考虑均衡型指标的多指标决策方法研究
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摘要
多指标决策是与多个指标有关的有限方案选择问题,它在经济管理及工程设计等领域有着广泛的实际背景,因此研究有效的多指标决策方法具有重要的现实意义。但是,在一些现实决策问题中,决策者在进行方案选择的过程中,不仅仅需要考虑决策者给出的关于方案的评价信息和指标权重信息,还需要考虑决策者给出的关于指标的期望要求,这种需要同时考虑方案的评价信息、指标权重以及期望信息的多指标决策问题,称为考虑指标期望的多指标决策问题。指标期望的类型有很多种,如决策者期望某一指标的评价值越大越好、越小越好或者在某一区间内最好等。有时决策者期望各指标评价值越均衡越好,称之为均衡型期望,将考虑指标带有均衡型期望的多指标决策问题称为考虑均衡型指标的多指标决策问题。考虑均衡型指标的多指标决策问题有着广泛实际背景,如供应商选择、人才选聘等问题,但是相关决策方法的研究还不多见,因此,如何解决考虑均衡型指标的多指标决策问题,具有学术研究价值和现实意义。
本文在总结分析考虑指标期望和均衡型指标的多指标决策研究现状与发展的基础上,对考虑均衡型指标的多指标决策问题进行了较为深入的研究。其研究目的和意义在于：在理论和方法研究层面,给出考虑均衡型指标的多指标决策问题的框架,并提出考虑均衡型指标的多指标决策方法和考虑部分均衡型指标的多指标决策方法,丰富或完善关于多指标决策理论和方法的研究；在应用研究层面,基于给出的决策方法,选择供应商选择及科研助理选聘的决策问题进行算例分析,验证本文给出方法的有效性和实用性,对投资决策、服务评价等实际决策问题具有指导和借鉴意义。
本文主要完成了以下几方面的研究工作：
(1)给出了解决考虑均衡型指标的多指标决策问题的框架。首先,提出了考虑均衡型指标的多指标决策问题的概念；然后,给出了求解考虑均衡型指标的多指标决策问题的原则；最后,给出了求解考虑均衡型指标的多指标决策问题的基本框架,为相关问题的研究提供了一般性的理论指导框架和分析框架,并为研究问题的扩展与应用提供了理论基础。
(2)给出了考虑均衡型指标的多指标决策方法。针对指标评价值为清晰数、区间数和语言短语的混合型多指标决策问题,给出了一种基于混合相对贴近度和混合指标均衡度的的多指标决策方法。首先将多种形式的评价信息都转化为梯形模糊数的形式,然后依据混合TOPSIS方法计算各方案的混合相对贴近度,并计算各方案的混合指标均衡度,在此基础上,通过对混合相对贴近度和混合指标均衡度进行几何加权计算方案的综合排序值,据此进行方案排序。
(3)给出了考虑部分均衡型指标的多指标决策方法。针对指标评价值全部为清晰数的多指标决策问题,给出一种基于方案相对贴近度和部分指标均衡度的多指标决策方法。首先依据TOPSIS方法计算各方案的相对贴近度,然后计算各方案的部分指标均衡度,在此基础上,通过对方案相对贴近度和部分指标均衡度进行几何加权计算方案的综合排序值,最后依据方案的综合排序值进行方案排序。
(4)通过对供应商选择以及科研助理选聘方面的一些决策问题进行算例分析,验证了提出方法的有效性和科学性,为本文给出的决策方法在经济管理及工程系统等领域的潜在应用提供有益的参考。
本文对考虑均衡型指标的多指标决策方法进行了系统的研究,不仅丰富了多指标决策的研究成果,也为实际决策问题提供了思路和指导。
Multiple attribute decision making (MADM) refers to the problem of selecting among alternatives associated with multiple attributes. It is a problem with extensive theoretical and practical backgrounds, so it has very important practical significance to research on MADM methods. In many real-world problems, it not only needs to consider the evaluation of alternatives and attribute weights, but also to consider the aspiration requirements on attributes given by decision makers in the process of selecting alternatives. The MADM problem taking into account alternative evaluation information, attribute weights and aspiration information called the MADM problems considering attributes aspiration. There are many types of attributes aspiration, for example, the decision maker expect that the greater evaluation of alternatives are, the better the alternative is, or the smaller evaluation of alternatives are, the better the alternative is, or the alternative is always better in a certain interval, sometimes the decision maker expect the more balanced the alternative evaluation values are, the better the alternative is, which be called as equilibrium aspiration. We call the MADM problem with equilibrium aspiration as the MADM problem considering equilibrium attribute. It is a problem with extensive theoretical and practical backgrounds, such as vendor selection, talent selection and so on. The research on how to solve the MADM problem considering equilibrium attribute has higher research value and academically significance.
