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Zedam, Lemnaouar; Bouremel, Hassane; De Baets, Bernard

Left- and right-compatibility of order relations and fuzzy tolerance relations. (English) Zbl 1423.06004

Fuzzy Sets Syst. 360, 65-81 (2019).
Summary: In a recent paper [ibid. 296, 35–50 (2016; Zbl 1374.06002)], the last author et al. have studied the compatibility of a(n) (strict) order relation with a fuzzy relation, and have characterized the fuzzy tolerance (and, in particular, fuzzy equivalence) relations that a given strict order relation is compatible with. We extend this study by considering the left- and right-compatibility of a(n) (strict) order relation with a fuzzy tolerance relation and vice versa. We characterize the fuzzy tolerance relations that are compatible with a given (strict) order relation. Conversely, we provide a representation of the fuzzy tolerance relations that a given strict order relation is left- or right-compatible with. Specific attention is paid to the case of fuzzy equivalence relations. We conclude by pointing out that the representation theorems in the above-mentioned paper need some minor rectification.

Cited in 1 Document

MSC:

06A06 Partial orders, general
03E72 Theory of fuzzy sets, etc.
06A99 Ordered sets

Keywords:

left-compatibility; right-compatibility; clone relation; order relation; fuzzy equivalence relation; fuzzy tolerance relation

Citations:

Zbl 1374.06002
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Full Text: DOI

References:

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