Utility function of fuzzy preferences on a countable set under max-*-transitivity

Fono, Louis Aimé; Andjiga, Nicolas Gabriel

doi:10.1007/s00355-006-0190-3

Cited by 19 publications

(16 citation statements)

References 18 publications

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“…In addition, several authors have shown that various forms of transitivity give rise to utility representable or numerically representable relations, also called fuzzy weak orders -see e.g. [26,35,36,37,38]. We will use the term ranking representability to establish a link with machine learning.…”

Section: Relationships With Fuzzy Set Theorymentioning

confidence: 99%

Learning Valued Relations from Data

Waegeman

Pahikkala

Airola

et al. 2011

Advances in Intelligent and Soft Computing

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Driven by a large number of potential applications in areas like bioinformatics, information retrieval and social network analysis, the problem setting of inferring relations between pairs of data objects has recently been investigated quite intensively in the machine learning community. To this end, current approaches typically consider datasets containing crisp relations, so that standard classification methods can be adopted. However, relations between objects like similarities and preferences are in many real-world applications often expressed in a graded manner. A general kernel-based framework for learning relations from data is introduced here. It extends existing approaches because both crisp and valued relations are considered, and it unifies existing approaches because different types of valued relations can be modeled, including symmetric and reciprocal relations. This framework establishes in this way important links between recent developments in fuzzy set theory and machine learning. Its usefulness is demonstrated on a case study in document retrieval.

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Section: Relationships With Fuzzy Set Theorymentioning

confidence: 99%

Learning Valued Relations from Data

Waegeman

Pahikkala

Airola

et al. 2011

Advances in Intelligent and Soft Computing

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“…We also remark that in recent literature ranking representability has been mainly studied for fuzzy preference relations. Billot (1995) and Fono & Andjiga (2007) establish links between the ranking representability of fuzzy preference relations and different types of fuzzy transitivity. For reciprocal relations we can derive a similar connection.…”

Section: Ranking Representability Of Preference Modelsmentioning

confidence: 99%

Learning to rank: a ROC-based graph-theoretic approach

Waegeman

2009

4OR-Q J Oper Res

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This note summarizes the main results presented in the author's Ph.D. thesis, supervised by Luc Boullart and Bernard De Baets. The thesis was defended on 14th October 2008 at Universiteit Gent. It is written in English and available for download at http://users.ugent.be/similar to wwaegemn/thesis.pdf. The work deals with preference learning, with emphasis on the ranking and ordinal regression machine learning settings and their connections to decision theory. Based on receiver operator characteristics analysis and graph theory, new performance measures are proposed to evaluate this type of models, and new algorithms are presented to compute and optimize these performance measures efficiently. Furthermore, the relationship with other settings like pairwise preference learning and multi-class classification is discussed

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“…In particular the term "total" is replaced by "connected" in Fono and Andjiga [2] and Fono and Salles [3].…”

Section: Definition 14mentioning

confidence: 99%

“…The literature concerning the (continuous) real representation of a fuzzy binary relation R : X × X → [0, 1] is concentrated on the cases of fuzzy total preorders (see e.g., Billot [1], Fono and Andjiga [2], Fono and Salles [3], and Agud et al [4]), and respectively fuzzy interval orders (see e.g., Mishra et Srivastava [5]). For any two points x, y ∈ X, R(x, y) is interpreted as "the degree to which the alternative x ∈ X is at least as good as the alternative y ∈ X", or equivalently as "the degree to which x ∈ X is weakly preferred to y ∈ X".…”

Section: Introductionmentioning

confidence: 99%