基于灰色关联和证据推理的直觉模糊信息决策方法研究
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摘要
1965年，Zadeh教授创立了模糊集理论，为人们处理模糊信息提供了有效的方法。1983年，保加利亚学者Atanassov对模糊集进行了推广，提出了直觉模糊集的概念。直觉模糊集同时考虑了隶属度和非隶属度两方面信息，在处理不确定信息更具有优势。直觉模糊集已经广泛地应用在社会、经济和军事等领域。本文对直觉模糊多属性决策、区间直觉模糊多属性决策、随机直觉模糊多属性决策以及大规模直觉模糊多属性群决策方法进行了研究，所取得的成果进一步丰富了直觉模糊集理论，也为决策者处理不确定决策问题提供了有效方法。
本文的研究成果概括如下：
（1）基于灰色关联的直觉模糊多属性决策方法研究。首先根据直觉模糊集的特点以及MYCIN不确定因子的相关性质，运用灰色关联方法得到证据的信度，提出了一种基于灰色关联和MYCIN不确定因子的决策方法；并运用灰色关联方法确定证据的信度，给出了一种基于灰色关联和证据理论的直觉模糊决策方法。
（2）基于灰色关联的区间直觉模糊多属性决策方法研究。提出了一种新的区间直觉模糊数的区间记分函数，并将区间记分函数根据决策者的风险偏好转化为记分函数，在此基础上将灰色关联方法分别与MYCIN不确定因子和证据理论结合得到了两种区间直觉模糊多属性决策方法。
（3）基于前景理论的随机直觉模糊决策方法研究。结合前景理论提出了三种随机直觉模糊决策方法。提出了一种基于集对分析理论的新记分函数，运用灰色关联方法得出属性的权重，在此基础上运用前景理论得到各个方案的综合前景值并进行决策；运用灰色关联方法确定属性权重，根据前景理论得到前景值，分别运用MYCIN不确定因子方法和证据理论对前景值进行信息融合，得到决策方法。
（4）直觉模糊聚类方法及其在大规模直觉模糊群决策的应用。提出一种新的直觉模糊相似度公式，在此基础上得到一种新的聚类方法；研究了群体规模较大情况下基于直觉模糊评价信息的决策方法。针对决策参与者数量较大的情形，首先将决策者分为若干类，在各个类中分别找出核心决策者，设计了一种确定核心决策者权重的方法，进而根据各核心决策者提供的决策信息进行决策。最后将决策方法运用到棕地开发项目上。
（5）某大型客机公司供应商运行业绩评价研究。首先明确了构建评价指标体系的基本原则，并在此基础上建立了含有11个评价指标的指标体系，并给出评价指标的量化方法，最后通过文章中介绍的基于灰色关联分析和MYCIN不确定因子的直觉模糊决策方法对4个供应商的运行业绩进行评价。
Fuzzy set theory, which was established by professor Zadeh in1965, provides a kind of approach todeal with fuzzy information. Atanassov introduced the concept of intuitionistic fuzzy set whichextended the theory of fuzzy set in1983. Because intuitionistic fuzzy set considers the information ofmembership and non-membership，it has more advantage over Zadeh’s fuzzy set to deal withuncertainty. Intuitionistic fuzzy set has been widely used in many fields, such as social, economic andmilitary. This dissertation studied the problems of multi-attribute intuitionistic fuzzy decision making,multi-attribute interval-valued intuitionistic fuzzy decision making, stochastic multi-attributeintuitionistic fuzzy decision making and multiple-attribute large-scaled group decision making inintuitionistic fuzzy set. The obtained results enrich the theory of intuitionistic fuzzy theory andprovide efficient methods when people facing uncertain problems.The main results can be summarized as follows:
(1)Research on multi-attribute intuitionistic fuzzy decision making based on grey incidenceanalysis. First, according to the characteristic of intuitionistic fuzzy set and relative properties ofMYCIN certainty factor, a kind of intuitionistic fuzzy decision making method based on greyincidence analysis and MYCIN certainty factor was proposed by using grey incidence analysis to getthe reliability of the evidences. Then, in view of the advantage of the evidence theory to deal withuncertainty, a kind of intuitionistic fuzzy decision making method based on grey incidence analysisand evidence theory was proposed by using grey incidence analysis to get the reliability of theevidences.
