A new method for Atanassov's interval-valued intuitionistic fuzzy MAGDM with incomplete attribute weight information

This paper develops a new method for solving multiple attribute group decision-making (MAGDM) problems with Atanassov's interval-valued intuitionistic fuzzy values (AIVIFVs) and incomplete attribute weight information. Firstly, we investigate the asymptotic property of the Atanassov's interval-valued intuitionistic fuzzy (AIVIF) matrix. It is demonstrated that after applying weights an infinite number of times, all elements in an AIVIF matrix will approach the same AIVIFV without regard to the initial values of elements. Then, the weight of each decision maker (DM) with respect to every attribute is determined by considering the similarity degree and proximity degree simultaneously. To avoid weighting an AIVIF matrix too many times, the collective decision matrix is transformed into an interval matrix using the risk coefficient of DMs. Subsequently, to derive the attribute weights objectively, we construct a multi-objective interval-programming model that is solved by transforming it into a linear program. The ranking order of alternatives is generated by the comprehensive interval values of alternatives. Finally, an example of a research and development (R&D) project selection problem is provided to illustrate the implementation process and applicability of the method developed in this paper.