Pure linguistic PROMETHEE I and II methods for heterogeneous MCGDM problems

Abstract

The PROMETHEE methods basic principle is focused on a pairwise comparison of alternatives for each criterion, selecting a preference function type that often requires parameters in order to obtain a preference value. When a MCGDM problem is defined in an heterogeneous context, an adequate and common approach is to unify the involved information in linguistic values. However, for each criterion, there is a difficulty to select the specific preference function and define its parameters because they are expressed by crisp values in the unit interval, when the information involved in the problem has been unified into linguistic values. In this paper, a methodology for modeling linguistic preference functions in order to facilitate the selecting of each linguistic preference function type and the definition of its parameters is proposed, providing a more realistic definition of the criteria. Therefore, a generic linguistic preference function is proposed whose inputs and outputs are linguistic values. According to the generic linguistic preference function, six basic preference function types are extended for linguistic values. To do so, a linguistic difference function between linguistic values is defined, being its output, the input of the linguistic preference function. Furthermore, the proposed methodology is integrated in linguistic PROMETHEE I and II for heterogeneous MCGDM problems to obtain partial rankings and a full ranking of alternatives. So, the methodology provides pure linguistic PROMETHEE I and II that offer interpretability and understandability. Finally, the feasibility and applicability of pure linguistic PROMETHEE I and II are illustrated in a case study for the selection of a green supplier.

Keywords:

• PROMETHEE
• linguistic preferences
• linguistic difference function
• linguistic preference functions
• heterogeneous information
• MCGDM
• outranking method