多属性行为决策方法研究
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摘要
多属性决策问题广泛存在于现实世界,有效解决此类问题十分重要。为了能够使决策者的价值偏好和行为特征更好地体现在决策结论中,本文对多属性行为决策方法进行了研究。研究从属性分析结构的简约、方案单属性价值和属性权重的确定,以及方案单属性价值和属性权重的集结即方案总价值的确定并对方案进行优选排序来分别展开的。本文针对上述四部分内容做了如下研究工作:提出了基于前馈模糊BP神经网络和交合分析法的属性结构简约方法,并给出了基于搜索思想和Hamming距离的前馈神经网络病态样本剔除方法:提出了基于DS理论的前景价值确定框架效应处理方法和基于RBT神经网络的前景价值确定方法,进而给出了基于心理账产和前景理论的方案单属性价值确定方法;提出了用于度量属性权重的基于AHP的模糊测度确定方法,并给出了方案优选排序方法。通过上述工作,本文提出了一种多属性行为决策方法。本文应用其对东北某信托公司的投资方案进行选择研究,方法较强的实用性和可操作性得到了证明。
The multiple attributes decision-making method (MADMM) consists of determining attributes' weights (AWs) and each alternative' s values on attributes (AAVs), and computing comprehensive AAVs (CAAV) of an alternative by aggregating AWs and AAVs of the alternative. However, traditional MADMMs suppose that an attribute is independent to another one, is not conformable to real conditions. So they can not rightly reflect interactive relations among attributes and valuable preferences of a decision-maker (DM). In addition, traditional MADMMs use expected utility theory developed by von Neumann and Morgenstern to determine AAVs, which can not explain the Allais paradox, the Ellsberg paradox and the risk aversion phenomena, etc. Although it is widely employed to obtain AAVs according to the DM' s valuable preferences, it is weaker than prospect theory on reflecting valuable references of the DM. Consequently, from the viewpoint of overcoming the two drawbacks of MADMMs and improving quality of decision-making, the dissertation does research on a method for multiple attributes behavioral decision-making (MABDMM) which can more efficiently reflect a DM' s valuable preferences than conventional MADMM.
The dissertation firstly studies on a simplification approach to the attributes' structure. A structure must be constructed before applying a MADMM to solve problems. Generally speaking, it initially given by a DM may contain redundant attributes. This kind attribute will burden the DM and bring unwanted attributes, then influence accurateness of a DM' s valuable judgments and quality of decision-making. For reasonably constructing an attributes' structure and reduce the dimensionality of attributes, the dissertation employs conjoint analysis (CA) to compute weights of attributes of an initial structure and then simplify the structure, through considering the trait of evaluating attributes according to their holistic utilities. However, such drawbacks of CA as probably being invalid under some conditions, having not enough ability to well reflect inherent relations of complex systems, and not considering the inaccurate characteristic of evaluations given by valuators, exist. To overcome the three drawbacks, according to the thought of the meta-synthesis from qualitative analysis to quantitative analysis of complex system theory, and based on the theory of the technique of fuzzy math and artificial neural network, the improved CA based on fuzzy BP neural network is presented (FBP-CA), namely, the simplification approach of a redundant attributes' structure. The distinguished advantages of the presented approach lie in that it can well capture inherent relations of complex systems, and thus it is a general approach. The results of numerical demonstration analysis show that the rank of evaluated attributes got by the developed approach is much closer to the real, and proves to be more reasonable than the classical CA. So FBP-CA can be employed to determine the structure of attributes.
For eliminating morbid samples rooting in judgments' error of a DM when FBP-CA is using, strengthening generalization capacities of fuzzy BP neural network and improving validity of FBP-CA and the network, the dissertation presents the approach to eliminate morbid samples in forward neural network based on a searching thought of morbid samples which is developed in dissertation and the Hamming distance (SI-HD-EMS). The approach can directly carry out searching and eliminating morbid samples, and does not consider prior knowledge, forms of samples, etc. Hence, its applicability is stronger. The results of numerical demonstration analysis show that the approach is a scientific, effective and it can effectively find out morbid samples of learning samples, so it has obvious application value to solve morbid samples' problems of FBP-CA. Due to RBT neural network used in the method for determining values of prospects on basis of RBT neural network (RN-PVD) presented in the dissertation also belonging to forward neural networks, hence, SI-HD-EMS can be employed to eliminate morbid samples of RN-PVD.
