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Down and up operators associated to fuzzy relations and t-norms: A definition of fuzzy semi-ideals. (English) Zbl 0965.03065

The author considers various generalized definitions of classical notions in set theory and lattices by means of a t-norm, a complete lattice \(L\) and an \(L\)-fuzzy relation \(R\) on a set \(X\). \(LF\)-semi-ideals and \(LF\)-semi-filters are considered and several characterizations are found. Particular cases and examples are shown.

MSC:

03E72 Theory of fuzzy sets, etc.
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