Abstract
In this paper we clarify the relation between two different kinds of fuzzy relations: Fuzzy Weak Orders [Bodenhofer, 99] and Resemblance Relations [Bouchon-Meunier & Valverde, 92]. The main idea to relate them is that any Fuzzy Weak Ordering defined on a set X can be isomorphically embedded into a Resemblance Relation on the fuzzy power set [0, 1]X by means of the Duality Principle for Fuzzy Sets [Ovchinnikov, 94]. In this way, Resemblance Relations can be seen as a generalization of Fuzzy Weak Orders.
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Partially supported by DGICYT PB98-0924.
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© 2001 Springer-Verlag Berlin Heidelberg
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Boixader, D., Recasens, J. (2001). Resemblance Relations and Fuzzy Weak Orderings. In: John, R., Birkenhead, R. (eds) Developments in Soft Computing. Advances in Soft Computing, vol 9. Physica, Heidelberg. https://doi.org/10.1007/978-3-7908-1829-1_5
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DOI: https://doi.org/10.1007/978-3-7908-1829-1_5
Publisher Name: Physica, Heidelberg
Print ISBN: 978-3-7908-1361-6
Online ISBN: 978-3-7908-1829-1
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