Secondly, mental accounting and prospect theory are introduced to determining AAVs by the dissertation. Mental accounting exists in real decision-making activity, and this is proved by lots of experiments. According to studies with regard to mental accounting, effective decision-making can not but reasonably consider mental accounting. However, the decision-making method rarely considers mental accounting. Although prospect theory is exceptional, it only takes in two basic accounting, namely, gains accounting and loss accounting. Otherwise, the decision-making method based on mental accounting has two shortages, namely, deeming every accounting same important and the accounting only existing in attributes measured by money. In consequence, the dissertation presents the method for determining AAVs based on mental accounting and prospect values (MP-AVD), through introducing mental accounting and computing their weights, and aggregating AAVs and the weights.
Owing to determining methods of subject weights and objective weights respectively do not consider objective and subject decision-making information, and determining methods of subject and objective integrated weights in existence have technical shortcomings, the dissertation presents the approach to determine weights of mental accounting, though introducing the entropy weighting method and the swing weighting method, and using the thought of TOPSIS for reference. Then, the method to determine maximum AAVs is developed, through constructing goal programming function concerning maximum AAVs on the value function of prospects and the weights of mental accounting basis.
Prospect theory is introduced in the dissertation to determine alternative' s values on mental accounting. The reason is that prospect theory perform at a level higher than expected utility theory, when they are utilized to reflect valuable references of a DM. Nevertheless, parametric models of determining prospects' values of prospect theory has such drawbacks, namely, the supposed probability weighting functions and outcome value functions may not be accord with real valuable preference functions of a DM, and the supposed function can not satisfy the statistical test so it is invalid in some conditions. Additionally, nonparametric models of determining prospects' values can not tackle or effectively tackle judgment' s error of valuable judgments given by a DM, and errors brought in prior judgment process will propagate in latter process. Still, nonparametric models do not rely on supposing functions is an excellent disadvantage, and it is propitious to determine probability weights, outcome values and prospect values that can effectively reflect valuable preferences of a decision-maker. In consequence, viewing from exerting the strength and overcoming the shortcoming of nonparametric models, the paper develops RN-PVD which can effectively reflect valuable preferences of a decision-maker according to probabilities and outcomes of prospects and certainty equivalence presented by a DM, through introducing RBT-NN which can implement complex logic operations and nonlinear relations. RN-PVD has three technical superiorities, namely, mechanism of RBF-NN can guarantee that effectively recognize relations between input data and output data of the network, RBF-NN allow some errors existing in judgment data presented by a DM, and SI-HD-EMS can be employed to eliminate morbid samples of RBT-NN. The results of numeric simulation analysis demonstrate that the rank of prospects drawn by RN-PVD is more close to the simulated real rank, and it is more excellent than classical models.
When RN-PVD is used to determine values of prospects, description frames of decision-making problems' prospects may influence judgment behaviors of a DM. This is called framing effect, and many experiments demonstrate its existence. If framing effect goes with a DM' s value judgments on prospects, then quality judgments must shrink. Despite some means introduced to play down and remove framing effect, they are described by simple languages, so lack favorable operation. The appearance reason of framing effect is that description frames influence a DM' s choice on reference point, then directly influence shapes of outcome value functions, probability weighting functions and prospect value functions. With an eye to this reason, the dissertation develops a thought to deal with framing effect, according to the thought of the frequency model. Whereafter, the dissertation presents the method to tackle framing effect based on DS theory (DS-VJI), through introducing DS theory which has uncertain reasoning ability. The results of experiment analysis show that occurrence likelihood of framing effect is obvious depressed, when DS-VJI is employed to capture valuable preferences of a DM, then its influence is weakened. Consequently, DS-VJI is an effective method to deal with framing effect, and it can be impactful to dispose framing effect that may come into being when AAVs are determined.
At last, the dissertation gives the main process of determining CAAVs of alternatives. For determining CAAVs, it needs AAVs of alternatives, weights of attributes and a method to aggregate them. Whereas traditional MADMMs' independent relation supposition among attributes is contradictable to object decision-making, and can not effectively reflect interactive relations between two attributes and weights of attributes, so the dissertation apply fuzzy measures which can reflect the relations among attributes to scale weights of attributes. Thanks to existing determining approaches of fuzzy measures have shortages on dealing with real problems, the dissertation presents the method for determining fuzzy measures based on AHP (AHP-FMD), by introducing AHP which technically predominant in distilling valuable preferences of a DM. The results of numeric simulation analysis demonstrate that fuzzy measures got by AHP-FMD are closer to real ones, and it obviously excels others in efficiency. As a result of classical MADMMs can not be used to aggregate fuzzy measures, the dissertation chooses Choquet fuzzy integral to determine CAAVs of alternatives through aggregating AAVs and attributes' weights. Then by summarizing above researches about the MADMM according to the logic relation among methods developed, the dissertation presents main steps of the MABDMM.
