Fractional programming methodology for multi-attribute group decision-making using IFS

Owing to more vague concepts frequently represented in decision data, mathematical objects introduced by K.T. Atanassov and studied under the name “intuitionistic fuzzy set” (IFS) are more flexibly used to model real-life decision situations. The aim of this paper is to develop a new methodology for solving multi-attribute group decision-making problems using IFS, in which multiple attributes are explicitly considered. In this methodology, for each decision maker in the group two auxiliary fractional programming models are derived from the TOPSIS to determine the relative closeness coefficient intervals of alternatives, which are aggregated for the group to generate the ranking order of all alternatives by computing their optimal degrees of membership based on the ranking method of interval numbers. The implementation process of the method proposed in this paper is illustrated with a numerical example.