基于关联的多属性决策分析理论及其应用研究
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摘要
工程、经济和管理领域中诸多问题均可以抽象为多属性决策分析问题。然而多属性决策分析领域的应用研究成果远远不如其理论研究成果丰富,为了加强多属性决策分析理论和实际决策问题的结合,基于关联的多属性决策分析近年来已成为决策领域的研究热点和前沿课题之一。
基于关联的多属性决策分析领域在许多方面有待进一步研究和完善,例如方案间关联问题、基于属性间关联的变权多属性决策分析问题、贫信息情形下基于属性间关联的层次多属性决策分析问题等。针对这些问题,本文开展了以下几个方面的研究工作。
(1)多属性决策分析中方案间关联研究。定义了多属性决策分析中方案间关联,分析了方案间关联、无关方案独立性和逆序间的关系。通过案例分析和理论推导等方式研究了线性分配方法、加权平均方法和理想解(TOPSIS)方法中方案间关联问题;并在此基础上提出了加权平均的两种保序方法,同时指出绝对TOPSIS方法同样可能引入方案间关联,而成对比较TOPSIS方法的决策结果可能不满足传递性。
(2)基于属性间关联的多属性决策分析理论研究。考虑到λ模糊测度在实际决策问题中应用较为普遍,在已有文献的基础上推导了λ模糊测度及其表现形式间的相互转化关系。考虑到常权决策的不足,在模糊测度理论和传统变权理论的基础上定义了基于关联的变权(R-变权)和状态变权(R-状态变权),并讨论了二者的性质;研究表明R-变权和R-状态变权较传统变权和状态变权更具有一般性。
(3)基于属性间关联的单层多属性决策分析方法研究。在模糊测度和积分理论的基础上提出了关联加权平均方法、关联线性分配方法、关联TOPSIS、关联ELECTRE方法和有序Sugeno方法,研究了这些方法的性质和应用步骤,并通过算例验证了这些方法的有效性。在R-变权理论的基础上讨论了基于属性间关联的变权单层多属性决策分析方法,构建了优化模型求解属性和属性集的权重,并用算例验证了方法和模型有效性。
(4)基于属性间关联的层次多属性决策分析方法研究。在决策实验室分析法和解释结构模型的基础上提出了划分复杂系统层次结构的新方法。分析了基于属性间关联的层次多属性决策分析问题的建模。考虑到实际决策问题中决策者和专家通常较难直接给出参考属性和方案的偏好信息,研究了贫信息情形下基于属性间关联的常权/变权层次多属性决策分析方法,指出基于属性间关联的常权/变权层次多属性决策分析方法较不考虑关联的常权/变权层次多属性决策分析方法更具有一般性。
(5)基于关联的多属性决策分析理论和方法在煤炭企业跨区投资中的应用研究。以煤炭企业跨区投资问题为背景,研究了这一投资决策行为时期选择的影响因素,通过引入基于属性间关联的变权多属性决策分析方法,对煤炭企业跨区投资时期选择问题进行了分析;接着研究了煤炭企业跨区投资区位选择的影响因素,通过引入基于属性间关联的层次多属性决策分析方法,对煤炭企业跨区投资的区位选择问题进行了分析。
Multi-attribute decision making (MADM) has always been a hot spot in research areas due to its wide application in practice fields of engineering, economics and management, where many problems can be modeled by MADM. However, application achievements in MADM are not as abundant as theoretical achievements in this area. In order to strengthen the combination of theory and application of MADM, MADM with interaction has recently turned out to be a forward position technology in decision-making field.
There are still many problems in the area of MADM with interaction needed to be studied and solved in the future, such as the definition of the correlation of alternatives, the MADM problems with variable weights when the criteria are interaction, and the hierarchical MADM problems under the poor-information situation when the attributes are interaction. Therefore, the purpose of this paper is to do a deep research on all of these three questions. The detailed arrangement of this paper stands out as follows:
(1) Study on the interaction among alternatives in MADM. First of all, the interaction among alternatives is defined, and then correlation among the alternatives’interaction, independence of irrelevant alternatives and reversal ranking are analyzed. Second, through case study and theory deduction, alternatives’interaction in linear allocation method, weighted average method and TOPSIS method are studied, based on which two ranking preservation methods for WA (Weighted Average) are proposed. Finally we can draw the conclusion that alternatives’interaction can also be introduced into absolute TOPSIS while the decision-making results from the pairwise comparison of TOPSIS may not satisfy the rule of transitivity.
