A fuzzy extension of Saaty's priority theory

Abstract

We present a fuzzy method for choosing among a number of alternatives under conflicting decision criteria: a fuzzy version of Saaty's pairwise comparison method (1980) extended by de Graan (1980) and Lootsma (1981).Each ratio expressing the relative significance of a pair of factors is displayed in a matrix, from which suitable weights can be extracted. Since these ratios are essentially fuzzy-they express the opinion of a decision-maker on the importance of a pair of factors-we have adapted the above-mentioned method in such a way, that decision-makers are asked to express their opinions in fuzzy numbers with triangular membership functions. We apply the method at two distinct levels: first to find fuzzy weights for the decision criteria, and second, to find fuzzy weights for the alternatives under each of the decision criteria. By a suitable combination of these results, we obtain fuzzy scores for the alternatives, as well as their sensitivities. Using these fuzzy scores, the decision-makers should be able to make a choice for one of the alternatives.