory of fuzzy relation equations under a special class of triangular norms. Here we continue this theory establishing new results under lower and upper semicontinuous triangular norms and surveying on the main theoretical results appeared in foregoing papers. Max-t fuzzy equations with Boolean solutions are recalled and studied. Many examples clarify the results established.

By substituting the classical lattice operator min of the unit real interval with a triangular norm of Schweizer and Sklar, the usual fuzzy relational equations theory of Sanchez can be generalized to wider theory of fuzzy equations. Considering a remarkable class of triangular norms, for such type of equations defined on finite sets, we characterize the upper an lower solutions. We also characterize the solutions posessing a minimal fuzziness measure of Yager valued with respect to...

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