On the basis of a comprehensive review of the research status and development of MADM research with attributes aspiration and equilibrium attribute, this thesis makes thorough research on the MADM problem considering equilibrium attribute. The purpose and significance of the research are as follows:in the theory and method research aspect, proposes the framework of the MADM problems considering equilibrium attribute, and proposes MADM methods considering equilibrium attribute, enriches or improves the research of MADM. In practical research aspect, take some decision problem of vendor selection and talent selection as numerical examples to illustrate the feasibility and validity of the proposed methods. It has great guidance and reference significance to project investment decision, service evaluation and so on.
The thesis has mainly finished the following works:
(1) The theoretical framework of solving the MADM problems considering equilibrium attribute is proposed. Firstly, the concept of the MADM problems considering equilibrium attribute is proposed. Then the principle of solving the MADM problems considering equilibrium attribute is given. Finally, the framework of solving the MADM problems considering equilibrium attribute is proposed. It provides a general theoretical guidance and an analytical framework, provides a theoretical basis on the expansion and application of the research questions.
(2) The MADM methods considering equilibrium attribute is proposed. With regard to the MADM problems where the attribute values of the alternatives are crisp numbers、interval numbers and linguistic terms, a MADM method based on hybrid relative closeness coefficient and hybrid attribute equilibrium degrees is proposed. Firstly, the multiple formats information is transformed into the form of trapezoidal fuzzy numbers. Then the hybrid relative closeness coefficient is calculated based on hybrid TOPSIS method, and the hybrid attribute equilibrium degree is calculated. On the basis, the comprehensive ranking values of alternatives are calculated by the geometric series of hybrid relative closeness coefficients and hybrid attribute equilibrium degrees. Finally, the alternatives are ranking according with each alternative's comprehensive ranking values.
(3) The MADM methods considering partial equilibrium attribute is proposed. With regard to the MADM problems where the attribute values of the alternatives are crisp numbers, a MADM method based on relative closeness coefficient and partial attribute equilibrium degree is proposed. Firstly, the relative closeness coefficient is calculated based on TOPSIS method. Then the partial attribute equilibrium degree is calculated. On the basis, the comprehensive ranking values of alternatives are calculated by the geometric series of relative closeness coefficients and partial attribute equilibrium degrees. Finally, the alternatives are ranking according with each alternative's comprehensive ranking values.
(4) Some numerical examples in the vendor selection and talent selection problem have been indicated and verified the feasibility, effectiveness and scientific of the proposed methods. It provided a useful reference for potential applications of the proposed methods in economic management, engineering systems and other relevant fields.
This thesis analyzes the methods of MADM methods with equilibrium attribute, not only enriched the research of MADM, but also provided the thought and guidance for the decision making problems in the real practices.
本文在总结分析考虑指标期望和均衡型指标的多指标决策研究现状与发展的基础上,对考虑均衡型指标的多指标决策问题进行了较为深入的研究。其研究目的和意义在于：在理论和方法研究层面,给出考虑均衡型指标的多指标决策问题的框架,并提出考虑均衡型指标的多指标决策方法和考虑部分均衡型指标的多指标决策方法,丰富或完善关于多指标决策理论和方法的研究；在应用研究层面,基于给出的决策方法,选择供应商选择及科研助理选聘的决策问题进行算例分析,验证本文给出方法的有效性和实用性,对投资决策、服务评价等实际决策问题具有指导和借鉴意义。
本文主要完成了以下几方面的研究工作：
(1)给出了解决考虑均衡型指标的多指标决策问题的框架。首先,提出了考虑均衡型指标的多指标决策问题的概念；然后,给出了求解考虑均衡型指标的多指标决策问题的原则；最后,给出了求解考虑均衡型指标的多指标决策问题的基本框架,为相关问题的研究提供了一般性的理论指导框架和分析框架,并为研究问题的扩展与应用提供了理论基础。
(2)给出了考虑均衡型指标的多指标决策方法。针对指标评价值为清晰数、区间数和语言短语的混合型多指标决策问题,给出了一种基于混合相对贴近度和混合指标均衡度的的多指标决策方法。首先将多种形式的评价信息都转化为梯形模糊数的形式,然后依据混合TOPSIS方法计算各方案的混合相对贴近度,并计算各方案的混合指标均衡度,在此基础上,通过对混合相对贴近度和混合指标均衡度进行几何加权计算方案的综合排序值,据此进行方案排序。
(3)给出了考虑部分均衡型指标的多指标决策方法。针对指标评价值全部为清晰数的多指标决策问题,给出一种基于方案相对贴近度和部分指标均衡度的多指标决策方法。首先依据TOPSIS方法计算各方案的相对贴近度,然后计算各方案的部分指标均衡度,在此基础上,通过对方案相对贴近度和部分指标均衡度进行几何加权计算方案的综合排序值,最后依据方案的综合排序值进行方案排序。
(4)通过对供应商选择以及科研助理选聘方面的一些决策问题进行算例分析,验证了提出方法的有效性和科学性,为本文给出的决策方法在经济管理及工程系统等领域的潜在应用提供有益的参考。
本文对考虑均衡型指标的多指标决策方法进行了系统的研究,不仅丰富了多指标决策的研究成果,也为实际决策问题提供了思路和指导。
