A new approach of Romero’s extended lexicographic goal programming: fuzzy extended lexicographic goal programming

Abstract

Goal programming (GP) is perhaps one of the most widely used approaches in the field of multicriteria decision making. The major advantage of the GP model is its great flexibility which enables the decision maker to easily incorporate numerous variations on constraints and goals. Romero provides a general structure, extended lexicographic goal programming (ELGP) for GP and some multiobjective programming approaches. In this work, we propose the extension of this unifying framework to fuzzy multiobjective programming. Our extension is carried out by several methodologies developed by the authors in the fuzzy GP approach. An interval GP model has been constructed where the feasible set has been defined by means of a relationship between fuzzy numbers. We will apply this model to our fuzzy extended lexicographic goal programming (FELGP). The FELGP is a general primary structure with the same advantages as Romero’s ELGP and moreover it has the capacity of working with imprecise information. An example is given in order to illustrate the proposed method.