Linear Programming-Based TOPSIS Method for Solving MADM Problems with Three Parameter IVIFNs

The aim of this paper is to develop a TOPSIS approach using fractional programming techniques for effective modelling of real-life multiattribute decision-making (MADM) problems in interval-valued intuitionistic fuzzy (IVIF) settings by considering hesitancy degree as a dimension together with membership and non-membership degrees. In three-parameter characterizations of intuitionistic fuzzy (IF) sets, a weighted absolute distance between two IF sets with respect to IF weights is defined and employed in TOPSIS to formulate intervals of relative closeness coefficients (RCCs). The lower and upper bounds of the intervals of RCCs are given by a pair of nonlinear fractional programming models which are further transformed into two auxiliary linear programming models using mathematical methods and fractional programming technique. A simpler technique is also proposed for estimating the optimal degrees as performance values of alternatives from the possibility degree matrix generated by pairwise comparisons of RCC intervals. The validity and effectiveness of the proposed approach are demonstrated through two numerical examples.