General results on the decomposition of transitive fuzzy relations

Díaz, Susana; Baets, Bernard De; Montes, Susana

doi:10.1007/s10700-010-9074-1

Cited by 29 publications

(9 citation statements)

References 34 publications

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“…Extensive results on the propagation of transitivity can be found in Díaz et al. 19,20,21,22,23 It is easy to verify that I is a T L -equivalence, R is a S L -complete T L -I-ordering and P is a fuzzy strict preference relation compatible with (R, I, T L , S L ). However, P (a, c).…”

Section: The Lukasiewicz T-normmentioning

confidence: 99%

Fuzzy Strict Preference Relations Compatible With Fuzzy Orderings

Llamazares

Baets

2010

Int. J. Unc. Fuzz. Knowl. Based Syst.

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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.

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Section: The Lukasiewicz T-normmentioning

confidence: 99%

Fuzzy Strict Preference Relations Compatible With Fuzzy Orderings

Llamazares

Baets

2010

Int. J. Unc. Fuzz. Knowl. Based Syst.

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“…While in Fuzzy Logic, a fuzzy role R is transitive iff for all x, y, z ∈ H I , it satisfies the following inequality [8]:…”

Section: Fuzzy Description Logic Programs and Their Representation Inmentioning

confidence: 99%

A Fuzzy Logic-Based Approach to Uncertainty Treatment in the Rule Interchange Format: From Encoding to Extension

Zhao

Boley

Jing

2013

Uncertainty Reasoning for the Semantic Web II

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Vous avez des questions? Nous pouvons vous aider. Pour communiquer directement avec un auteur, consultez la première page de la revue dans laquelle son article a été publié afin de trouver ses coordonnées. Si vous n'arrivez pas à les repérer, communiquez avec nous à PublicationsArchive-ArchivesPublications@nrc-cnrc.gc.ca. NRC Publications Record / Notice d'Archives des publications de CNRC:http://nparc.cisti-icist.nrc-cnrc.gc.ca/eng/view/object/?id=d016e61a-7236-421e-8ee1-60d96cc1008d http://nparc.cisti-icist.nrc-cnrc.gc.ca/fra/voir/objet/?id=d016e61a-7236-421e-8ee1-60d96cc1008d Abstract. The Rule Interchange Format (RIF) is a W3C recommendation that allows rules to be exchanged between rule systems. Uncertainty is an intrinsic feature of real world knowledge, hence it is important to take it into account when building logic rule formalisms. However, the set of truth values in the RIF Basic Logic Dialect (RIF-BLD) currently consists of only two values (t and f), although the RIF Framework for Logic Dialects (RIF-FLD) allows for more. In this paper, we first present two techniques of encoding uncertain knowledge and its fuzzy semantics in RIF-BLD presentation syntax. We then propose an extension leading to an Uncertainty Rule Dialect (RIF-URD) to support a direct representation of uncertain knowledge. In addition, rules in Logic Programs (LP) are often used in combination with the other widely-used knowledge representation formalism of the Semantic Web, namely Description Logics (DL), in many application scenarios of the Semantic Web. To prepare DL as well as LP extensions, we present a fuzzy extension to Description Logic Programs (DLP), called Fuzzy DLP, and discuss its mapping to RIF. Such a formalism not only combines DL with LP, as in DLP, but also supports uncertain knowledge representation. 4

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“…This is another reason to state that (I) does not imply (II) for t-norms without zero divisors. General expressions about the transitivity that P and I satisfy when R is T-transitive can be found in Díaz et al (2010).…”

Section: Proofmentioning

confidence: 99%

On complete fuzzy preorders and their characterizations

2010

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In the context of crisp or classical relations, one may find several alternative characterizations of the concept of a total preorder. In this contribution, we first discuss the way of translating those characterizations to the framework of fuzzy relations. Those new properties depend on t-norms. We focus on two important families of t-norms, namely those that do not admit zero divisors and those that are rotation invariant. For these families, we study whether or not the properties shown for fuzzy relations lead to characterizations of complete fuzzy preorders. Special attention is paid to the minimum operator, which shows the best behaviour in preserving most of the characterizations known for crisp relations.

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General results on the decomposition of transitive fuzzy relations

Cited by 29 publications

References 34 publications

Fuzzy Strict Preference Relations Compatible With Fuzzy Orderings

Fuzzy Strict Preference Relations Compatible With Fuzzy Orderings

A Fuzzy Logic-Based Approach to Uncertainty Treatment in the Rule Interchange Format: From Encoding to Extension

On complete fuzzy preorders and their characterizations

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