基于证据推理的不确定多属性决策方法研究
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摘要
现实世界中的大多数决策都是多属性决策,它是人工智能研究的一个重要领域。由于客观事物认知的复杂性和不确定性以及人类思维的模糊性,不确定情况下的多属性决策方法的研究越来越受到人们的关注并已经取得了一些成果,但是,与趋于完善的确定性多属性决策相比还相差甚远。因此,有必要对其理论和应用做深入的研究。本文借鉴在不确定知识合成方面具有优势的证据推理方法,利用规则理论、模糊集、直觉模糊集、区间直觉模糊集及多属性效用理论,研究了不确定性多属性决策问题,重点解决了以精确值或区间值表示的定量属性以及以语言变量、直觉模糊数、区间直觉模糊等不同形式表现的不确定系统的定性属性表达与合成问题,结合一定的决策理论完成方案的排序与择优。主要工作有以下几个方面：
1.针对D-S合成法则在处理高度冲突信息时,会得出与直觉相反的结论这一问题,提出了基于证据综合权重折扣的加权平均综合法。首先,利用证据自身的重要性或可靠性及证据间的相似性,将证据的静态权重与动态权重线性综合形成证据的综合权重,然后,将综合权重作为折扣因子建立具有信任折扣的证据推理模型,最后,利用加权平均法对修正后的证据进行组合。针对基于置信测度决策法,给出了两种基于赌博概率转换的mass函数近似法。数值算例说明了所提出方法在处理高冲突证据融合时的有效性。
2.针对含有定量、定性指标的混合型多方案不确定多属性决策问题,提出了一种具有层次结构的包含不精确、不完全信息的多属性决策模型,并给出了相应的基于属性权重的证据推理算法。给出了基于等价规则对以精确数或区间数表示的定量属性以及定性描述的属性构造基本概率分派函数的方法,使决策信息以统一的分布评估形式给出。结合ER、加权和综合法以及基于证据综合权重折扣的加权平均法等证据推理方法完成所有方案综合属性的评价,基于多属性效用理论,利用区间效用以及基于赌博概率的近似期望单值效用完成方案的综合排序。最后,通过项目投资、供应商评价选择的实例应用,说明这些评价与决策方法的有效性。
3.研究了不确定情况下基于证据推理的群体语言多属性决策问题,其中对群体纯语言多属性决策及群体混合语言多属性决策均进行了探讨。提出了基于三角模糊语言变量转换及直接等级语言评价的基于证据推理的多属性群体纯语言及群体混合语言决策方法。具体地,针对三角模糊语言变量转换法,是将不同粒度下的语言变量等价变换为三角模糊数,再应用COWA (Continuous Ordered Weighted Averaging)算子把三角模糊数转化为精确数,并构造初始置信度,应用证据推理方法对方案进行综合评价,最后采用多属性效用理论及一种有优序的排序方法完成方案的排序与择优。针对直接等级语言评价法,直接将属性评价信息评价到一个或两个相邻的评价等级或不做评价,直接构造初始置信度,最后,采用证据推理方法及多属性效用理论完成群决策。算例表明,该方法评估结果合理、有效,适于解决群体语言多属性决策问题。
4.研究了基于证据推理的直觉模糊多属性群决策方法及区间直觉模糊多属性群决策方法,主要讨论了具有两个或多个等级判定的直觉模糊决策信息的基于证据推理的多属性群决策方法以及对具有两个等级判定的区间直觉模糊决策信息的基于证据推理的多属性群决策方法,为直觉模糊集、区间直觉模糊集应用于多属性群决策中提供新的思路,扩展了模糊多属性决策的应用范围。数值算例说明上述方法的可行性和有效性。
Most decision problems in the real-word are multi-attribute decision making (MADM) which is an important branch of artificial intelligence. The complexity and uncertainty of real-life and vagueness of human judgement have arisen great interest in the development of scientific and objective methods for uncertain MADM (UMADM). Currently, although much effort has been made in the field, the results are far fewer than those on UMADM. So it is necessary and significant to further researches on theories and applications for UMADM. In this dissertation, by using the advanced evidential resoning (ER) approach which has perfect performance in solving the uncertainty, rule theory, fuzzy sets, intuitionistic fuzzy sets and muti-attribute utility theory, we study the problems of UMADM, in which we solve the expression and aggregation of evidences with incompele and imprecise information taking forms of mumbers, interval numbers linguistic variable, intuitionistic fuzzy and interval-valued intuitionistic fuzzy numbers and finish the ranking and decision of schemes. The main contributions are as follows:
1. The D-S evidence method would involved invalid results in dealing with high conflict information. Considering this problem and combination efficiently the evidences with different importance and credibility, a new weighted average method based on overall weight discounted of evidences is proposed. First, according to the importance or credibility and the associated characteristic between evidences, the overall weight is acquired by aggregating linearly the static weight and dynamic weight of each evidence.Then, an evidential reasoning model with discounting trust is built, where the overall weight plays the role as a discounting factor. Finally, the modified evidences are combined together by the weighted average method proposed. Two kinds of pignistic transformation schemes are given to get approximate probability function in the decision making approach based on belief measure. A numerical example shows the effectiveness of the new combination method in the integration of those evidences which are in sharp conflict with each other.
