基于区间AHP与粗糙集的决策系统的排序

针对决策系统中属性值以区间数形式给出的多指标决策问题,根据区间层次分析法(IAHP)与粗糙集的特点,提出了一种合理的排序方法.在保持分类能力不变的前提下,利用粗糙集理论中的知识约简方法,删除其中不相关或不重要的知识,结合区间层次分析法计算权重进行有效的排序.最后,给出算例说明了该方法的可行性和有效性.     

层次分析中的关联分析法

在假设某一目标下各因素间存在一个客观的排序权重情况下,通过分析排序权重的误差来源,给出了单个评委排序权重的关联分析法     

基于层次分析法和最短路算法的配货模型

本文利用层次分析法,将时间、费用、客户满意度、人力资源等因素结合起来,定量给出了供货商的配货过程中每条线路的权重系数,然后结合最短路算法寻找出运送货物的最优路线．     

一类广义AHP判断下的保序性问题

本讨论了一类基于两组元素比较的广义AHP判断下所用排序方法的保序性,并提出了一种特殊的广义判断阵,四四比较判断矩阵,供实际操作时参考。     

基于层次分析法的几种家用汽车购车模型

目前,随着我国人民生活水平的不断提高,家庭购车逐渐成为一种新的需求.但面对纷繁多变的汽车市场,很多消费者苦于车型的抉择.为了解决家庭购车中的科学决策问题,根据来自汽车销售市场的实际信息,以目前几种10万元以下的主流家用轿车为研究对象,应用层次分析法得到购买家用汽车的数学模型,从而使定量化地解决了车型抉择问题.     

改进层次分析法在PPP项目绩效评估中的应用

PPP(Public Private Partnership)融资模式,代表了公共部门与私人部门之间不同程度的合作关系.针对PPP项目绩效管理问题,提出运用改进层次分析法进行评估.在传统的层次分析法基础上,采用三标度法,引入最优传递矩阵,进而转化成一致性判断矩阵,避免了传统方法判断矩阵的一致性检验,简化了计算.可为投资者和项目决策者提供科学合理的参考依据.     

基于层次分析法的课程表的模糊综合评价

建立了高校课程表的评价指标体系,在此基础上提出了基于层次分析法的课程表的模糊综合评价方法,并用方根法简化模糊评价的权重集求解过程.通过对具体课程表的模糊综合评价,验证了该方法是科学的、可行的.     

区间判断的性态测度与调整

区间判断矩阵是区间判断下进行决策的依据，其性态将直接影响排序的正确性。本文在区间判断的凸锥模型基础上，对区间判断矩阵的性态提出了实用测度方法和可采用的调整措施。     

Decision making with interval probabilities

Handling uncertainty by interval probabilities is recently receiving considerable attention by researchers. Interval probabilities are used when it is difficult to characterize the uncertainty by point-valued probabilities due to partially known information. Most of researches related to interval probabilities, such as combination, marginalization, condition, Bayesian inferences and decision, assume that interval probabilities are known. How to elicit interval probabilities from subjective judgment is a basic and important problem for the applications of interval probability theory and till now a computational challenge. In this work, the models for estimating and combining interval probabilities are proposed as linear and quadratic programming problems, which can be easily solved. The concepts including interval probabilities, interval entropy, interval expectation, interval variance, interval moment, and the decision criteria with interval probabilities are addressed. A numerical example of newsvendor problem is employed to illustrate our approach. The analysis results show that the proposed methods provide a novel and effective alternative for decision making when point-valued subjective probabilities are inapplicable due to partially known information.     

A goal programming method for obtaining interval weights from an interval comparison matrix

Crisp comparison matrices lead to crisp weight vectors being generated. Accordingly, an interval comparison matrix should give an interval weight estimate. In this paper, a goal programming (GP) method is proposed to obtain interval weights from an interval comparison matrix, which can be either consistent or inconsistent. The interval weights are assumed to be normalized and can be derived from a GP model at a time. The proposed GP method is also applicable to crisp comparison matrices. Comparisons with an interval regression analysis method are also made. Three numerical examples including a multiple criteria decision-making (MCDM) problem with a hierarchical structure are examined to show the potential applications of the proposed GP method.     

A decision-support model for investment decisions in new ventures

The decision to invest in new ventures is characterized by incomplete information, where some measures of firm performance are quantitative, while some others are substituted by qualitative indicators. Qualitative attributes are defined in a relative sense. We develop a decision support model for identifying successful new ventures. The model integrates quantitative and qualitative variables through the use of the Analytic Hierarchy Process (AHP). The decision model gains in predictive accuracy through the use of qualitative attributes, and AHP imparts robustness to the qualitative measures.     

基于二次联系数的区间数多属性决策方法及应用

针对属性权重与属性值都是区间数的多属性决策问题,提出基于联系数基本决策模型的二次联系数概念,再利用二次联系数值的变化对区间数多属性决策中的不确定性进行分析,从而客观地反映出区间数多属性决策中不确定性对决策结果的影响,算法简明清晰,结论可靠。     

基于联系数不确定性分析的区间数多属性决策

区间数多属性决策通常是在某一算法下得到方案的排序,很少考虑区间数不确定性的影响,通过区间数转换成联系数,可以客观地反映区间数的不确定性,在此基础上,建立基于联系数的多属性决策模型,从而对不确定性进行较全面的取值分西,使决策结果更为合理.     

