Abstract
This paper presents consensus based multi-person decision making (MPDM) using consistency graphs (additive consistent and order consistent) in a fuzzy environment. At the first level, consistency analysis is put forward after defining consistent fuzzy preference graph (CFPG) with the help of additive transitivity. This analysis further leads us to determine priority weights vector of the decision-makers (DMRs) after evaluation consistency weights. At the second level, the consensus analysis helps us to determine whether the selection process should be initiated or not. If the consensus degree amongst DMRs does not reach a minimum acceptable level, then the enhancement mechanism plays a central role to improve the consensus level by giving suitable suggestions to DMRs. In the end, the weighted sum operator (WSO) is used to get aggregated consistency fuzzy preference graph (AgCFPG) and the order consistency property provides us sufficient information to rank the alternatives.
Highlights
AND PRELIMINARY RESULTSDecision making (DM) is a rational process being used to choose the best option(s) from a set of different options, it pledges when someone has to do something but does not know what
GROUP DECISION MAKING USING FUZZY PREFERENCE GRAPHS This section presents an hybrid consistency and consensus based GDM using fuzzy preference graph (FPG) under the transitive consistency, and final decision is established based on order consistency property
The DMRs provide their average information in form fuzzy preference graphs Gqfp shown in the Figure 3, where vertices denote the franchises of the school system and weighted directed edges pairwise preference values, as: To reach the acceptable result, following steps have to be performed: (i) Consistency analysis: Consistency analysis derive us to measure and allocate the weights to the experts in order to have quality information
Summary
Decision making (DM) is a rational process being used to choose the best option(s) from a set of different options, it pledges when someone has to do something but does not know what. Numerous consensus models have been proposed in literature: Herrera-Viedma et al [8], in 2002, presented a consensus based scheme to handle GDM situations in different preference formats, utility values, and multiplicative preference relations. In 2007, Herrera-Viedma et al [10] proposed a procedure to investigate the consistency level and consensus measure for incomplete fuzzy preference relations and a feedback mechanism was introduces to improve the consistency and consensus degrees, simultaneously. In 2016, Zhang et al [14] developed a consensus building method based on multiplicative consistency for GDM with IRPRs. Zhang and Pedrycz [15], in 2018, presented goal programming models in order to enhance consistency and consensus measures for intuitionistic fuzzy and multiplicative preference relations, respectively. Definition 5 Additive Consistent Fuzzy Preference Graph: A FPG is said to be additive consistent if for all intermediate alternatives wik = wij + wjk − 0.5.
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