Sustainable Decision Making Using a Consensus Model for Consistent Hesitant Fuzzy Preference Relations—Water Allocation Management Case Study

Abstract

This paper presents an improved consensus-based procedure to handle multi-person decision making (MPDM) using hesitant fuzzy preference relations (HFPRs) which are not in normal format. At the first level, we proposed a ukasiewicz transitivity (TL-transitivity) based scheme to get normalized hesitant fuzzy preference relations (NHFPRs), subject to which, a consensus-based model is established. Then, a transitive closure formula is defined to construct TL-consistent HFPRs and creates symmetrical matrices. Following this, consistency analysis is made to estimate the consistency degrees of the information provided by the decision-makers (DMs), and consequently, to assign the consistency weights to them. The final priority weights vector of DMs is calculated after the combination of consistency weights and predefined priority weights (if any). The consensus process concludes whether the aggregation of data and selection of the best alternative should be originated or not. The enhancement mechanism is indulged in improving the consensus measure among the DMs, after introducing an identifier used to locate the weak positions, in case of the poor consensus reached. In the end, a comparative example reflects the applicability and the efficiency of proposed scheme. The results show that the proposed method can offer useful comprehension into the MPDM process.

Keywords

• consistency weights
• fuzzy preference relation (FPR)
• hesitant fuzzy preference relation (HFPR)
• Łukasiewicz consistency
• normal hesitant fuzzy preference relation (NHFPR)