A General Method for Consistency Improving in Decision-Making Under Uncertainty

Abstract

In order to ascertain and solve a particular Multiple Criteria Decision Making (MCDM) problem, frequently a diverse group of experts must share their knowledge and expertise, and thus uncertainty arises from several sources. In those cases, the Multiplicative Preference Relation (MPR) approach can be a useful technique. An MPR is composed of judgements between any two criteria components which are declared within a crisp rank and to express decision maker(s) (DM) preferences. Consistency of an MPR is obtained when each expert has her/his information and, consequently, her/his judgments free of contradictions. Since inconsistencies may lead to incoherent results, individual Consistency should be sought after in order to make rational choices. In this paper, based on the Hadamard’s dissimilarity operator, a methodology to derive intervals for MPRs satisfying a consistency index is introduced. Our method is proposed through a combination of a numerical and a nonlinear optimization algorithms. As soon as the synthesis of an interval MPR is achieved, the DM can use these acceptably consistent intervals to express flexibility in the manner of her/his preferences, while accomplishing some a priori decision targets, rules and advice given by her/his current framework. Thus, the proposed methodology provides reliable and acceptably consistent Interval MPR, which can be quantified in terms of Row Geometric Mean Method (RGMM) or the Eigenvalue Method (EM). Finally, some examples are solved through the proposed method in order to illustrate our results and compare them with other methodologies.