Through applying the MABDDM to choose investment alternatives of a northeast trust company, both practicability and maneuverability of the MABDDM is proved.
The multiple attributes decision-making method (MADMM) consists of determining attributes' weights (AWs) and each alternative' s values on attributes (AAVs), and computing comprehensive AAVs (CAAV) of an alternative by aggregating AWs and AAVs of the alternative. However, traditional MADMMs suppose that an attribute is independent to another one, is not conformable to real conditions. So they can not rightly reflect interactive relations among attributes and valuable preferences of a decision-maker (DM). In addition, traditional MADMMs use expected utility theory developed by von Neumann and Morgenstern to determine AAVs, which can not explain the Allais paradox, the Ellsberg paradox and the risk aversion phenomena, etc. Although it is widely employed to obtain AAVs according to the DM' s valuable preferences, it is weaker than prospect theory on reflecting valuable references of the DM. Consequently, from the viewpoint of overcoming the two drawbacks of MADMMs and improving quality of decision-making, the dissertation does research on a method for multiple attributes behavioral decision-making (MABDMM) which can more efficiently reflect a DM' s valuable preferences than conventional MADMM.
The dissertation firstly studies on a simplification approach to the attributes' structure. A structure must be constructed before applying a MADMM to solve problems. Generally speaking, it initially given by a DM may contain redundant attributes. This kind attribute will burden the DM and bring unwanted attributes, then influence accurateness of a DM' s valuable judgments and quality of decision-making. For reasonably constructing an attributes' structure and reduce the dimensionality of attributes, the dissertation employs conjoint analysis (CA) to compute weights of attributes of an initial structure and then simplify the structure, through considering the trait of evaluating attributes according to their holistic utilities. However, such drawbacks of CA as probably being invalid under some conditions, having not enough ability to well reflect inherent relations of complex systems, and not considering the inaccurate characteristic of evaluations given by valuators, exist. To overcome the three drawbacks, according to the thought of the meta-synthesis from qualitative analysis to quantitative analysis of complex system theory, and based on the theory of the technique of fuzzy math and artificial neural network, the improved CA based on fuzzy BP neural network is presented (FBP-CA), namely, the simplification approach of a redundant attributes' structure. The distinguished advantages of the presented approach lie in that it can well capture inherent relations of complex systems, and thus it is a general approach. The results of numerical demonstration analysis show that the rank of evaluated attributes got by the developed approach is much closer to the real, and proves to be more reasonable than the classical CA. So FBP-CA can be employed to determine the structure of attributes.
For eliminating morbid samples rooting in judgments' error of a DM when FBP-CA is using, strengthening generalization capacities of fuzzy BP neural network and improving validity of FBP-CA and the network, the dissertation presents the approach to eliminate morbid samples in forward neural network based on a searching thought of morbid samples which is developed in dissertation and the Hamming distance (SI-HD-EMS). The approach can directly carry out searching and eliminating morbid samples, and does not consider prior knowledge, forms of samples, etc. Hence, its applicability is stronger. The results of numerical demonstration analysis show that the approach is a scientific, effective and it can effectively find out morbid samples of learning samples, so it has obvious application value to solve morbid samples' problems of FBP-CA. Due to RBT neural network used in the method for determining values of prospects on basis of RBT neural network (RN-PVD) presented in the dissertation also belonging to forward neural networks, hence, SI-HD-EMS can be employed to eliminate morbid samples of RN-PVD.
Secondly, mental accounting and prospect theory are introduced to determining AAVs by the dissertation. Mental accounting exists in real decision-making activity, and this is proved by lots of experiments. According to studies with regard to mental accounting, effective decision-making can not but reasonably consider mental accounting. However, the decision-making method rarely considers mental accounting. Although prospect theory is exceptional, it only takes in two basic accounting, namely, gains accounting and loss accounting. Otherwise, the decision-making method based on mental accounting has two shortages, namely, deeming every accounting same important and the accounting only existing in attributes measured by money. In consequence, the dissertation presents the method for determining AAVs based on mental accounting and prospect values (MP-AVD), through introducing mental accounting and computing their weights, and aggregating AAVs and the weights.
