A qualitative approach to face uncertainty in decision models

Abstract

Inaccurate determination, uncertainty, imprecision and ambiguity are often present in complex decision situations where decision aid is requested. Instead of reducing complexity via quantitative models of preferences, as traditional preference modeling does, it may be necessary to represent these situations explicitly. There exist operational methods that face these problems, the principal reference being the partial comparability theory. The lack of an axiomatization however limits the operational potentialities of this theory. In the paper an axiomatic foundation of the partial comparability theory is outlined based on a sound and complete four valued logic (the truth values “true”, “false”, “unknown”, “contradictory” are accepted). This logic is extended to the first order predicate calculus. Four basic preference relations are thus defined, namely: strict preference, weak preference, indifference and incomparability. The operational perspectives are discussed in the paper as some problems in multicriteria methods can be solved in a much easier and natural way. Moreover non monotonic reasoning devices could be built enhancing the potentialities of the theory.