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|Left-and right-compatibility of order relations and fuzzy tolerance relations
Clone relation; Order relation; Fuzzy equivalence relation; Fuzzy tolerance relation
|Fuzzy Sets and Systems
|In a recent paper, DeBaets 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. ©2018 Elsevier B.V. All rights reserved.
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|Department of Maths - قسم الرياضيات
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