Fuzzy mathematical programming approach to heterogeneous multiattribute decision-making with interval-valued intuitionistic fuzzy truth degrees

Considering the hesitancy degrees on pair-wise comparisons of alternatives as interval-valued intuitionistic fuzzy (IVIF) sets (IVIFSs), we develop a new fuzzy mathematical programming method for solving heterogeneous multiattribute decision-making problems based on the Linear Programming Technique for Multidimensional Analysis of Preference. In this method, IVIFSs, intuitionistic fuzzy sets (IFSs), trapezoidal fuzzy numbers, linguistic variables, intervals and real numbers are used to represent multiple types of attribute values and the attribute weights are not completely known. The preference relations between alternatives given by decision maker are expressed with IVIFSs of ordered pairs of alternatives. The consistency and inconsistency indices are defined as IVIFSs on the basis of comparisons of alternatives with IVIF truth degrees. The attribute weights and fuzzy ideal solution (FIS) are estimated through constructing a fuzzy mathematical programming model, which is solved by the technically developed method of IVIF mathematical programming. Hereby the distances of alternatives to the FIS are computed to rank the alternatives. Some generalization and discussion on the constructed IVIF mathematical programming model are also presented. A green supplier selection example is provided to illustrate the effectiveness of the proposed model and method. The comparison analyses verify the superiorities of the proposed method.