Partial ordering in L-underdeterminate sets. (English) Zbl 0576.06004

Höhle, Ulrich; Blanchard, Nicole

Inf. Sci. 35, 133-144 (1985).

The paper introduces a new approach to the consideration of fuzzy relations. Properties of fuzzy relations are defined with respect to a fuzzy equivalence E in the crisp set X considered (the pair (X,E) is called an underdeterminate set). In particular, fuzzy partial order in (X,E) is considered and the existence of a linear extension in (X,E) is proved (a generalization of the Szpilrain theorem).

Reviewer: J.Drewniak

MSC:

06A06	Partial orders, general
08A30	Subalgebras, congruence relations
08A02	Relational systems, laws of composition

Keywords:

fuzzy relations; fuzzy equivalence; fuzzy partial order; linear extension

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