模糊多目标决策理论、方法及其应用研究
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摘要
决策是一种主观活动，是人类主体对社会客体的认知和选择过程。大量的决策是模糊的、多层次的、多目标的和群体的非(半)结构性决策。本文以陈守煜工程模糊集理论和方法为思路和基础，主要研究了多目标、多层次、群体的模糊决策理论、方法、模型及其应用，研究了模糊模式识别和模糊聚类的理论、方法、模型及其应用，并具有一定的理论意义和实用价值。
权重和定性目标是模糊多目标决策的二类主要偏好信息。在陈守煜建立的非结构性决策单元系统理论的基础上，提出了在明晰数和模糊数情况下，基于相邻目标(方案)相对模糊标度值确定、计算权重和定性目标相对优属度的方法；研究了利用二元比较、模糊优选模型、集值统计原理和Borda打分法集结群体偏好的方法；以相邻目标(方案)相对模糊标度值和模糊数作为确定权重和定性目标相对优属度的手段，能充分利用决策者给定的优序信息，更好地反映决策者的偏好，使语义到数值的转化更为合理。
考虑到模糊优选、模糊模式识别和模糊聚类中存在大量模糊信息的特点，基于一般化模糊距离和模糊数，推导了模糊数状态下模糊优选和模糊模式识别的一般化公式，使这些模型对特征信息的要求变得更为宽泛，模型的适用范围更广，从而拓展了工程模糊集理论的应用；在特殊模糊数和近似模糊距离情况下，推导了权重和聚类中心矩阵均为未知的模糊聚类循环迭代模型。这些方法和模型都是对工程模糊集理论有益扩充。
在吸收工程模糊集理论中相对优思想的基础上，将经典多维偏好分析线性规划决策方法(LINMAP)作了改进，并推广为非(半)结构性状态下的LINMAP方法，避免了经典方法中求解理想解的复杂过程，简化了计算，使所得的解总是有效解，并使该方法的物理意义更加明确。在此基础上，进一步将该方法推广到特殊模糊数状态下，即F-LINMAP方法，扩大了应用范围，并具有较好的推广应用价值。在一般性模糊距离和模糊数状态下，将经典TOPSIS方法推广为模糊状态，简化了计算，是一种实用的决策方法。
考虑到群体决策的广泛性，按照独裁综合或者综合独裁的群决策程序，将基于模糊数的模糊优选模型应用于群决策中；研究了将Borda打分法、模糊优选模型、模糊TOPSIS法和F-LINMAP分别相结合的群决策方法；以线性加权决策方法为例，说明了用相对隶属度思想对决策、识别和聚类问题中特征值作归一化处理的必要性；在工程模糊集理论
的基础上，导出了既适合单人决策和群决策，又适合明晰数和模糊数场合的综合型模糊
群决策模型，该模型物理意义清晰，并具有更好的普适性和灵活性:提出了应用模糊优
选模型进行多层次模糊群决策的思路和方法。
在理论研究的基础上，还分别将上述各种模型和方法应用到若干具体领域:将模糊
聚类模型应用到地下水资源的分析上;将模糊群决策方法、多层次决策思想和模糊切比
雪夫决策方法分别应用到大连市水资源和经济规划、舰艇作战能力分析等问题上;应用
模糊优选模型和模糊模式识别模型求解威胁判断问题，取得了较好的效果。
本文提出的模型和方法都是以工程模糊集理论为基础，同时也是对工程模糊集理论
在理论和应用上的拓展，并具有较好的可操作性和一定的实际应用价值。
最后，对全文作了总结，并对有待进一步研究的问题作了展望。
Decision-making is activities that human realize the world. Many decision-making problems are often fuzzy, multi-layer, multi-objective and multi-person. Based on the Engineering Fuzzy Sets Theory(EFST) established by Prof. Chen Shouyu, this paper mainly focuses on theories, models and methodologies for fuzzy, multi-layer, multi-objective and multi-person decision-making problems with their applications, and are of value to scientific researches and real applications. The results are as follows:
Weight and qualitative objective are two types of primary preference information in fuzzy multi-objective decision-making. Based on the theory of unit system for non-structural decision-making proposed by Prof. Chen Shouyu, a new methodology and algorithm are proposed to resolve the objective weight and relative membership degree of qualitative objective using fuzzy value of relative important degree of adjacent objectives and alternatives. Based on pairwise comparison, the fuzzy optimum-seeking model, the set-value statistics theory and Borda method, several models and methods are proposed to aggregate individual preference into a group preference. These methods can effectively utilize individual preference, and make it easy to convert linguistic estimation into fuzzy value.
