Fuzzy LINMAP approach to heterogeneous MADM considering comparisons of alternatives with hesitation degrees

Multiattribute decision making (MADM) with multiple formats of information, which is called heterogeneous MADM for short, is very complex and interesting in applications. The purpose of this paper is to extend the Linear Programming Technique for Multidimensional Analysis of Preference (LINMAP) for solving heterogeneous MADM problems which involve intuitionistic fuzzy (IF) sets (IFSs), trapezoidal fuzzy numbers (TrFNs), intervals and real numbers. In this method, DM's preference is given through pair-wise comparisons of alternatives with hesitation degrees which are represented as IFSs. The IF consistency and inconsistency indices are defined on the basis of pair-wise comparisons of alternatives. Each alternative is assessed on the basis of its distance to a fuzzy ideal solution (FIS) unknown a priori. Based on the defined IF consistency and inconsistency indices, we construct a new fuzzy mathematical programming model, which is solved by the developed method of fuzzy mathematical programming with IFSs. Once the FIS and the attribute weights are obtained, we can calculate the distances of all alternatives to the FIS, which are used to determine the ranking order of the alternatives. A supplier selection example is presented to demonstrate the validity and applicability of the proposed method.