European Journal of Operational Research 53 (1991) 337-347 337 North-Holland Theory and Methodology Cardinal ranking of alternative actions: extension of the PROMETHEE method D. Diakoulaki and N. Koumoutsos Department of Chemical Engineering, National Technical University of Athens, Athens 15773, Greece Received March 1989; revised July 1989 Abstract: The method presented in this paper is an extension of the PROMETHEE, one of the most known multicriteria outranking methods. This extension consists in a more detailed investigation of the dif- ferences existing among the performances of the actions examined, achieved through the notion of ideal and anti-ideal alternative. Hence, the state of strict preference relating various pairs of actions can be differentiated with reference to the extreme performances attained by the alternatives under consideration. The more accurate description of the reality leads to a relatively more reliable ranking of the available solutions and allows the exploitation of the results for the construction of a cardinal scale, assigning to each action a numerical value between 0 and 1. The quantitative differentiation of the alternatives, thus achieved, gives another dimension of information, which is extremely useful for the decision making process. A comparative study of the two methods shows the greater sensitivity of EXPROM and its ability to reflect in the quantitative results any probable deviation in the initial data of a problem. This sensitivity is accompanied with a greater stability, due to the smoothing of the discontinuities characterizing most preference functions in PROMETHEE. Keywords: Decision, multiple criteria programming, fuzzy sets 1. Introduction The PROMETHEEmethod, as well as ELECTRE III are two of the most known and widely applied techniques belonging to the family of multicriteria outranking methods [1--4]. They are based on the construction of an outranking relation in the set of actions examined and provide partial preorders, such that some of these actions can remain incom- parable. The information included in a partial preorder of alternative solutions, especially with regard to incomparabilities, is very useful for the decision making process. The PROMETHEE method advances the exploitation of the outranking rela- tions to a step forward, providing a complete preorder of the actions, which excludes incom- parabilities between them. Such a preorder con- stitutes a more concrete, but also a less realistic tool for the decision maker. Both partial and complete preorders express preferences by means of an ordinal scale: solu- tions are rank-ordered, so in the case where two actions are neither equal, nor incomparable, we can say only that solution a is preferred to b, but we cannot say by how much. No value associated to each of them exists, providing a measure of the global preference of the decision maker. This con- stitutes the main disadvantage of the outranking methods in regard to the multiattribute utility theory (MAUT) methods. 0377-2217/91/$03.50 ~') 1991 - Elsevier Science Publishers B.V. (North-Holland)