Title: Preference Representation in Multiple Criteria Decision Aiding with Seven-Valued Logic
Abstract: We present a methodology for preference modelling able to represent multidimensional and conflicting preferences when true, false, and unknown arguments contribute to the partial comparability of alternatives. The basic idea of this methodology is to define an extended preference structure using a new seven-valued logic. The seven-valued logic naturally arises within the rough set theory framework, allowing to distinguish vagueness due to imprecision from ambiguity due to coarseness. Recently, we discussed its utility for reasoning about data describing multi-attribute classification. Here, we present how the seven-valued logic, as well as the other logics that derive from it, can be used to represent preferences in Multiple Criteria Decision Aiding (MCDA). In particular, we propose procedures for aggregating multiple criteria using value functions and outranking preference models, while accounting for a plurality of perspectives and indeterminacy in preference model parameters. This results in a mix of true, false, and unknown preference information. We demonstrate that our approach effectively addresses common challenges in preference modelling for MCDA, such as uncertainty, imprecision, and ill-determination of performances and preferences. To this end, we present a specific procedure to construct a seven-valued preference relation and use it to define recommendations that consider robustness concerns by utilizing multiple value functions or outranking models representing the decision maker’s preferences. Moreover, we discuss the main properties of the proposed seven-valued preference structure and compare it with current approaches in MCDA, such as ordinal regression, robust ordinal regression, stochastic multiattribute acceptability analysis, stochastic ordinal regression, and so on. We illustrate and discuss the application of our approach using a didactic example. Finally, we propose directions for future research and potential applications of the proposed methodology.
