Multi-attribute decision making model based on optimal membership and relative entropy

To study the problems of multi-attribute decision making in which the attribute values are given in the form of linguistic fuzzy numbers and the information of attribute weights are incomplete, a new multi-attribute decision making model is presented based on the optimal membership and the relative entropy. Firstly, the definitions of the optimal membership and the relative entropy are given. Secondly, for all alternatives, a set of preference weight vectors are obtained by solving a set of linear programming models whose goals axe all to maximize the optimal membership. Thirdly, a relative entropy model is established to aggregate the preference weight vectors, thus an optimal weight vector is determined. Based on this optimal weight vector, the algorithm of deviation degree minimization is proposed to rank all the alternatives. Finally, a decision making example is given to demonstrate the feasibility and rationality of this new model.

Application of fuzzy optimal selection of similar slopes to the evaluation of slope stability

The numerical calculation method is widely used in the evaluation of slope stability,but it cannot take the randomness and fuzziness into account that exist in rock and soil engineering objectively.The fuzzy optimization theory is thus introduced to the evaluation of slope stability by this paper and a method of fuzzy optimal selection of similar slopes is put forward to analyze slope stability.By comparing the relative membership degrees that the evaluated object sample of slope is similar to the source samples of which the stabilities are detected clearly,the source sample with the maximal relative membership degree will be chosen as the best similar one to the object sample,and the stability of the object sample can be evaluated by that of the best similar source sample.In the process many uncertain influential factors are considered and characteristics and knowledge of the source samples are obtained.The practical calculation indicates that it can achieve good results to evaluate slope stability by using this method.

引入SPA的6级模糊模式识别模型在水质综合评价中的应用

为了解决普遍意义上的水质模糊识别理论不能评价指标数据超过5级标准值和最大隶属度原则的缺点,本文提出6级水质计算方法来改进模糊模式识别模型。再者,引入Set Pair Analysis(SPA)理论处理等级标准间的不确定性信息。从而构建引入SPA的6级模糊模式识别模型,将其运用于河流实例中。评价结果表明:引入SPA的6级模糊模式识别模型更能准确地确定水质综合等级,为治理河流水质污染提供理论支持。

Fuzzy Optimum Model of Semi-Structural Decision for Lectotype Optimization of Offshore Platforms

In the process of concept design of offshore platforms, it is necessary to select the best from feasible alternatives through comparison and filter. The criterion set, used to evaluate and select the satisfying alternative, consists of many qualitative and quantitative factors. Therefore, the selection is a problem of multicriteria and semi-structural decision-making. Different from traditional methods in semi-structural decision-making, a new framework and methodology is presented in this paper for evaluation of offshore platform alternatives, First, the criterion set is established for the evaluation of alternatives. Next, the approach is studied to construct the relative membership degree matrix, in which both qualitative and quantitative factors are consistent with the uniform calculating standard. And then a new weight-assessing method is developed for calculation of the weights based on the relative membership degree matrix. Finally, a multi-hierarchy fuzzy optimum model is adopted to select the satisfying offshore platform alternative. A case study shows that the new framework and methodology are scientific, reasonable and easy to use in practice.

大型水轮机设计方案多属性灰色模糊决策模型

针对大型水轮机方案设计中属性信息的不完全性和不确定性,研究了复杂产品方案设计的决策问题,给出了基于灰色系统理论的灰区间数关联决策方法和基于模糊理论的模糊多属性决策方法的优属度的实现过程,建立了基于优属度的多属性灰色模糊决策模型。该模型综合考虑了决策过程中的灰色信息和模糊信息,通过比较设计方案与正负理想区间方案的接近程度,从整体的角度获得最优方案。最后,以大型水轮机方案设计为例,验证了该模型的有效性和可操作性。

沥青路面预养护方案的区间关联模糊优化决策

预防性养护措施选择是预防性养护的关键问题,属于多目标、多因素、多层次的复杂决策问题。在全面分析各影响因素和技术对策的基础上,综合运用专家打分法、区间数学理论、层次分析法、区间关联分析法,建立了预养护措施决策的区间关联模糊决策方法。首先建立预养护多层次模糊决策模型,通过专家打分法确定评价指标区间属性值,根据区间判断矩阵得出各评价指标和影响因素的区间数权向量;对评价模型进行层次分析和区间关联分析,最后得出各预养护措施的隶属度,进而排序。以上海某高速公路为例,运用该方法对各预养护措施进行优选,并与其它方法计算结果进行对比,结果表明该方法合理可行,且对预养护措施的优劣有较好的区分度。

Method for Risky Multiobjective Group Decision-Making and Its Application

The multiobjective group decision-making problem under risk is common in reality. This paper focuses on the study about risky multiobjective group decision-making problem where the index value is not certain. We give indexes classifying method and index normalizing formula of this type problem. By building objective function that minimizes general weighted distance from every alternative to the relatively best and worst alternative, the optimal membership degree of every decision-maker to every alternative can be obtained, and by building another objective function that minimizes general weighted distance from the optimal membership degree of every decision-maker to every alternative to the group optimal alternative and the group inferior alternative, the optimal membership degree of every decision-maker to every alternative can be obtained, which are both based on probability theory and fuzzy theory. Aftermost a model is established which collects group preferences. This method provides a new idea and approach for solving multiobjective decision-making problem among uncertain system, which is applicable for practical problem. Finally a case study shows a satisfactory result.

基于多指标灰区间数关联决策模型的产品方案设计

针对复杂产品方案设计中属性信息的不完全性和不确定性,研究了方案设计中多指标灰区间数关联决策计算方法,提出一种基于灰色系统理论的多指标灰区间数关联决策模型.该模型通过引入灰区间数序列的范数实现多指标决策矩阵的规范化处理,构建了综合考虑灰色信息的正负理想区间方案,利用方案的优属度从整体性的角度获得最优决策方案.最后,通过大型水轮机的方案设计,验证了该模型的有效性和实用性.

路基软基处理方案优选的区间层次决策

针对传统决策方法在评价指标量化和权值确定时主观性较强、误差较大的问题,综合运用区间数学理论法、层次分析法和区间关联分析法,建立了软土路基处理方案优选的区间层次决策法。通过对某工程软基处理方案进行优选,计算各方案的隶属度,得出各方案的优劣次序。研究结果表明:与模糊相似优先比等方法计算结果进行对比,优选结果一致;区间层次决策法充分考虑了主观判断的不确定性,将评价指标值和权值区间化,大大提高了决策精度,为路基软基处理方案决策提供了一种新方法。