Lower Solutions of Max-Min Fuzzy Equations
The whole of this Ch. is devoted to the study of the lower solutions of max-min fuzzy equations. In all the Secs., except Secs. 5 and 6, we assume L to be a linear lattice with universal bounds 0 and 1 and the domains, on which fuzzy sets and fuzzy relations are defined, to be finite sets, we denote by |X| the cardinality of a finite set X. In Secs. 1 and 2, we deal with max-min fuzzy equations of type (2.5) and (2.6), respectively. Further lattice results in the set S are given in Sec.3 and interesting properties of a particular fuzzy relation of S are pointed out in Sec.4. Secs.5 and 6 are devoted to the study of lower solutions of max-min fuzzy equations defined on complete Brouwerian lattices and on complete completely distributive lattices, respectively.
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