Analytical Hierarchy Process based Multi-Person Decision Making using Hesitant Fuzzy Preference Relations

Abstract

The problem of multi-person decision-making (MPDM) possesses a solution, the quality of which may be influenced by the inclinations of experts. In certain essential conditions, employing the fuzzy MPDM approach can yield more acceptable and efficient outcomes for the selection of optimal alternatives. This study introduces a consensus-based technique designed for the selection of alternatives within an environment characterized by hesitant fuzzy preference relations (HFPRs). At the initial stage, we introduced a scheme grounded in Lukasiewicz transitivity ( - transitivity) to derive normalized hesitant fuzzy preference relations (NHFPRs). Within this framework, a consensus-based model is formulated. Subsequently, a transitive closure formula is defined to generate -consistent HFPRs, yielding symmetrical matrices. Following this, a consistency analysis is conducted to assess the consistency levels of information provided by decision-makers (DMs) and, consequently, to allocate consistency weights to them. The ultimate priority weights vector of DMs is computed by combining consistency weights with predefined priority weights, if applicable. The consensus process determines whether data aggregation and selection of the optimal alternative should proceed. An enhancement mechanism is employed to refine the consensus measure among DMs, involving the introduction of an identifier for identifying weak positions in cases of inadequate consensus. The proposed approach is formulated using the Analytical Hierarchy Process (AHP) framework criteria, and the decision matrix is created through the utilization of consistent hesitant fuzzy preference relations (HFPRs