(2) Research on multi-attribute interval-valued intuitionistic fuzzy decision making based ongrey incidence analysis. In this section, the object of study is changed into interval-valuedintuitionistic fuzzy set from intuitionistic fuzzy set. A new interval-valued score function ofinterval-valued intuitionistic fuzzy number is proposed. And the interval-valued score function can betransformed into score function according to the decision maker’s appetite for risk. On the basis of theabove mentioned method, two interval-valued intuitionistic fuzzy decision making methods areobtained by combining grey incidence analysis with MYCIN certainty factor and evidence theoryrespectively.
(3) Research on stochastic multi-attribute intuitionistic fuzzy decision making method based onprospect theory. In this section, the decision making environment decision maker faced is uncertain.Three kinds of stochastic multi-attribute intuitionistic fuzzy decision making methods are proposedbased on prospect theory. First, a new score function of intuitionistic fuzzy number is proposedaccording to the theory of set pairing, and the weights of attributes are obtained by grey incidenceanalysis. The integrated prospect value of every alternative is obtained by using prospect theory andthe decision making method is obtained. Second, the weights of attributes can be obtained by usinggrey incidence analysis. The prospect values are obtained by applying the prospect theory and theprospect values are fused by MYCIN certainty factor and the decision making method is put forward.Finally, the weights of attributes can be obtained by using grey incidence analysis. The prospectvalues are obtained by applying the prospect theory and the prospect values are fused by evidence theory and the decision making method is put forward.
(4) Research on new clustering method on intuitionistic fuzzy sets and its application to multiple-attribute large-scaled group decision making method. In this section, new formula to derive theintuitionistic fuzzy similarity degree between two intuitionistic fuzzy sets is proposed. And aclustering method is developed based on the new formula. The large-scale multiple attribute groupdecision making (MAGDM) method with intuitionistic fuzzy information is studied. Because themembers of decision makers are too many, it is necessary to clustere the decision makers intodifferent classes by the above method and the core decision makers can be found in the differentclasses. Then a method is designed to determine the weights of the core decision makers. Andaccording to the information provided by the core decision makers we can make a decision making.Finally, the decision making method is applied to brownfield development project.
(5) Research on the evaluation of the suppliers running performance for a large aircraft company.In this section, the principles of building evaluation index system are analyzed. On this basis, elevencorresponding evaluation index are summarized. And the quantification method of index evaluation isprovided. Finally, the running performance of four suppliers is evaluated by the intuitionistic fuzzynumbers decision-making method based on grey incidence analysis and MYCIN certainty factor.
本文的研究成果概括如下：
（1）基于灰色关联的直觉模糊多属性决策方法研究。首先根据直觉模糊集的特点以及MYCIN不确定因子的相关性质，运用灰色关联方法得到证据的信度，提出了一种基于灰色关联和MYCIN不确定因子的决策方法；并运用灰色关联方法确定证据的信度，给出了一种基于灰色关联和证据理论的直觉模糊决策方法。
（2）基于灰色关联的区间直觉模糊多属性决策方法研究。提出了一种新的区间直觉模糊数的区间记分函数，并将区间记分函数根据决策者的风险偏好转化为记分函数，在此基础上将灰色关联方法分别与MYCIN不确定因子和证据理论结合得到了两种区间直觉模糊多属性决策方法。
（3）基于前景理论的随机直觉模糊决策方法研究。结合前景理论提出了三种随机直觉模糊决策方法。提出了一种基于集对分析理论的新记分函数，运用灰色关联方法得出属性的权重，在此基础上运用前景理论得到各个方案的综合前景值并进行决策；运用灰色关联方法确定属性权重，根据前景理论得到前景值，分别运用MYCIN不确定因子方法和证据理论对前景值进行信息融合，得到决策方法。
（4）直觉模糊聚类方法及其在大规模直觉模糊群决策的应用。提出一种新的直觉模糊相似度公式，在此基础上得到一种新的聚类方法；研究了群体规模较大情况下基于直觉模糊评价信息的决策方法。针对决策参与者数量较大的情形，首先将决策者分为若干类，在各个类中分别找出核心决策者，设计了一种确定核心决策者权重的方法，进而根据各核心决策者提供的决策信息进行决策。最后将决策方法运用到棕地开发项目上。
（5）某大型客机公司供应商运行业绩评价研究。首先明确了构建评价指标体系的基本原则，并在此基础上建立了含有11个评价指标的指标体系，并给出评价指标的量化方法，最后通过文章中介绍的基于灰色关联分析和MYCIN不确定因子的直觉模糊决策方法对4个供应商的运行业绩进行评价。
