Fuzzy power structures. (English) Zbl 1156.03051
For every \(n\)-ary operation \(f\) on a set \(X\), one can define an \(n\)-ary operation \(f^+\) on the set \({\mathcal F}(X)\) of fuzzy subsets of \(X\). Any fuzzy relation \(R\) on \(X\) can be extended to a fuzzy relation \(R^+\) on \({\mathcal F}(X)\). In this paper, the author investigates some algebraic properties preserved by the transformation \(\chi \mapsto {\mathcal F}(\chi)\). Then he defines the notions of good, very good, Hoare good and Smith good, and studies the relationships between them.
Reviewer: Fu-Gui Shi (Beijing)
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