A heuristic approach for deriving the priority vector in AHP

This paper proposes an approach for deriving the priority vector from an inconsistent pair-wise comparison matrix through the nearest consistent matrix and experts judgments, which enables balancing the consistency and experts judgments. The developed algorithm for achieving a nearest consistent matrix is based on a logarithmic transformation of the pair-wise comparison matrix, and follows an iterative feedback process that identifies an acceptable level of consistency while complying with experts preferences. Three numerical examples are examined to illustrate applications and advantages of the developed approach.     

一致性互反Fuzzy判断矩阵的传递性

研究矩阵元素为Fuzzy数的互反判断矩阵的传递性质.首先得到了判断两个Fuzzy数近似相等的等价条件,并得到了揭示Fuzzy数的核之间关系的一个充要条件.在此基础上,进一步证明了一致性互反Fuzzy判断矩阵具有传递性的两个结论.这两个结论说明:在层次分析法中,用一致性互反Fuzzy判断矩阵表示一组方案在同一目标下的两两重要性比较是符合理性决策的思维特征的.     

A cosine maximization method for the priority vector derivation in AHP

The derivation of a priority vector from a pair-wise comparison matrix (PCM) is an important issue in the Analytic Hierarchy Process (AHP). The existing methods for the priority vector derivation from PCM include eigenvector method (EV), weighted least squares method (WLS), additive normalization method (AN), logarithmic least squares method (LLS), etc. The derived priority vector should be as similar to each column vector of the PCM as possible if a pair-wise comparison matrix (PCM) is not perfectly consistent. Therefore, a cosine maximization method (CM) based on similarity measure is proposed, which maximizes the sum of the cosine of the angle between the priority vector and each column vector of a PCM. An optimization model for the CM is proposed to derive the reliable priority vector. Using three numerical examples, the CM is compared with the other prioritization methods based on two performance evaluation criteria: Euclidean distance and minimum violation. The results show that the CM is flexible and efficient.     

Bivariate interval semi-infinite programming with an application to environmental decision-making analysis

This paper proposed a bivariate interval semi-infinite linear programming (BV-ISIP) method to address a type decision-making problem where various uncertainties exist in functional relations and parameter uncertainty. The performance of the method is also demonstrated via an illustrative example and an environmental decision-making problem. As BV-ISIP guarantees that each of the constraints is satisfied under all possible levels of independent variables, the system-failure risk can be reduced. The BV-ISIP solutions can be more robust to the variation of coefficients associated with independent variables than the ILP ones. Other features of BV-ISIP are as follows: (i) flexible decision-making schemes can be developed for decision makers in terms of the BV-ISIP solutions; (ii) BV-ISIP can conveniently be applied to many large-scale optimization problems as no significantly-increased computational costs are required; (iii) the method can easily be improved for addressing functional intervals associated with multiple independent variables.     

A Midpoint-Radius approach to regression with interval data

In this paper, a revisited interval approach for linear regression is proposed. In this context, according to the Midpoint-Radius (MR) representation, the uncertainty attached to the set-valued model can be decoupled from its trend. The estimated interval model is built from interval input-output data with the objective of covering all available data. The constrained optimization problem is addressed using a linear programming approach in which a new criterion is proposed for representing the global uncertainty of the interval model. The potential of the proposed method is illustrated by simulation examples.     

Restricted Robust Uniform Matroid Maximization Under Interval Uncertainty

For the problem of selecting p items with interval objective function coefficients so as to maximize total profit, we introduce the r-restricted robust deviation criterion and seek solutions that minimize the r-restricted robust deviation. This new criterion increases the modeling power of the robust deviation (minmax regret) criterion by reducing the level of conservatism of the robust solution. It is shown that r-restricted robust deviation solutions can be computed efficiently. Results of experiments and comparisons with absolute robustness, robust deviation and restricted absolute robustness criteria are reported. This work is supported by a grant from Turkish Academy of Science(TUBA).     

A feasible implementation procedure for interval analysis method from measurement data

An uncertain quantification and propagation procedure via interval analysis is proposed to deal with the uncertain structural problems in the case of the small sample measurement data in this study. By virtue of the construction of a membership function, a finite number of sample data on uncertain structural parameters are processed, and the effective interval estimation on uncertain parameters can be obtained. Moreover, uncertainty propagation based on interval analysis is performed to obtain the structural responses interval according to the quantified results of the uncertain structural parameters. The proposed method can decrease the demanding on the sample number of measurement data in comparison with the classical probabilistic method. For instance, the former only need several to tens of sample data, whereas the latter usually need several tens to several hundreds of them. The numerical examples illustrate the feasibility and validity of the proposed method for non-probabilistic quantification of limited uncertain information as well as propagation analysis.