2. A hierarchical evaluation framework and ER approach for hybrid UMADM problem involving multiple schemes of both quatitative and qualitative attributes with imprecise and incomplete information is presented.Based on equivalent rule techniques and muti-attribute utility theory (MAUT), the quatitative datas with precise numbers or interval numbers and qualitative attirbutes can be transformed to construct the basic probabity assignments (bpa) in order that various types of information can be assessed in a unified manner using belief distribution assessment matrixes. The synthetic assessment is realized using the evidential reasoning(ER),or the weighted sum method and the new weighted averaging method based on overall weight discounting of evidence. Based on the expected utility value intervals and an approximate single-valued expected utility function via the pignistic transformation, the ranking order is determined. An investment assessment and a supplier evaluation and selection problem show the effectiveness of the proposed synthetical assessment and decision making.
3. Group linguistic MADM in uncertain environment using ER approach is studied, while the pure and mix linguistic MADM are also concerned. Particularly, the group pure or mix linguistic MADM based the weighted sum method approach by two transforming methods in the forms of triangular fuzzy number and the direct grade assesement is presented, in which the former is that transforms linguistic variable to triangular fuzzy numbers under the different scales of language, then transforms it to a precise number by COWA operations, and constructs the original belief degrees. At last, the alternatives are ranged using the the weighted sum method, MAUT and a priority ordered approach. The latter is that the linguistic values are directly assessed to one or two continuous overall linguistic assessment grades or not be given by the decision makers, the original belief degrees can be constructed and evaluated by the weighted sum method approach. Finally, ranging is ended by MAUT. Numerical example is provided to illustrate that the proposed method is rational and efficient for group linguistic MADM.
4. The methods for dealing with GMADM problems, the decision attribute values with intuitionistic fuzzy and interval intuitionistic fuzzy multiple attributes group decision making based on the the weighted sum method are studied. In the former, the decision attribute values with intuitionistic fuzzy information evaluated to the two or more than two evaluation grades for GMADM problems are synthesized based the weighted sum method and made a decision.Then, the decision making method using the the weighted sum method involving the interval intuitionistic fuzzy information for GMADM problems is presented. These methods provide a new idea in using the intuitionistic fuzzy set or interval intuitionistic fuzzy set in solving the problems of GMADM based on the evidence theory, and broaden the using scope of the fuzzy MADM. The examples show that the feasibility and availability of these methods.
1.针对D-S合成法则在处理高度冲突信息时,会得出与直觉相反的结论这一问题,提出了基于证据综合权重折扣的加权平均综合法。首先,利用证据自身的重要性或可靠性及证据间的相似性,将证据的静态权重与动态权重线性综合形成证据的综合权重,然后,将综合权重作为折扣因子建立具有信任折扣的证据推理模型,最后,利用加权平均法对修正后的证据进行组合。针对基于置信测度决策法,给出了两种基于赌博概率转换的mass函数近似法。数值算例说明了所提出方法在处理高冲突证据融合时的有效性。
2.针对含有定量、定性指标的混合型多方案不确定多属性决策问题,提出了一种具有层次结构的包含不精确、不完全信息的多属性决策模型,并给出了相应的基于属性权重的证据推理算法。给出了基于等价规则对以精确数或区间数表示的定量属性以及定性描述的属性构造基本概率分派函数的方法,使决策信息以统一的分布评估形式给出。结合ER、加权和综合法以及基于证据综合权重折扣的加权平均法等证据推理方法完成所有方案综合属性的评价,基于多属性效用理论,利用区间效用以及基于赌博概率的近似期望单值效用完成方案的综合排序。最后,通过项目投资、供应商评价选择的实例应用,说明这些评价与决策方法的有效性。
3.研究了不确定情况下基于证据推理的群体语言多属性决策问题,其中对群体纯语言多属性决策及群体混合语言多属性决策均进行了探讨。提出了基于三角模糊语言变量转换及直接等级语言评价的基于证据推理的多属性群体纯语言及群体混合语言决策方法。具体地,针对三角模糊语言变量转换法,是将不同粒度下的语言变量等价变换为三角模糊数,再应用COWA (Continuous Ordered Weighted Averaging)算子把三角模糊数转化为精确数,并构造初始置信度,应用证据推理方法对方案进行综合评价,最后采用多属性效用理论及一种有优序的排序方法完成方案的排序与择优。针对直接等级语言评价法,直接将属性评价信息评价到一个或两个相邻的评价等级或不做评价,直接构造初始置信度,最后,采用证据推理方法及多属性效用理论完成群决策。算例表明,该方法评估结果合理、有效,适于解决群体语言多属性决策问题。
4.研究了基于证据推理的直觉模糊多属性群决策方法及区间直觉模糊多属性群决策方法,主要讨论了具有两个或多个等级判定的直觉模糊决策信息的基于证据推理的多属性群决策方法以及对具有两个等级判定的区间直觉模糊决策信息的基于证据推理的多属性群决策方法,为直觉模糊集、区间直觉模糊集应用于多属性群决策中提供新的思路,扩展了模糊多属性决策的应用范围。数值算例说明上述方法的可行性和有效性。
Most decision problems in the real-word are multi-attribute decision making (MADM) which is an important branch of artificial intelligence. The complexity and uncertainty of real-life and vagueness of human judgement have arisen great interest in the development of scientific and objective methods for uncertain MADM (UMADM). Currently, although much effort has been made in the field, the results are far fewer than those on UMADM. So it is necessary and significant to further researches on theories and applications for UMADM. In this dissertation, by using the advanced evidential resoning (ER) approach which has perfect performance in solving the uncertainty, rule theory, fuzzy sets, intuitionistic fuzzy sets and muti-attribute utility theory, we study the problems of UMADM, in which we solve the expression and aggregation of evidences with incompele and imprecise information taking forms of mumbers, interval numbers linguistic variable, intuitionistic fuzzy and interval-valued intuitionistic fuzzy numbers and finish the ranking and decision of schemes. The main contributions are as follows:
