Boolean Solutions of Max-Min Fuzzy Equations
This Ch. is entirely dedicated to the study of the Boolean (i.e. non-fuzzy) solutions of a max-min fuzzy equation defined on a complete Brouwerian lattice L with universal bounds 0 and 1. In Sec.1, we give a simple necessary and sufficient condition for the existence of the greatest Boolean solution of S and in Sec.2, using some results of Ch.3, we determine the minimal Boolean elements of S if L is a linear lattice. In Sec.3, if Boolean solutions do not exist, an algorithm is presented to find the elements of S with maximum Boolean degree, i.e. with the maximum number of 0 and 1. The referential sets are assumed to be necessarily finite in Secs.2 and 3.
KeywordsFundamental Theorem Minimal Element Fuzzy Relation Fuzzy Entropy Linear Lattice
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