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

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.