Some properties of linguistic preference relation and its ranking in group decision making

2010 ◽  
Vol 21 (2) ◽  
pp. 244-249 ◽  
Author(s):  
Yejun Xu ◽  
Qingli Oa ◽  
Xinwang Liu
Keyword(s):  
Decision Making ◽  
Group Decision Making ◽  
Group Decision ◽  
Preference Relation ◽  
Linguistic Preference Relation

Expected consistency-based model and multiplicative DEA cross-efficiency for group decision-making with incomplete distribution linguistic preference relations

2021 ◽  
pp. 1-21
Author(s):  
Jinpei Liu ◽  
Longlong Shao ◽  
Ligang Zhou ◽  
Feifei Jin
Keyword(s):  
Decision Making ◽  
Group Decision Making ◽  
Optimization Model ◽  
Group Decision ◽  
Preference Relation ◽  
Preference Relations ◽  
Priority Vector ◽  
Linguistic Preference Relation ◽  
Multiplicative Preference Relations ◽  
High Consistency

Faced with complex decision problems, Distribution linguistic preference relation (DLPR) is an effective way for decision-makers (DMs) to express preference information. However, due to the complexity of the decision-making environment, DMs may not be able to provide complete linguistic distribution for all linguistic terms in DLPRs, which results in incomplete DLPRs. Therefore, in order to solve group decision-making (GDM) with incomplete DLPRs, this paper proposes expected consistency-based model and multiplicative DEA cross-efficiency. For a given incomplete DLPRs, we first propose an optimization model to obtain complete DLPR. This optimization model can evaluate the missing linguistic distribution and ensure that the obtained DLPR has a high consistency level. And then, we develop a transformation function that can transform DLPRs into multiplicative preference relations (MPRs). Furthermore, we design an improved multiplicative DEA model to obtain the priority vector of MPR for ranking all alternatives. Finally, a numerical example is provided to show the rationality and applicability of the proposed GDM method.

AN APPROACH TO GROUP DECISION MAKING BASED ON INCOMPLETE LINGUISTIC PREFERENCE RELATIONS

2005 ◽  
Vol 04 (01) ◽  
pp. 153-160 ◽  
Author(s):  
ZESHUI XU
Keyword(s):  
Decision Making ◽  
Group Decision Making ◽  
Group Decision ◽  
Preference Relation ◽  
Linguistic Variables ◽  
Preference Relations ◽  
Weighted Arithmetic ◽  
Operational Laws ◽  
Linguistic Preference Relation

In this paper, we introduce some operational laws of linguistic variables and define some linguistic preference relations such as incomplete linguistic preference relation and improved linguistic preference relation, etc. We then utilize the extended arithmetic averaging (EAA) operator and the extended weighted arithmetic averaging (EWAA) operator to develop an approach to group decision making based on incomplete linguistic preference relations. Finally, we give an illustrative example to verify the developed approach.

EOWA AND EOWG OPERATORS FOR AGGREGATING LINGUISTIC LABELS BASED ON LINGUISTIC PREFERENCE RELATIONS

2004 ◽  
Vol 12 (06) ◽  
pp. 791-810 ◽  
Author(s):  
Z. S. XU
Keyword(s):  
Decision Making ◽  
Group Decision Making ◽  
Group Decision ◽  
Preference Relation ◽  
Geometric Mean ◽  
Weighted Averaging ◽  
Preference Relations ◽  
Ordered Weighted Averaging ◽  
Linguistic Preference Relation ◽  
Linguistic Labels

In this paper, we define two types of linguistic preference relations (multiplicative linguistic preference relation and additive linguistic preference relation), and study some of their desirable properties. We introduce the extended geometric mean (EGM) operator, extended arithmetical averaging (EAA) operator, extended ordered weighted averaging (EOWA) operator and extended ordered weighted geometric (EOWG) operator. An approach based on the EGM and EOWG operators and multiplicative linguistic preference relations and an approach based on the EAA and EOWA operators and additive linguistic preference relations are proposed to ranking the alternatives in the group decision-making problems. Finally, we give a numerical example to illustrate the developed approaches.

ON COMPATIBILITY OF UNCERTAIN MULTIPLICATIVE LINGUISTIC PREFERENCE RELATIONS AND ITS APPLICATION TO GROUP DECISION MAKING

2013 ◽  
Vol 21 (01) ◽  
pp. 9-28 ◽  
Author(s):  
LIGANG ZHOU ◽  
HUAYOU CHEN
Keyword(s):  
Decision Making ◽  
Group Decision Making ◽  
Group Decision ◽  
Preference Relation ◽  
Scientific Basis ◽  
Decision Makers ◽  
Preference Relations ◽  
Compatibility Index ◽  
Optimal Weights ◽  
Linguistic Preference Relation

The aim of this work is to develop a new compatibility for the uncertain multiplicative linguistic preference relations and determine the optimal weights of decision makers (DMs), which are very suitable to deal with group decision making (GDM) problems involving uncertain multiplicative linguistic preference relations. First, the concepts of compatibility degree and compatibility index for the two uncertain multiplicative linguistic preference relations are proposed. Then we prove the property that the synthetic uncertain linguistic preference relation is of acceptable compatibility under the condition that uncertain multiplicative linguistic preference relations given by DMs are all of acceptable compatibility with a specific linguistic preference relation, which is the scientific basis of using the uncertain multiplicative linguistic preference relations in the GDM. Next, in order to determine the weights of decision makers, we construct an optimal model based on the criterion of minimizing the compatibility index. Finally, we develop an application of the optimal weights approach compared with the equal weights approach where we analyze a GDM regarding the selection of investment.

scholarly journals Large-scale group decision-making based on Pythagorean linguistic preference relations using experts clustering and consensus measure with non-cooperative behavior analysis of clusters

2021 ◽  
Author(s):  
Prasenjit Mandal ◽  
Sovan Samanta ◽  
Madhumangal Pal
Keyword(s):  
Decision Making ◽  
Group Decision Making ◽  
Large Scale ◽  
Group Decision ◽  
Cooperative Behavior ◽  
Preference Relation ◽  
Consensus Model ◽  
Proposed Model ◽  
Linguistic Preference Relation ◽  
Consensus Index

AbstractTo represent qualitative aspect of uncertainty and imprecise information, linguistic preference relation (LPR) is a powerful tool for experts expressing their opinions in group decision-making (GDM) according to linguistic variables (LVs). Since for an LV, it generally means that membership degree is one, and non-membership and hesitation degrees of the experts cannot be expressed. Pythagorean linguistic numbers/values (PLNs/PLVs) are novel choice to address this issue. The aim of this paper which we propose a GDM problem involved a large number of the experts is called large-scale GDM (LSGDM) based on Pythagorean linguistic preference relation (PLPR) with a consensus model. Sometimes, the experts do not modify their opinions to achieve consensus. Therefore, the experts’ proper opinions’ management with their non-cooperative behaviors (NCBs) is necessary to establish a consensus model. At the same time, it is essential to ensure the proper adjustment of the credibility information. The proposed model using grey clustering method is divided with the experts’ similar evaluations into a subgroup. Then, we aggregate the experts’ evaluations in each cluster. A cluster consensus index (CCI) and a group consensus index (GCI) are presented to measure consensus level among the clusters. Then, we provide a mechanism for managing the NCBs of the clusters, which contain two parts: (1) NCB degree is defined using CCI and GCI for identifying the NCBs of the clusters; (2) implemented the weight punishment mechanism of the NCBs clusters to consensus improvement. Finally, an example is offered for usefulness of the proposed approach.

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