A fuzzy approach to preference structure in multicriteria ranking

The family of Promethee methods for multicriteria ranking of a finite set of alternatives is well known in literature and used in practice. In order to express her/his preference structure the decision maker is asked to select, for each criterion, a preference function from a predefined set. It is a function that maps differences between criterion values of pairs of alternatives into interval [0, 1]. For each preference function, the decision maker has to fix parameters that define indifference and strict preference areas. A weak point in Promethee methods is that imprecision in judgement of preference functions is handled by relatively simple and rigid mathematical artifacts. We propose fuzzy sets theory and associate approximate reasoning as an appropriate framework to imitate human reasoning in expressing a preference structure. For each criterion, the decision maker uses linguistic terms ‘small difference’, ‘medium difference’, and ‘big difference’, which enable him/her to express his/her preference structure in a linguistic and thus more natural way. These descriptors interpret the system of decision maker's values and are context dependent. We introduce fuzzy IF–THEN rules that relate the difference of criterion values to the preference function. The proposed modification extends the applicability of Promethee methods significantly, because it enables ranking of alternatives in the case when criteria values are fuzzy variables. The corresponding software is developed and tested on a number of examples.