Managing acceptability and eliciting weights for hesitant fuzzy preference relations with additive consistency

Hesitant fuzzy preference relations (HFPRs) provide an effective tool for capturing the uncertainty and imprecision present in decision makers’ (DMs) judgments. As a significant modelling approach, HFPRs contribute to preserving the coherence of preference data and enhancing the credibility of ultimate decision outcomes. Consistency and uncertainty exert a significant impact on the logical consistency and ultimate decision outcome. We introduce two novel definitions about additive consistency in HFPRs: arithmetic-mean-based HFPR consistency, upper and lower bounds based HFPR consistency. A novel acceptability framework for HFPRs that incorporates two aspects: acceptable consistency and acceptable indefiniteness. When unacceptability of an HFPR occurs, we design modification models that corrects it by minimising both the quantity of adjusted elements and the deviation from the initial matrix. Considering that DMs may sometimes provide incomplete information, we develop models for incomplete HFPRs to predict absent values and ultimately ascertain the priority weights. Finally, to illustrate its utility, the method is examined through numerical examples and comparative studies, assessing both its feasibility and effectiveness.