A method for multiple pseudo-criteria decision problems

Abstract Most complex decision problems involve conflicting multicriteria to be reconciled. It is not uncommon that the numerical values of alternatives of some criteria are subject to imprecision, uncertainty, and indetermination. The concept of pseudo-criterion and its two thresholds allow them to be taken into account. So far, outranking relation methods, which are called ELECTRE I–IV and others, in which an outranking relation between alternatives is constructed from pseudo-criteria have been developed. Among others, ELECTRE III is the most familiar and has been widely used. The purpose of this paper is to propose a new procedure for treating the pseudo-criterion based on the ternary AHP. This procedure differs from ELECTRE III and requires only the incomplete information on the weights but not precise weights. Strict preference, weak preference, and indifference relations associated with a pseudo-criterion are formulated by a ternary comparison. In general, the procedures for dealing with the pseudo-criterion necessarily involve a certain amount of arbitrariness. Therefore, it is preferable to derive the rankings of alternatives from several procedures for the pseudo-criterion in order to promote complementary viewpoints. Comparing our procedure with ELECTRE III, the strengths and weaknesses of the proposed procedure are discussed. Scope and purpose Most decision problems involve multiple and conflicting objectives, goals, or attributes. In the past three decades, many approaches have been developed. These include decision analysis based on multiattribute utility theory and interactive approaches based on the progressive articulation of preferences. They are built on sound theoretical foundations but rely on strict assumptions about the underlying preference structure. It is not uncommon that the numerical values of alternatives of some criteria are imprecise and ambiguous in complex decision problems. In such cases, the above approaches may not be appropriate. To cope with them, the concept of pseudo-criterion was introduced. So far, the outranking relation methods based on the pseudo-criterion which do not require the assumption of transitivity nor the complete comparability in the underlying preference structure have been developed. In this paper, we propose a new procedure for treating the pseudo-criterion based on the ternary AHP that differs from the outranking relation methods. In general, the procedures for dealing with the pseudo-criterion necessarily involve a certain amount of arbitrariness. Therefore, it is preferable to derive the rankings of alternatives from several procedures based on the pseudo-criterion in order to promote complementary viewpoints.