Probabilistic AHP and TOPSIS for multi-attribute decision-making under uncertainty

Abstract

One challenging aspect in designing complex engineering systems is the task of making informed design decisions in the face of uncertainty. <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1,2</sup> This paper presents a probabilistic methodology to facilitate such decision-making, in particular under uncertainty in decision-maker preferences. This methodology builds on the frequently-used multi-attribute decision-making techniques of the Analytic Hierarchy Process (AHP) and Technique for Order Preference by Similarity to Ideal Solution (TOPSIS), and it overcomes some typical limitations that exist in relying on these deterministic techniques. The methodology is divided into three segments, each of which consists of multiple steps. The first segment (steps 1-4) involves setting up the problem by defining objectives, priorities, uncertainties, design attributes, and candidate designs. The second segment (steps 5-8) involves applications of AHP and TOPSIS using AHP prioritization matrices generated from probability density functions. The third segment (steps 9-10) involves visualization of results to assist in selecting a final design. A key characteristic measured in these final steps is the consistency with which a design ranks among the top several alternatives. An example satellite orbit and launch vehicle selection problem illustrates the methodology throughout the paper.