Fuzzy set theory, which was established by professor Zadeh in1965, provides a kind of approach todeal with fuzzy information. Atanassov introduced the concept of intuitionistic fuzzy set whichextended the theory of fuzzy set in1983. Because intuitionistic fuzzy set considers the information ofmembership and non-membership，it has more advantage over Zadeh’s fuzzy set to deal withuncertainty. Intuitionistic fuzzy set has been widely used in many fields, such as social, economic andmilitary. This dissertation studied the problems of multi-attribute intuitionistic fuzzy decision making,multi-attribute interval-valued intuitionistic fuzzy decision making, stochastic multi-attributeintuitionistic fuzzy decision making and multiple-attribute large-scaled group decision making inintuitionistic fuzzy set. The obtained results enrich the theory of intuitionistic fuzzy theory andprovide efficient methods when people facing uncertain problems.The main results can be summarized as follows:
(1)Research on multi-attribute intuitionistic fuzzy decision making based on grey incidenceanalysis. First, according to the characteristic of intuitionistic fuzzy set and relative properties ofMYCIN certainty factor, a kind of intuitionistic fuzzy decision making method based on greyincidence analysis and MYCIN certainty factor was proposed by using grey incidence analysis to getthe reliability of the evidences. Then, in view of the advantage of the evidence theory to deal withuncertainty, a kind of intuitionistic fuzzy decision making method based on grey incidence analysisand evidence theory was proposed by using grey incidence analysis to get the reliability of theevidences.
(2) Research on multi-attribute interval-valued intuitionistic fuzzy decision making based ongrey incidence analysis. In this section, the object of study is changed into interval-valuedintuitionistic fuzzy set from intuitionistic fuzzy set. A new interval-valued score function ofinterval-valued intuitionistic fuzzy number is proposed. And the interval-valued score function can betransformed into score function according to the decision maker’s appetite for risk. On the basis of theabove mentioned method, two interval-valued intuitionistic fuzzy decision making methods areobtained by combining grey incidence analysis with MYCIN certainty factor and evidence theoryrespectively.
(3) Research on stochastic multi-attribute intuitionistic fuzzy decision making method based onprospect theory. In this section, the decision making environment decision maker faced is uncertain.Three kinds of stochastic multi-attribute intuitionistic fuzzy decision making methods are proposedbased on prospect theory. First, a new score function of intuitionistic fuzzy number is proposedaccording to the theory of set pairing, and the weights of attributes are obtained by grey incidenceanalysis. The integrated prospect value of every alternative is obtained by using prospect theory andthe decision making method is obtained. Second, the weights of attributes can be obtained by usinggrey incidence analysis. The prospect values are obtained by applying the prospect theory and theprospect values are fused by MYCIN certainty factor and the decision making method is put forward.Finally, the weights of attributes can be obtained by using grey incidence analysis. The prospectvalues are obtained by applying the prospect theory and the prospect values are fused by evidence theory and the decision making method is put forward.
(4) Research on new clustering method on intuitionistic fuzzy sets and its application to multiple-attribute large-scaled group decision making method. In this section, new formula to derive theintuitionistic fuzzy similarity degree between two intuitionistic fuzzy sets is proposed. And aclustering method is developed based on the new formula. The large-scale multiple attribute groupdecision making (MAGDM) method with intuitionistic fuzzy information is studied. Because themembers of decision makers are too many, it is necessary to clustere the decision makers intodifferent classes by the above method and the core decision makers can be found in the differentclasses. Then a method is designed to determine the weights of the core decision makers. Andaccording to the information provided by the core decision makers we can make a decision making.Finally, the decision making method is applied to brownfield development project.
(5) Research on the evaluation of the suppliers running performance for a large aircraft company.In this section, the principles of building evaluation index system are analyzed. On this basis, elevencorresponding evaluation index are summarized. And the quantification method of index evaluation isprovided. Finally, the running performance of four suppliers is evaluated by the intuitionistic fuzzynumbers decision-making method based on grey incidence analysis and MYCIN certainty factor.
引文
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