Multiple attribute decision making (MADM) refers to the problem of selecting among alternatives associated with multiple attributes. It is a problem with extensive theoretical and practical backgrounds, so it has very important practical significance to research on MADM methods. In many real-world problems, it not only needs to consider the evaluation of alternatives and attribute weights, but also to consider the aspiration requirements on attributes given by decision makers in the process of selecting alternatives. The MADM problem taking into account alternative evaluation information, attribute weights and aspiration information called the MADM problems considering attributes aspiration. There are many types of attributes aspiration, for example, the decision maker expect that the greater evaluation of alternatives are, the better the alternative is, or the smaller evaluation of alternatives are, the better the alternative is, or the alternative is always better in a certain interval, sometimes the decision maker expect the more balanced the alternative evaluation values are, the better the alternative is, which be called as equilibrium aspiration. We call the MADM problem with equilibrium aspiration as the MADM problem considering equilibrium attribute. It is a problem with extensive theoretical and practical backgrounds, such as vendor selection, talent selection and so on. The research on how to solve the MADM problem considering equilibrium attribute has higher research value and academically significance.
On the basis of a comprehensive review of the research status and development of MADM research with attributes aspiration and equilibrium attribute, this thesis makes thorough research on the MADM problem considering equilibrium attribute. The purpose and significance of the research are as follows:in the theory and method research aspect, proposes the framework of the MADM problems considering equilibrium attribute, and proposes MADM methods considering equilibrium attribute, enriches or improves the research of MADM. In practical research aspect, take some decision problem of vendor selection and talent selection as numerical examples to illustrate the feasibility and validity of the proposed methods. It has great guidance and reference significance to project investment decision, service evaluation and so on.
The thesis has mainly finished the following works:
(1) The theoretical framework of solving the MADM problems considering equilibrium attribute is proposed. Firstly, the concept of the MADM problems considering equilibrium attribute is proposed. Then the principle of solving the MADM problems considering equilibrium attribute is given. Finally, the framework of solving the MADM problems considering equilibrium attribute is proposed. It provides a general theoretical guidance and an analytical framework, provides a theoretical basis on the expansion and application of the research questions.
(2) The MADM methods considering equilibrium attribute is proposed. With regard to the MADM problems where the attribute values of the alternatives are crisp numbers、interval numbers and linguistic terms, a MADM method based on hybrid relative closeness coefficient and hybrid attribute equilibrium degrees is proposed. Firstly, the multiple formats information is transformed into the form of trapezoidal fuzzy numbers. Then the hybrid relative closeness coefficient is calculated based on hybrid TOPSIS method, and the hybrid attribute equilibrium degree is calculated. On the basis, the comprehensive ranking values of alternatives are calculated by the geometric series of hybrid relative closeness coefficients and hybrid attribute equilibrium degrees. Finally, the alternatives are ranking according with each alternative's comprehensive ranking values.
(3) The MADM methods considering partial equilibrium attribute is proposed. With regard to the MADM problems where the attribute values of the alternatives are crisp numbers, a MADM method based on relative closeness coefficient and partial attribute equilibrium degree is proposed. Firstly, the relative closeness coefficient is calculated based on TOPSIS method. Then the partial attribute equilibrium degree is calculated. On the basis, the comprehensive ranking values of alternatives are calculated by the geometric series of relative closeness coefficients and partial attribute equilibrium degrees. Finally, the alternatives are ranking according with each alternative's comprehensive ranking values.
(4) Some numerical examples in the vendor selection and talent selection problem have been indicated and verified the feasibility, effectiveness and scientific of the proposed methods. It provided a useful reference for potential applications of the proposed methods in economic management, engineering systems and other relevant fields.
This thesis analyzes the methods of MADM methods with equilibrium attribute, not only enriched the research of MADM, but also provided the thought and guidance for the decision making problems in the real practices.
引文
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