Interval hybrid judgment priority vector method in group decision

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

International Journal of Uncertainty Fuzziness and Knowledge-Based Systems ◽

10.1142/s0218488512500183 ◽

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.

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TWO-STAGE PRIORITIZATION PROCEDURE FOR MULTIPLICATIVE AHP-GROUP DECISION MAKING

Technological and Economic Development of Economy ◽

10.3846/tede.2020.12037 ◽

2020 ◽

Vol 26 (2) ◽

pp. 525-545

Author(s):

Changsheng Lin ◽

Gang Kou ◽

Yi Peng ◽

Fawaz E. Alsaadi

Keyword(s):

Decision Making ◽

Group Decision Making ◽

Group Decision ◽

Two Stage ◽

Analytic Hierarchy ◽

Priority Vector ◽

The Individual ◽

Collective Preference ◽

Hierarchy Process ◽

Multiplicative Ahp

In this paper, we propose two-stage prioritization procedure (TSPP) for multiplicative Analytic Hierarchy Process-group decision making (AHP-GDM), which involves determining the group priority vector based on the individual pair-wise comparison matrices (PCMs), simultaneously considering the consensus and consistency of the individual PCMs. The first stage of the TSPP involves checking and revising the individual PCMs for reaching the acceptable consensus and consistency. The second stage of the TSPP involves estimating the group priority vector using Bayesian approach. The main characteristics of the proposed TSPP are as follows: 1) It makes full use of the prior information as well as the sample information during the Bayesian revision of the individual PCMs and the Bayesian estimation of the group priority vector; 2) It ensures that the revised individual PCMs reach the acceptable consensus and consistency; 3) It enriches the aggregation methods for the collective preference in multiplicative AHP-GDM. Finally, two numerical examples are used to evaluate the applicability and effectiveness of the proposed TSPP by the comparisons with several other methods.

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A Similarity Measure-based Optimization Model for Group Decision Making with Multiplicative and Fuzzy Preference Relations

International Journal of Computers Communications & Control ◽

10.15837/ijccc.2017.1.2781 ◽

2016 ◽

Vol 12 (1) ◽

pp. 26 ◽

Cited By ~ 1

Author(s):

Xiangrui Chao ◽

Yi Peng ◽

Gang Kou

Keyword(s):

Decision Making ◽

Group Decision Making ◽

Group Decision ◽

Optimization Methods ◽

Decision Makers ◽

Preference Relations ◽

Priority Vector ◽

Proposed Model ◽

Fuzzy Preference Relations ◽

Preference Structures

Group decision making (GDM) problem based on different preference relations aims to obtain a collective opinion based on various preference structures provided by a group of decision makers (DMs) or experts, those who have varying backgrounds and interests in real world. The decision process in proposed question includes three steps: integrating varying preference structures, reaching consensus opinion, selecting the best alternative. Two major approaches: preference transformation and optimization methods have been developed to deal with the issue in first step. However, the transformation processes causes information lose and existing optimization methods are so computationally complex that it is not easy to be used by management practice. This study proposes a new consistency-based method to integrate multiplicative and fuzzy preference relations, which is based on a cosine similarity measure to derive a collective priority vector. The basic idea is that a collective priority vector should be as similar per column as possible to a pairwise comparative matrix (PCM) in order to assure the group preference has highest consistency for each decision makers. The model is computationally simple, because it can be solved using a Lagrangian approach and obtain a collective priority vector following four simple steps. The proposed method can further used to derive priority vector of fuzzy AHP. Using three illustrative examples, the effectiveness and simpleness of the proposed model is demonstrated by comparison with other methods. The results show that the proposed model achieves the largest cosine values in all three examples, indicating the solution is the nearest theoretical perfectly consistent opinion for each decision makers.

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