(2) Study on the MADM theory with attributes’interaction. Considering the wide application ofλfuzzy measure in decision-making problem,λfuzzy measure and its two transforming forms-M?bius transformation and interaction coefficients-are deduced based on the existing references. Taking the shortcoming of the constant weights into consideration, the definitions and properties of the variable weights with interaction (R-variable weights) and local state variable weight vector with interaction (R-local state variable weight) are analyzed based on fuzzy measure theory and traditional variable-weight theory. The research results demonstrate the fact that the R-variable weight (or R-local state variable weight) is the general form of the variable weight (or local state variable weight).
(3) Study on the MADM method with attributes’interaction. The new methods called linear allocation method with interaction, weighted average method with interaction, TOPSIS method with interaction, ELECTRE method with interaction and ordered Sugeno method are proposed in the light of fuzzy measures and integrals. Then the properties and application steps of these methods are also discussed, and their validity is tested with examples. After that, MADM method with variable weights when attributes are interaction is discussed based on the R-variable weights theory. Finally, corresponding model is established to compute the weights of attributes and their coalitions, and one example is used to illustrate the validity of the model as well as the method.
(4) Study on the hierarchical MADM method with attributes’interaction. Firstly, a new method to divide hierarchical structures for complex systems is put forward based on the integration of DEMATEL and ISM, and then the hierarchical MADM model is analyzed. Since it is often difficult for decision makers and experts to provide enough preference information for reference attributes and alternatives, under the poor-information situation the method of solving the hierarchical MADM problem with constant weights and variable weights are analyzed respectively when attributes are interactive. The fact that the hierarchical MADM method with constant weights and variable weights when attributes are interaction are the general form of hierarchical MADM method with constant weights and variable weights when attributes are independent is concluded.
(5) Study on application of the MADM theory with attributes’interaction to trans-regional investment of coal enterprise. Firstly, setting in the background of trans-regional investment of coal enterprise, it studies determinants of period choice, and with variable-weights MADM method with interaction, the period choice for the trans-regional investment of coal enterprise is discussed. Then the determinants of location choice are researched, based on which, the location choice for the trans-regional investment of coal enterprise is solved by hierarchical MADM theory with interaction.
基于关联的多属性决策分析领域在许多方面有待进一步研究和完善,例如方案间关联问题、基于属性间关联的变权多属性决策分析问题、贫信息情形下基于属性间关联的层次多属性决策分析问题等。针对这些问题,本文开展了以下几个方面的研究工作。
(1)多属性决策分析中方案间关联研究。定义了多属性决策分析中方案间关联,分析了方案间关联、无关方案独立性和逆序间的关系。通过案例分析和理论推导等方式研究了线性分配方法、加权平均方法和理想解(TOPSIS)方法中方案间关联问题;并在此基础上提出了加权平均的两种保序方法,同时指出绝对TOPSIS方法同样可能引入方案间关联,而成对比较TOPSIS方法的决策结果可能不满足传递性。
(2)基于属性间关联的多属性决策分析理论研究。考虑到λ模糊测度在实际决策问题中应用较为普遍,在已有文献的基础上推导了λ模糊测度及其表现形式间的相互转化关系。考虑到常权决策的不足,在模糊测度理论和传统变权理论的基础上定义了基于关联的变权(R-变权)和状态变权(R-状态变权),并讨论了二者的性质;研究表明R-变权和R-状态变权较传统变权和状态变权更具有一般性。
(3)基于属性间关联的单层多属性决策分析方法研究。在模糊测度和积分理论的基础上提出了关联加权平均方法、关联线性分配方法、关联TOPSIS、关联ELECTRE方法和有序Sugeno方法,研究了这些方法的性质和应用步骤,并通过算例验证了这些方法的有效性。在R-变权理论的基础上讨论了基于属性间关联的变权单层多属性决策分析方法,构建了优化模型求解属性和属性集的权重,并用算例验证了方法和模型有效性。
(4)基于属性间关联的层次多属性决策分析方法研究。在决策实验室分析法和解释结构模型的基础上提出了划分复杂系统层次结构的新方法。分析了基于属性间关联的层次多属性决策分析问题的建模。考虑到实际决策问题中决策者和专家通常较难直接给出参考属性和方案的偏好信息,研究了贫信息情形下基于属性间关联的常权/变权层次多属性决策分析方法,指出基于属性间关联的常权/变权层次多属性决策分析方法较不考虑关联的常权/变权层次多属性决策分析方法更具有一般性。
(5)基于关联的多属性决策分析理论和方法在煤炭企业跨区投资中的应用研究。以煤炭企业跨区投资问题为背景,研究了这一投资决策行为时期选择的影响因素,通过引入基于属性间关联的变权多属性决策分析方法,对煤炭企业跨区投资时期选择问题进行了分析;接着研究了煤炭企业跨区投资区位选择的影响因素,通过引入基于属性间关联的层次多属性决策分析方法,对煤炭企业跨区投资的区位选择问题进行了分析。
Multi-attribute decision making (MADM) has always been a hot spot in research areas due to its wide application in practice fields of engineering, economics and management, where many problems can be modeled by MADM. However, application achievements in MADM are not as abundant as theoretical achievements in this area. In order to strengthen the combination of theory and application of MADM, MADM with interaction has recently turned out to be a forward position technology in decision-making field.