1. The D-S evidence method would involved invalid results in dealing with high conflict information. Considering this problem and combination efficiently the evidences with different importance and credibility, a new weighted average method based on overall weight discounted of evidences is proposed. First, according to the importance or credibility and the associated characteristic between evidences, the overall weight is acquired by aggregating linearly the static weight and dynamic weight of each evidence.Then, an evidential reasoning model with discounting trust is built, where the overall weight plays the role as a discounting factor. Finally, the modified evidences are combined together by the weighted average method proposed. Two kinds of pignistic transformation schemes are given to get approximate probability function in the decision making approach based on belief measure. A numerical example shows the effectiveness of the new combination method in the integration of those evidences which are in sharp conflict with each other.
2. A hierarchical evaluation framework and ER approach for hybrid UMADM problem involving multiple schemes of both quatitative and qualitative attributes with imprecise and incomplete information is presented.Based on equivalent rule techniques and muti-attribute utility theory (MAUT), the quatitative datas with precise numbers or interval numbers and qualitative attirbutes can be transformed to construct the basic probabity assignments (bpa) in order that various types of information can be assessed in a unified manner using belief distribution assessment matrixes. The synthetic assessment is realized using the evidential reasoning(ER),or the weighted sum method and the new weighted averaging method based on overall weight discounting of evidence. Based on the expected utility value intervals and an approximate single-valued expected utility function via the pignistic transformation, the ranking order is determined. An investment assessment and a supplier evaluation and selection problem show the effectiveness of the proposed synthetical assessment and decision making.
3. Group linguistic MADM in uncertain environment using ER approach is studied, while the pure and mix linguistic MADM are also concerned. Particularly, the group pure or mix linguistic MADM based the weighted sum method approach by two transforming methods in the forms of triangular fuzzy number and the direct grade assesement is presented, in which the former is that transforms linguistic variable to triangular fuzzy numbers under the different scales of language, then transforms it to a precise number by COWA operations, and constructs the original belief degrees. At last, the alternatives are ranged using the the weighted sum method, MAUT and a priority ordered approach. The latter is that the linguistic values are directly assessed to one or two continuous overall linguistic assessment grades or not be given by the decision makers, the original belief degrees can be constructed and evaluated by the weighted sum method approach. Finally, ranging is ended by MAUT. Numerical example is provided to illustrate that the proposed method is rational and efficient for group linguistic MADM.
4. The methods for dealing with GMADM problems, the decision attribute values with intuitionistic fuzzy and interval intuitionistic fuzzy multiple attributes group decision making based on the the weighted sum method are studied. In the former, the decision attribute values with intuitionistic fuzzy information evaluated to the two or more than two evaluation grades for GMADM problems are synthesized based the weighted sum method and made a decision.Then, the decision making method using the the weighted sum method involving the interval intuitionistic fuzzy information for GMADM problems is presented. These methods provide a new idea in using the intuitionistic fuzzy set or interval intuitionistic fuzzy set in solving the problems of GMADM based on the evidence theory, and broaden the using scope of the fuzzy MADM. The examples show that the feasibility and availability of these methods.
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