According to the characteristics of optimum-seeking, pattern recognition and clustering with fuzzy information in real world, ordinary fuzzy number and ordinary fuzzy distance are introduced in the optimum-seeking model and the fuzzy pattern recognition model, and special fuzzy numbers and special fuzzy distance are introduced in fuzzy clustering model which were all proposed by Prof. Chen Shouyu. The research enriches the EFST, and makes it possible for these models to be applied more widely and effectively.
Based on the concept of relative membership degree in the fuzzy sets theory, F-LINMAP model and F-TOPSIS model are proposed. Traditional Linear Programming Techniques for Multidimensional Analysis of Preference(LINMAP) decision-making model is improved to non-structural or semi-structural decision-making problems with special fuzzy numbers and special fuzzy distance, and traditional TOPSIS model is improved to fuzzy decision-making model with ordinary fuzzy numbers and ordinary fuzzy distance. It proved that the F-LINMAP and the F-TOPSIS are more easy, effective, useful and practicable than traditional models.
Considered universality of group decision-making, the fuzzy optimum-seeking model is applied to group decision-making respectively according to the decision-making sequence of
integration-autarchy or autarchy-integration. New decision-making models are proposed depending respectively on the combination of the fuzzy optimum-seeking model, Borda method, the F-LINMAP and the F-TOPSIS. In order to demonstrate the advantages of relative membership degree in optimum-seeking, pattern recognition and clustering, SWA decision-making method is be studied as an example. Based on the EFST, integrative fuzzy group decision-making model is established, and it can be applied to individual decision-making, group decision-making, fuzzy decision-making and traditional decision-making. All method and conception is presentd to deal with multi-layer fuzzy group decision-making problems with the optimum-seeking model.
Applications of these new models and methods are mainly focused on four problems: the research on threat judgment model and method with the new optimum-seeking model and new fuzzy pattern recognition model, the analysis of groundwater resource with the new fuzzy clustering model, the research on water resources and macro-economic sustainable development of DaLian with the multi-layer multi-criteria multi-person fuzzy optimum-seeking method and Tchebycheff decision-making theory, and the analysis of operational effectiveness for warship with the multi-layer multi-criteria multi-person fuzzy optimum-seeking method.
All models and methods presented in this paper are depended on the EFST. And at the same time they enrich the EFST theoretically and
权重和定性目标是模糊多目标决策的二类主要偏好信息。在陈守煜建立的非结构性决策单元系统理论的基础上，提出了在明晰数和模糊数情况下，基于相邻目标(方案)相对模糊标度值确定、计算权重和定性目标相对优属度的方法；研究了利用二元比较、模糊优选模型、集值统计原理和Borda打分法集结群体偏好的方法；以相邻目标(方案)相对模糊标度值和模糊数作为确定权重和定性目标相对优属度的手段，能充分利用决策者给定的优序信息，更好地反映决策者的偏好，使语义到数值的转化更为合理。
考虑到模糊优选、模糊模式识别和模糊聚类中存在大量模糊信息的特点，基于一般化模糊距离和模糊数，推导了模糊数状态下模糊优选和模糊模式识别的一般化公式，使这些模型对特征信息的要求变得更为宽泛，模型的适用范围更广，从而拓展了工程模糊集理论的应用；在特殊模糊数和近似模糊距离情况下，推导了权重和聚类中心矩阵均为未知的模糊聚类循环迭代模型。这些方法和模型都是对工程模糊集理论有益扩充。
在吸收工程模糊集理论中相对优思想的基础上，将经典多维偏好分析线性规划决策方法(LINMAP)作了改进，并推广为非(半)结构性状态下的LINMAP方法，避免了经典方法中求解理想解的复杂过程，简化了计算，使所得的解总是有效解，并使该方法的物理意义更加明确。在此基础上，进一步将该方法推广到特殊模糊数状态下，即F-LINMAP方法，扩大了应用范围，并具有较好的推广应用价值。在一般性模糊距离和模糊数状态下，将经典TOPSIS方法推广为模糊状态，简化了计算，是一种实用的决策方法。
考虑到群体决策的广泛性，按照独裁综合或者综合独裁的群决策程序，将基于模糊数的模糊优选模型应用于群决策中；研究了将Borda打分法、模糊优选模型、模糊TOPSIS法和F-LINMAP分别相结合的群决策方法；以线性加权决策方法为例，说明了用相对隶属度思想对决策、识别和聚类问题中特征值作归一化处理的必要性；在工程模糊集理论
的基础上，导出了既适合单人决策和群决策，又适合明晰数和模糊数场合的综合型模糊
群决策模型，该模型物理意义清晰，并具有更好的普适性和灵活性:提出了应用模糊优
选模型进行多层次模糊群决策的思路和方法。
在理论研究的基础上，还分别将上述各种模型和方法应用到若干具体领域:将模糊
聚类模型应用到地下水资源的分析上;将模糊群决策方法、多层次决策思想和模糊切比
雪夫决策方法分别应用到大连市水资源和经济规划、舰艇作战能力分析等问题上;应用
模糊优选模型和模糊模式识别模型求解威胁判断问题，取得了较好的效果。
本文提出的模型和方法都是以工程模糊集理论为基础，同时也是对工程模糊集理论
在理论和应用上的拓展，并具有较好的可操作性和一定的实际应用价值。
最后，对全文作了总结，并对有待进一步研究的问题作了展望。
