Group decision making with incomplete interval-valued q-rung orthopair fuzzy preference relations

In this paper, we focus on group decision making (GDM) with incomplete interval-valued q-rung orthopair fuzzy preference relations (IV q-ROFPRs). On the basis of interval-valued q-rung orthopair fuzzy set (IV q-ROFS), the novel concepts of IV q-ROFPR, incomplete IV q-ROFPR, additive consistent IV q-ROFPR, and acceptably additive consistent IV q-ROFPR are proposed. Subsequently, two optimization models are established for deriving the complete IV q-ROFPRs and acceptably additive consistent IV q-ROFPRs. Inspired by the Markov model, the weight-generating method is designed to obtain the weights of decision makers. For the purpose of improving the consensus level, a modification process is constructed under the consideration of minimizing the deviations between the adjusted IV q-ROFPRs and the original ones. Afterward, a goal programming model is constructed to derive the normalized q-rung orthopair fuzzy ( q-ROF) priority weights. The interval-valued q-rung orthopair fuzzy (IV q-ROF) priority weights of alternatives are further determined. Thus, an algorithm for the GDM method with IV q-ROFPRs is completed. Finally, the applications to examples and comparisons with previous approaches are conducted to illustrate the validity and effectiveness of the proposed method.