Fuzzy strict preference relations compatible with fuzzy orderings
- Author
- Bonifacio Llamazares and Bernard De Baets (UGent)
- Organization
- Abstract
- One of the most important issues in the field of fuzzy preference modelling is the construction of a fuzzy strict preference relation and a fuzzy indifference relation from a fuzzy weak preference relation. Here, we focus on a particular class of fuzzy weak preference relations, the so-called fuzzy orderings. The definition of a fuzzy ordering involves a fuzzy equivalence relation and, in this paper, the latter will be considered as the corresponding fuzzy indifference relation. We search for fuzzy strict preference relations compatible with a given fuzzy ordering and its fuzzy indifference relation. In many situations, depending on the t-norm and t-conorm used, this quest results in a unique fuzzy strict preference relation. Our aim is to characterize these fuzzy strict preference relations and to study their transitivity.
- Keywords
- fuzzy strict preference relation, transitivity, Fuzzy ordering, LUKASIEWICZ TRIPLETS, PRE-ORDERS, DEFINITION, DECOMPOSITION, TRANSITIVITY, SIMILARITY, PLEA
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Citation
Please use this url to cite or link to this publication: http://hdl.handle.net/1854/LU-1085550
- MLA
- Llamazares, Bonifacio, and Bernard De Baets. “Fuzzy Strict Preference Relations Compatible with Fuzzy Orderings.” INTERNATIONAL JOURNAL OF UNCERTAINTY FUZZINESS AND KNOWLEDGE-BASED SYSTEMS, vol. 18, no. 1, 2010, pp. 13–24, doi:10.1142/S0218488510006350.
- APA
- Llamazares, B., & De Baets, B. (2010). Fuzzy strict preference relations compatible with fuzzy orderings. INTERNATIONAL JOURNAL OF UNCERTAINTY FUZZINESS AND KNOWLEDGE-BASED SYSTEMS, 18(1), 13–24. https://doi.org/10.1142/S0218488510006350
- Chicago author-date
- Llamazares, Bonifacio, and Bernard De Baets. 2010. “Fuzzy Strict Preference Relations Compatible with Fuzzy Orderings.” INTERNATIONAL JOURNAL OF UNCERTAINTY FUZZINESS AND KNOWLEDGE-BASED SYSTEMS 18 (1): 13–24. https://doi.org/10.1142/S0218488510006350.
- Chicago author-date (all authors)
- Llamazares, Bonifacio, and Bernard De Baets. 2010. “Fuzzy Strict Preference Relations Compatible with Fuzzy Orderings.” INTERNATIONAL JOURNAL OF UNCERTAINTY FUZZINESS AND KNOWLEDGE-BASED SYSTEMS 18 (1): 13–24. doi:10.1142/S0218488510006350.
- Vancouver
- 1.Llamazares B, De Baets B. Fuzzy strict preference relations compatible with fuzzy orderings. INTERNATIONAL JOURNAL OF UNCERTAINTY FUZZINESS AND KNOWLEDGE-BASED SYSTEMS. 2010;18(1):13–24.
- IEEE
- [1]B. Llamazares and B. De Baets, “Fuzzy strict preference relations compatible with fuzzy orderings,” INTERNATIONAL JOURNAL OF UNCERTAINTY FUZZINESS AND KNOWLEDGE-BASED SYSTEMS, vol. 18, no. 1, pp. 13–24, 2010.
@article{1085550,
abstract = {{One of the most important issues in the field of fuzzy preference modelling is the construction of a fuzzy strict preference relation and a fuzzy indifference relation from a fuzzy weak preference relation. Here, we focus on a particular class of fuzzy weak preference relations, the so-called fuzzy orderings. The definition of a fuzzy ordering involves a fuzzy equivalence relation and, in this paper, the latter will be considered as the corresponding fuzzy indifference relation. We search for fuzzy strict preference relations compatible with a given fuzzy ordering and its fuzzy indifference relation. In many situations, depending on the t-norm and t-conorm used, this quest results in a unique fuzzy strict preference relation. Our aim is to characterize these fuzzy strict preference relations and to study their transitivity.}},
author = {{Llamazares, Bonifacio and De Baets, Bernard}},
issn = {{0218-4885}},
journal = {{INTERNATIONAL JOURNAL OF UNCERTAINTY FUZZINESS AND KNOWLEDGE-BASED SYSTEMS}},
keywords = {{fuzzy strict preference relation,transitivity,Fuzzy ordering,LUKASIEWICZ TRIPLETS,PRE-ORDERS,DEFINITION,DECOMPOSITION,TRANSITIVITY,SIMILARITY,PLEA}},
language = {{eng}},
number = {{1}},
pages = {{13--24}},
title = {{Fuzzy strict preference relations compatible with fuzzy orderings}},
url = {{http://doi.org/10.1142/S0218488510006350}},
volume = {{18}},
year = {{2010}},
}
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