On Consensus in Group Decision Making Based on Fuzzy Preference Relations (original) (raw)
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Consensus-Based Multi-Person Decision Making Using Consistency Fuzzy Preference Graphs
IEEE Access, 2019
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 (A g CFPG) and the order consistency property provides us sufficient information to rank the alternatives. INDEX TERMS Fuzzy graph (FG), fuzzy preference graph (FPG), additive consistent fuzzy preference graph (ACFPG), order consistent fuzzy preference graph (OCFPG), fuzzy compatibility graph (FCG).
International Journal of Information Technology & Decision Making, 2014
As we may have a set of possible values when comparing alternatives (or criteria), the hesitant fuzzy preference relation becomes a suitable and powerful technique to deal with this case. This paper mainly focuses on the consistency of the hesitant fuzzy preference relation. Before that, we explore some properties of the hesitant fuzzy preference relation and develop some new aggregation operators. Then we introduce the concepts of multiplicative consistency, perfect multiplicative consistency and acceptable multiplicative consistency for a hesitant fuzzy preference relation, based on which, two algorithms are given to improve the inconsistency level of a hesitant fuzzy preference relation. Furthermore, the consensus of group decision making is studied based on the hesitant fuzzy preference relations. Finally, several illustrative examples are given to demonstrate the practicality of our algorithms.
Mathematics, 2019
In this paper, a consensus-based method for multi-person decision making (MPDM) using product transitivity with incomplete fuzzy preference relations (IFPRs) is proposed. Additionally, an average aggregation operator has been used at the first level to estimate the missing preference values and construct the complete fuzzy preference relation (FPR). Then it is confirmed to be product consistent by using the transitive closure formula. Following this, weights of decision makers (DMs) are evaluated by merging consistency weights and predefined priority weights (if any). The consistency weights for the DMs are estimated through product consistency investigation of the information provided by each DM. The consensus process determines whether the selection procedure should be initiated or not. The hybrid comprises of a quitting process and feedback mechanism, and is used to enhance the consensus level amongst DMs in case of an inadequate state. The quitting process arises when some DMs d...
Information Sciences, 2016
Triangular fuzzy numbers are effective in modeling imprecise and uncertain information, and have been widely applied in decision making. This paper uses a cross-ratio-expressed triplet to characterize a positive triangular fuzzy number, and introduces notions of crossratio-expressed triangular fuzzy numbers (CRETFNs) and triangular fuzzy additive reciprocal preference relations (TFARPRs). We present transformation methods between TFARPRs and triangular fuzzy multiplicative reciprocal preference relations, and develop operational laws of CRETFNs, such as complement, addition, multiplication and power. A crossratio-expressed triangular fuzzy multiplication based transitivity equation is established to define multiplicative consistency of TFARPRs. The new consistency captures Tanino's multiplicative consistency among the cross-ratio-expressed modal values, and geometric consistency of the interval fuzzy preference relation constructed from lower and upper support values of cross-ratio-expressed triangular fuzzy judgments. Some desirable properties are furnished for multiplicatively consistent TFARPRs. We propose a cross-ratio-expressed triangular fuzzy weighted geometric operator to aggregate CRETFNs, and extend it to fuse TFARPRs. Score and uncertainty index functions are defined and employed to devise a novel comparison method for CRETFNs. A detailed procedure is put forward to solve group decision making problems with TFARPRs. Six numerical examples are provided to illustrate the validity and applicability of the proposed models.
Consensus and Consistency Level Optimization of Fuzzy Preference Relation: A Soft Computing Approach
In group decision making (GDM) problems fuzzy preference relations (FPR) are widely used for representing decision makers' opinions on the set of alternatives. In order to avoid misleading solutions, the study of consistency and consensus has become a very important aspect. This article presents a simulated annealing (SA) based soft computing approach to optimize the consistency/consensus level (CCL) of a complete fuzzy preference relation in order to solve a GDM problem. Consistency level indicates as expert's preference quality and consensus level measures the degree of agreement among experts' opinions. This study also suggests the set of experts for the necessary modifications in their prescribed preference structures without intervention of any moderator.
Group decision-making model with incomplete fuzzy preference relations based on additive consistency
2007
Abstract In decision-making problems there may be cases in which experts do not have an in-depth knowledge of the problem to be solved. In such cases, experts may not put their opinion forward about certain aspects of the problem, and as a result they may present incomplete preferences, ie, some preference values may not be given or may be missing. In this paper, we present a new model for group decision making in which experts' preferences can be expressed as incomplete fuzzy preference relations.
Some issues on consistency of fuzzy preference relations
2004
In decision making, in order to avoid misleading solutions, the study of consistency when the decision makers express their opinions by means of preference relations becomes a very important aspect in order to avoid misleading solutions. In decision making problems based on fuzzy preference relations the study of consistency is associated with the study of the transitivity property. In this paper, a new characterization of the consistency property defined by the additive transitivity property of the fuzzy preference relations is presented.