A Reliable Method for Consistency Improving of Interval Multiplicative Preference Relations Expressed under Uncertainty

Abstract

When a diverse group of experts share their knowledge to ascertain and solve a particular multiple criteria decision-making (MCDM) problem, uncertainty arises from several sources. In those cases, the interval multiplicative preference relation (IMPR) approach is a useful technique when verifying consistency. As illustrated in this paper, the validation and the improvement of consistency require robust analysis tools and algorithms. The proposed methodology provides reliable and consistent IMPR, which can be quantified in terms of row geometric mean method (RGMM) or the eigenvalue method (EM). In this manner, decision makers’ choices are implicitly including their uncertainty while maintaining acceptable consistency. The present approach is based on the Hadamard’s dissimilarity operator and through an algorithm, the derivation of a reliable and consistent IMPR is synthesized. In order to illustrate our results and compare them appropriately with other methodologies, a few examples are addressed and solved.