Multiattribute decision making based on nonlinear programming methodology, particle swarm optimization techniques and interval-valued intuitionistic fuzzy values

Abstract In this paper, we propose a new multiattribute decision making (MADM) method by applying the nonlinear programming (NLP) methodology and particle swarm optimization (PSO) techniques using interval-valued intuitionistic fuzzy values (IVIFVs) to conquer the drawbacks of Chen and Huang's MADM method (2017), which has three drawbacks, i.e., (1) multiple different preference orders (POs) of alternatives are obtained in some situations, (2) the PO of alternatives cannot be distinguished in some circumstances, and (3) the PO of alternatives cannot be obtained in some circumstances. Moreover, the proposed MADM method also can conquer the shortcomings of Chen and Chiou's MADM method (2015), Li's MADM method (2010) and Zhitao and Yingjun's method (2011).