A Graded Quadrivalent Logic for Ordinal Preference Modelling: Loyola–Like Approach

We extend a quadrivalent logic of Belnap to graded truth values in order to handle graded relevance of positive and negative arguments provided in preferential information concerning ranking of a finite set of alternatives. This logic is used to design the preference modelling and exploitation phases of decision aiding with respect to the ranking problem. The graded arguments are presented on an ordinal scale and their aggregation leads to preference model in form of four graded outranking relations (true, false, unknown and contradictory). The exploitation procedure combines the min-scoring procedure with the leximin rule. Aggregation of positive and negative arguments as well as exploitation of the resulting outranking relations is concordant with an advice given by St. Ignatius of Loyola (1548) “how to make a good choice”.

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