OWA-BASED NONLINEAR MATHEMATICAL PROGRAMMING APPROACH TO FUZZY MULTI-ATTRIBUTE GROUP DECISION MAKING WITH LINGUISTIC VARIABLES

The purpose of this paper is to develop a nonlinear programming model and method for solving fuzzy multi-attribute group decision making (FMAGDM) problems with linguistic variables. In this methodology, alternatives are assessed on qualitative attributes using linguistic terms from the designated linguistic term set, which can be expressed with the triangular fuzzy number set designated a priori. Alternatives for decision makers are assessed on the basis of the distances between the ordered weighted averaging (OWA) comprehensive value and the group best alternative which is unknown a priori. The group best alternative is then estimated through solving an auxiliary nonlinear programming model based on the concept that the sum of the distances of alternatives from the group best alternative for the decision makers should be as small as possible. The obtained group best alternative can be expressed using the designated triangular fuzzy numbers, which are corresponding to the designated linguistic terms. A numerical example is examined to demonstrate the difference between the proposed method and the generalized induced OWA operator method.