A note on “A goal programming model for incomplete interval multiplicative preference relations and its application in group decision-making”

2015 ◽  
Vol 247 (3) ◽  
pp. 867-871 ◽  
Author(s):  
Zhou-Jing Wang
Keyword(s):  
Decision Making ◽  
Group Decision Making ◽  
Goal Programming ◽  
Group Decision ◽  
Programming Model ◽  
Preference Relations ◽  
Goal Programming Model ◽  
Multiplicative Preference Relations

A GOAL PROGRAMMING APPROACH TO GROUP DECISION MAKING WITH INCOMPLETE FUZZY AND INTERVAL PREFERENCE RELATIONS

2012 ◽  
Vol 20 (03) ◽  
pp. 355-367
Author(s):  
JIANG JIANG ◽  
XUAN LI ◽  
YINGWU CHEN ◽  
DAWEI TANG
Keyword(s):  
Decision Making ◽  
Group Decision Making ◽  
Goal Programming ◽  
Group Decision ◽  
Programming Model ◽  
Decision Makers ◽  
Programming Approach ◽  
Interval Numbers ◽  
Preference Relations ◽  
Priority Vector

In order to solve group decision making (GDM) problems where the preference relations are provided by decision makers with incomplete fuzzy and interval numbers, this paper develops a GDM approach on the basis of multiple objective optimization and goal programming methods. The proposed approach first analyzes the two types of preference relations and then builds their respective optimization models. Subsequently, an integrated programming model combining the two preference relations is developed to minimize the inconsistency among the decision makers' opinions. By solving the programming model, the ranking of alternatives or selection of the most desirable alternative can be obtained using the intermediate priority vector. Two numerical examples including incomplete fuzzy and interval preference relations are examined to illustrate and show the applicability of the proposed approach.

Generalized Linguistic Ordered Weighted Hybrid Logarithm Averaging Operators and Applications to Group Decision Making

2015 ◽  
Vol 23 (03) ◽  
pp. 421-442 ◽  
Author(s):  
Jinpei Liu ◽  
Huayou Chen ◽  
Ligang Zhou ◽  
Zhifu Tao
Keyword(s):  
Decision Making ◽  
Group Decision Making ◽  
Goal Programming ◽  
Group Decision ◽  
Programming Model ◽  
Averaging Operators ◽  
New Approach ◽  
Goal Programming Model ◽  
Weighting Vector ◽  
Partial Weight

In this paper, we develop the generalized linguistic weighted logarithm averaging (GLWLA) operator and the generalized linguistic ordered weighted logarithm averaging (GLOWLA) operator in the group decision making under the linguistic surrounding. Then some properties of the families of the GLOWLA operator by different weighting vector are investigated. Furthermore, we present the generalized linguistic ordered weighted hybrid logarithm averaging (GLOWHLA) operator, which extends the GLOWLA operator. We also construct a nonlinear goal programming model to determine GLOWHLA weights from observational linguistic variable values under partial weight information. Finally, a numerical example is given to illustrate the new approach to evaluating university faculty for tenure and promotion, which indicates the feasibility and effectiveness of the new approach.

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.

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