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A theoretical look at ordinal classification methods based on reference sets composed of characteristic actions

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  • Eduardo Fernandez
  • Jorge Navarro
  • Efrain Solares

Abstract

From a theoretical view, this paper addresses the general problem of designing ordinal classification methods based on comparing actions with subset of actions, which are representative of their classes (categories). The basic demand of the proposal consists in setting a relational system (D, S), where S is a reflexive relation compatible with the preferential order of the set of classes, and D is a transitive relation such that D is a subset of S. Different ordinal classification methods can be derived from diverse model of preferences fulfilling the basic conditions on S and D. Two complementary assignment procedures compose each method, which correspond through the transposition operation and should be used complementarily. The methods work under relatively slight conditions on the representative actions and satisfy several fundamental properties. ELECTRE TRI-nC, INTERCLASS-nC, and the hierarchical ELECTRE TRI-nC with interacting criteria, can be considered as particular cases of this general framework.

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  • Eduardo Fernandez & Jorge Navarro & Efrain Solares, 2021. "A theoretical look at ordinal classification methods based on reference sets composed of characteristic actions," Papers 2107.04656, arXiv.org.
    • Handle: RePEc:arx:papers:2107.04656
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    References listed on IDEAS

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    1. Fernandez, Eduardo & Navarro, Jorge, 2011. "A new approach to multi-criteria sorting based on fuzzy outranking relations: The THESEUS method," European Journal of Operational Research, Elsevier, vol. 213(2), pages 405-413, September.
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    5. Fernández, Eduardo & Figueira, José Rui & Navarro, Jorge, 2019. "An interval extension of the outranking approach and its application to multiple-criteria ordinal classification," Omega, Elsevier, vol. 84(C), pages 189-198.
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