Theorem Verification of the Quantifier-Guided Dominance Degree with the Mean Operator for Additive Preference Relations

José Ramón Trillo, Francisco Javier Cabrerizo, Francisco Chiclana, María Ángeles Martínez, Francisco Mata and Enrique Herrera-Viedma
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José Ramón Trillo: Department of Computer Science and Artificial Intelligence, Andalusian Research Institute in Data Science and Computational Intelligence, DaSCI, University of Granada, 18071 Granada, Spain
Francisco Javier Cabrerizo: Department of Computer Science and Artificial Intelligence, Andalusian Research Institute in Data Science and Computational Intelligence, DaSCI, University of Granada, 18071 Granada, Spain
Francisco Chiclana: Institute of Artificial Intelligence, Faculty of Computing, Engineering and Media, De Montfort University, Leicester LE1 9BH, UK
María Ángeles Martínez: Department of Social Work and Social Services, University of Granada, 18001 Granada, Spain
Francisco Mata: Department of Computer Science, Andalusian Research Institute in Data Science and Computational Intelligence, DaSCI, University of Jaén, 23071 Jaén, Spain
Enrique Herrera-Viedma: Department of Computer Science and Artificial Intelligence, Andalusian Research Institute in Data Science and Computational Intelligence, DaSCI, University of Granada, 18071 Granada, Spain

Mathematics, 2022, vol. 10, issue 12, 1-10

Abstract: Deciding which film is the best or which portfolio is the best for investment are examples of decisions made by people every day. Decision-making systems aim to help people make such choices. In general, a decision-making system processes and analyses the available information to arrive at the best alternative solution of the problem of interest. In the preference modelling framework, decision-making systems select the best alternative(s) by maximising a score or choice function defined by the decision makers’ expressed preferences on the set of feasible alternatives. Nevertheless, decision-making systems may have logical errors that cannot be appreciated by developers. The main contribution of this paper is the provision of a verification theorem of the score function based on the quantifier-guided dominance degree (QGDD) with the mean operator in the context of additive preference relations. The provided theorem has several benefits because it can be applied to verify that the result obtained is correct and that there are no problems in the programming of the corresponding decision-making systems, thus improving their reliability. Moreover, this theorem acts on different parts of such systems, since not only does the theorem verify that the order of alternatives is correct, but it also verifies that the creation of the global preference relation is correct.

Keywords: quantifier-guided dominance degree; verification; additive matrix; decision-making system; selection process (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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