Owing to determining methods of subject weights and objective weights respectively do not consider objective and subject decision-making information, and determining methods of subject and objective integrated weights in existence have technical shortcomings, the dissertation presents the approach to determine weights of mental accounting, though introducing the entropy weighting method and the swing weighting method, and using the thought of TOPSIS for reference. Then, the method to determine maximum AAVs is developed, through constructing goal programming function concerning maximum AAVs on the value function of prospects and the weights of mental accounting basis.
Prospect theory is introduced in the dissertation to determine alternative' s values on mental accounting. The reason is that prospect theory perform at a level higher than expected utility theory, when they are utilized to reflect valuable references of a DM. Nevertheless, parametric models of determining prospects' values of prospect theory has such drawbacks, namely, the supposed probability weighting functions and outcome value functions may not be accord with real valuable preference functions of a DM, and the supposed function can not satisfy the statistical test so it is invalid in some conditions. Additionally, nonparametric models of determining prospects' values can not tackle or effectively tackle judgment' s error of valuable judgments given by a DM, and errors brought in prior judgment process will propagate in latter process. Still, nonparametric models do not rely on supposing functions is an excellent disadvantage, and it is propitious to determine probability weights, outcome values and prospect values that can effectively reflect valuable preferences of a decision-maker. In consequence, viewing from exerting the strength and overcoming the shortcoming of nonparametric models, the paper develops RN-PVD which can effectively reflect valuable preferences of a decision-maker according to probabilities and outcomes of prospects and certainty equivalence presented by a DM, through introducing RBT-NN which can implement complex logic operations and nonlinear relations. RN-PVD has three technical superiorities, namely, mechanism of RBF-NN can guarantee that effectively recognize relations between input data and output data of the network, RBF-NN allow some errors existing in judgment data presented by a DM, and SI-HD-EMS can be employed to eliminate morbid samples of RBT-NN. The results of numeric simulation analysis demonstrate that the rank of prospects drawn by RN-PVD is more close to the simulated real rank, and it is more excellent than classical models.
When RN-PVD is used to determine values of prospects, description frames of decision-making problems' prospects may influence judgment behaviors of a DM. This is called framing effect, and many experiments demonstrate its existence. If framing effect goes with a DM' s value judgments on prospects, then quality judgments must shrink. Despite some means introduced to play down and remove framing effect, they are described by simple languages, so lack favorable operation. The appearance reason of framing effect is that description frames influence a DM' s choice on reference point, then directly influence shapes of outcome value functions, probability weighting functions and prospect value functions. With an eye to this reason, the dissertation develops a thought to deal with framing effect, according to the thought of the frequency model. Whereafter, the dissertation presents the method to tackle framing effect based on DS theory (DS-VJI), through introducing DS theory which has uncertain reasoning ability. The results of experiment analysis show that occurrence likelihood of framing effect is obvious depressed, when DS-VJI is employed to capture valuable preferences of a DM, then its influence is weakened. Consequently, DS-VJI is an effective method to deal with framing effect, and it can be impactful to dispose framing effect that may come into being when AAVs are determined.
At last, the dissertation gives the main process of determining CAAVs of alternatives. For determining CAAVs, it needs AAVs of alternatives, weights of attributes and a method to aggregate them. Whereas traditional MADMMs' independent relation supposition among attributes is contradictable to object decision-making, and can not effectively reflect interactive relations between two attributes and weights of attributes, so the dissertation apply fuzzy measures which can reflect the relations among attributes to scale weights of attributes. Thanks to existing determining approaches of fuzzy measures have shortages on dealing with real problems, the dissertation presents the method for determining fuzzy measures based on AHP (AHP-FMD), by introducing AHP which technically predominant in distilling valuable preferences of a DM. The results of numeric simulation analysis demonstrate that fuzzy measures got by AHP-FMD are closer to real ones, and it obviously excels others in efficiency. As a result of classical MADMMs can not be used to aggregate fuzzy measures, the dissertation chooses Choquet fuzzy integral to determine CAAVs of alternatives through aggregating AAVs and attributes' weights. Then by summarizing above researches about the MADMM according to the logic relation among methods developed, the dissertation presents main steps of the MABDMM.
Through applying the MABDDM to choose investment alternatives of a northeast trust company, both practicability and maneuverability of the MABDDM is proved.
引文
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