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.
Highlights
Making decisions is an integral part of human life
A new procedure to normalize hesitant fuzzy preference relations (HFPRs) is proposed, because in most of the cases for any two hesitant fuzzy preference values (HFPVs) hij and hlm, hij 6= |hlm | for i, j, l, m ∈ {1, 2, 3, . . . , n} where hij and |hlm | represent the cardinalities of sets of pairwise comparisons at ijth and lmth positions
After getting motivation from Xu et al [31]’s work, we put forward a new scheme to estimate the elements to be added in HFPVs regarding the normalization of the given HFPRs
Summary
Making decisions is an integral part of human life. Many of them require “rational” or “good”. Zhang [28] developed a goal-programming model for an incomplete HFPR and derive priority weight vectors based on α and β normalization methods respectively. Based on the additive consistency and multiplicative consistency of incomplete HFPRs in local and group decision-making settings, Xu et al [21] designed mixed 0–1 programming models to find a priority weight vector from incomplete HFPRs. To estimate the missing elements for an incomplete HFPR, Khalid and Beg [35] proposed an algorithm by utilizing hesitant upper bound condition for the DMs. The stability of preference relations plays a critical role in the decision-making phase in the pairwise assessments of DM’s preferences [36].
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