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Geometric consistency of triangular fuzzy multiplicative preference relation and its application to group decision making

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KNOWLEDGE AND INFORMATION SYSTEMS 2021年第1期63卷 21-38页

作者： Wang, Feng Guangdong Univ Finance & Econ Sch Business Adm Guangzhou Peoples R China

The triangular fuzzy multiplicative preference relation (TFMPR) has attracted the attention of many scholars. This paper investigates the geometric consistency of TFMPR and applies it to group decision making (GDM). Firstly, by introducing two parameters, a triangular fuzzy number is transformed into an interval. According to the geometric consistency of interval multiplicative preference relation (IMPR), the geometric consistency of TFMPR is defined. Then, two corresponding IMPRs are extracted from the TFMPR by programming models in the majority case and minority case, respectively. Using the constructed linear programming models, two interval priority weight vectors are obtained from the two extracted IMPRs, respectively. Combining two interval priority weight vectors, a linear programming model is established to derive the triangular fuzzy priority weights. Subsequently, the closeness degrees of alternatives by experts are defined to obtain the group utility indices and individual regret indices of alternatives. Then, the compromise indices of alternatives are calculated considering experts' compromise attitude. By minimizing the compromise indices of alternatives, a multi-objective programming model is constructed to obtain experts' weights. By aggregating the individual TFMPRs, the collective TFMPR is obtained to derive the triangular fuzzy priority weights. Using the arithmetic mean values, the ranking order of alternatives is generated. Therefore, a method is proposed to solve GDM with TFMPRs. Finally, a performance evaluation example of precise poverty alleviation is provided to illustrate the advantage of the proposed method.

关键词： triangular fuzzy multiplicative preference relation Geometric consistency Group decision making Interval multiplicative preference relation

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Acceptability measurement and priority weight elicitation of triangular fuzzy multiplicative preference relations based on geometric consistency and uncertainty indices

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INFORMATION SCIENCES 2017年 402卷 105-123页

作者： Wang, Zhou-Jing Lin, Jian Zhejiang Univ Finance & Econ Sch Informat Hangzhou 310018 Zhejiang Peoples R China

This paper investigates consistency and uncertainty measurements as well as acceptability checking for triangular fuzzy multiplicative preference relations (TFMPRs). A geometric consistency index is proposed to measure the consistency degree of a TFMPR, and thresholds of acceptable consistency are discussed for TFMPRs. Uncertainty indices are introduced to measure indeterminacy degrees of triangular fuzzy judgments and of TFMPRs and a notion of acceptable TFMPRs are put forward by considering both acceptable consistency and acceptable uncertainty in TFMPRs. We also explore the elicitation of triangular fuzzy weights from acceptable TFMPRs and the aggregation of local triangular fuzzy weights for solving hierarchical multi-criteria decision-making problems. A geometric mean-based equation and a logarithmic least square model are developed to elicit normalized acceptable triangular fuzzy multiplicative weights from an acceptable TFMPR. An equation and a linear program are established to transform triangular fuzzy multiplicative weights into triangular fuzzy additive weights. A geometric weighting-based equation and a pair of linear programs are devised to generate global priority fuzzy weights from local triangular fuzzy multiplicative weights. Three numerical examples, including a hierarchical multi-criteria decision-making problem, are used to illustrate how to apply the developed framework, and comparative studies are provided to show its availability and advantages. (C) 2017 Elsevier Inc. All rights reserved.

关键词： Multi-criteria decision making triangular fuzzy multiplicative preference relation Consistency Acceptability triangular fuzzy multiplicative weight

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A Consistency-Based Method to Decision Making with triangular fuzzy multiplicative preference relations

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INTERNATIONAL JOURNAL OF fuzzy SYSTEMS 2017年第5期19卷 1317-1332页

作者： Tang, Jie Meng, Fanyong Cent S Univ Business Sch Changsha 410083 Hunan Peoples R China Nanjing Audit Univ Sch Int Audit Nanjing 211815 Jiangsu Peoples R China

triangular fuzzy multiplicative preference relations (TFMPRs) enable decision makers to apply triangular fuzzy numbers to denote their preferences, which can express their vagueness and fuzziness. Consistency analysis is an important research topic that can guarantee logical ranking order. Considering previous research regarding the consistency of TFMPRs, several issues and limitations exist with these relations. The researches cannot cope well with certain situations, such as unacceptably consistent TFMPRs and incomplete TFMPRs. In this paper, a new consistency definition for TFMPRs is defined that can overcome the issues in the previous concepts. Next, several desirable properties of the definition are discussed, and the relationship between the new definition and two existing ones is presented. A linear goal programming model is also built to judge the consistency of TFMPRs, and a method is introduced to obtain an acceptably consistent TFMPR from an inconsistent one. Furthermore, several goal programming models are constructed to estimate missing values in an incomplete TFMPR. Finally, a decision-making method with TFMPRs is developed. Illustrative examples are offered to demonstrate the concrete application of the developed procedure, and a comparison analysis is also made.

关键词： Decision making triangular fuzzy multiplicative preference relation Consistency analysis Programming model

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An axiomatic property based triangular fuzzy extension of Saaty's consistency

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COMPUTERS & INDUSTRIAL ENGINEERING 2019年 137卷 106086-000页

作者： Wang, Zhou-Jing Zhejiang Univ Finance & Econ Sch Informat Hangzhou 310018 Zhejiang Peoples R China

The fuzzy analytic hierarchy process (FAHP) is a widely applied fuzzy multi-criteria decision making method. In triangular FAHP, consistency of triangular fuzzy multiplicative preference relations (TFMPRs) plays a very important role for checking the quality of human fuzzy judgments. This paper introduces some indices to measure fuzziness of triangular fuzzy judgments and row fuzziness proportionalities in a TFMPR. An expected interval based possibility degree formula is developed to compare two triangular fuzzy judgments and used to judge whether the average-based intensity of a triangular fuzzy judgment is changed. The paper proposes four axiomatic properties aimed at characterizing multiplicative consistency of TFMPRs, and illustrates that four known consistency definitions fail to meet all the four axiomatic properties. By analyzing the axiomatic property of restriction on ambiguity of single judgments, a constrained triangular fuzzy multiplication based transitivity equation is devised and used to construct a triangular fuzzy matrix from a TFMPR. Based on the constructed fuzzy matrix, the paper establishes an ordinary triangular fuzzy multiplication based transitivity equation to define consistency of TFMPRs. Important properties of consistent TFMPRs are offered to demonstrate that all the four axiomatic properties are satisfied by the proposed consistency definition. Three numerical examples are given to illustrate the use of the proposed consistency model and the obtained properties for judging consistency of TFMPRs and determining unknown values of incomplete TFMPRs.

关键词： Analytic hierarchy process triangular fuzzy multiplicative preference relation Axiomatic property Consistency Fuzziness

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