There are still many problems in the area of MADM with interaction needed to be studied and solved in the future, such as the definition of the correlation of alternatives, the MADM problems with variable weights when the criteria are interaction, and the hierarchical MADM problems under the poor-information situation when the attributes are interaction. Therefore, the purpose of this paper is to do a deep research on all of these three questions. The detailed arrangement of this paper stands out as follows:
(1) Study on the interaction among alternatives in MADM. First of all, the interaction among alternatives is defined, and then correlation among the alternatives’interaction, independence of irrelevant alternatives and reversal ranking are analyzed. Second, through case study and theory deduction, alternatives’interaction in linear allocation method, weighted average method and TOPSIS method are studied, based on which two ranking preservation methods for WA (Weighted Average) are proposed. Finally we can draw the conclusion that alternatives’interaction can also be introduced into absolute TOPSIS while the decision-making results from the pairwise comparison of TOPSIS may not satisfy the rule of transitivity.
(2) Study on the MADM theory with attributes’interaction. Considering the wide application ofλfuzzy measure in decision-making problem,λfuzzy measure and its two transforming forms-M?bius transformation and interaction coefficients-are deduced based on the existing references. Taking the shortcoming of the constant weights into consideration, the definitions and properties of the variable weights with interaction (R-variable weights) and local state variable weight vector with interaction (R-local state variable weight) are analyzed based on fuzzy measure theory and traditional variable-weight theory. The research results demonstrate the fact that the R-variable weight (or R-local state variable weight) is the general form of the variable weight (or local state variable weight).
(3) Study on the MADM method with attributes’interaction. The new methods called linear allocation method with interaction, weighted average method with interaction, TOPSIS method with interaction, ELECTRE method with interaction and ordered Sugeno method are proposed in the light of fuzzy measures and integrals. Then the properties and application steps of these methods are also discussed, and their validity is tested with examples. After that, MADM method with variable weights when attributes are interaction is discussed based on the R-variable weights theory. Finally, corresponding model is established to compute the weights of attributes and their coalitions, and one example is used to illustrate the validity of the model as well as the method.
(4) Study on the hierarchical MADM method with attributes’interaction. Firstly, a new method to divide hierarchical structures for complex systems is put forward based on the integration of DEMATEL and ISM, and then the hierarchical MADM model is analyzed. Since it is often difficult for decision makers and experts to provide enough preference information for reference attributes and alternatives, under the poor-information situation the method of solving the hierarchical MADM problem with constant weights and variable weights are analyzed respectively when attributes are interactive. The fact that the hierarchical MADM method with constant weights and variable weights when attributes are interaction are the general form of hierarchical MADM method with constant weights and variable weights when attributes are independent is concluded.
(5) Study on application of the MADM theory with attributes’interaction to trans-regional investment of coal enterprise. Firstly, setting in the background of trans-regional investment of coal enterprise, it studies determinants of period choice, and with variable-weights MADM method with interaction, the period choice for the trans-regional investment of coal enterprise is discussed. Then the determinants of location choice are researched, based on which, the location choice for the trans-regional investment of coal enterprise is solved by hierarchical MADM theory with interaction.
引文
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