Decision-making is activities that human realize the world. Many decision-making problems are often fuzzy, multi-layer, multi-objective and multi-person. Based on the Engineering Fuzzy Sets Theory(EFST) established by Prof. Chen Shouyu, this paper mainly focuses on theories, models and methodologies for fuzzy, multi-layer, multi-objective and multi-person decision-making problems with their applications, and are of value to scientific researches and real applications. The results are as follows:
Weight and qualitative objective are two types of primary preference information in fuzzy multi-objective decision-making. Based on the theory of unit system for non-structural decision-making proposed by Prof. Chen Shouyu, a new methodology and algorithm are proposed to resolve the objective weight and relative membership degree of qualitative objective using fuzzy value of relative important degree of adjacent objectives and alternatives. Based on pairwise comparison, the fuzzy optimum-seeking model, the set-value statistics theory and Borda method, several models and methods are proposed to aggregate individual preference into a group preference. These methods can effectively utilize individual preference, and make it easy to convert linguistic estimation into fuzzy value.
According to the characteristics of optimum-seeking, pattern recognition and clustering with fuzzy information in real world, ordinary fuzzy number and ordinary fuzzy distance are introduced in the optimum-seeking model and the fuzzy pattern recognition model, and special fuzzy numbers and special fuzzy distance are introduced in fuzzy clustering model which were all proposed by Prof. Chen Shouyu. The research enriches the EFST, and makes it possible for these models to be applied more widely and effectively.
Based on the concept of relative membership degree in the fuzzy sets theory, F-LINMAP model and F-TOPSIS model are proposed. Traditional Linear Programming Techniques for Multidimensional Analysis of Preference(LINMAP) decision-making model is improved to non-structural or semi-structural decision-making problems with special fuzzy numbers and special fuzzy distance, and traditional TOPSIS model is improved to fuzzy decision-making model with ordinary fuzzy numbers and ordinary fuzzy distance. It proved that the F-LINMAP and the F-TOPSIS are more easy, effective, useful and practicable than traditional models.
Considered universality of group decision-making, the fuzzy optimum-seeking model is applied to group decision-making respectively according to the decision-making sequence of
integration-autarchy or autarchy-integration. New decision-making models are proposed depending respectively on the combination of the fuzzy optimum-seeking model, Borda method, the F-LINMAP and the F-TOPSIS. In order to demonstrate the advantages of relative membership degree in optimum-seeking, pattern recognition and clustering, SWA decision-making method is be studied as an example. Based on the EFST, integrative fuzzy group decision-making model is established, and it can be applied to individual decision-making, group decision-making, fuzzy decision-making and traditional decision-making. All method and conception is presentd to deal with multi-layer fuzzy group decision-making problems with the optimum-seeking model.
Applications of these new models and methods are mainly focused on four problems: the research on threat judgment model and method with the new optimum-seeking model and new fuzzy pattern recognition model, the analysis of groundwater resource with the new fuzzy clustering model, the research on water resources and macro-economic sustainable development of DaLian with the multi-layer multi-criteria multi-person fuzzy optimum-seeking method and Tchebycheff decision-making theory, and the analysis of operational effectiveness for warship with the multi-layer multi-criteria multi-person fuzzy optimum-seeking method.
All models and methods presented in this paper are depended on the EFST. And at the same time they enrich the EFST theoretically and
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