基于区间直觉模糊数相关系数的多准则决策模型

针对权重信息完全未知,评价信息为区间直觉模糊数的多准则决策问题,提出新的基于区间直觉模糊数相关系数的决策方法,弥补了基于距离测度决策方法造成信息混淆的不足,同时考虑了犹豫度的影响,进而降低了评价信息损失.通过构建并求解基于参照方案相关系数总偏差最小的非线性规划模型获得准则权重,从新的视角给出准则权重的确定方法.利用各备选方案与理想方案、临界方案的加权相关系数得到与理想方案的相对贴近度,以此对方案进行排序.最后通过实例对比分析说明了该方法的有效性.     

权重信息不完全的区间直觉模糊数多属性决策方法

针对权重信息不完全的区间直觉模糊数多属性决策问题,首先,引入了区间直觉模糊数的一些运算法则、区间直觉模糊数的得分函数和精确函数。然后,对权重信息不完全的区间直觉模糊数的多属性决策方法进行了研究,给出了一个基于最大偏差的目标规划模型,从而获得相应的属性权重,并基于IIWAA算子对区间直觉模糊数信息进行集结,进而根据得分函数和精确函数对方案进行排序。最后,进行了实例分析,说明了该方法的实用性和有效性。     

一种评价信息不完全的混合型多属性群决策方法

针对一类评价信息不完全且属性值由精确数、语言评价值等定量、定性形式构成的混合型不完全信息多属性群决策问题,提出了一种基于直觉模糊集和证据理论的决策方法。首先定义了转换函数将不同类型属性值一致转换为更符合决策实际的直觉模糊数,接着根据信息熵原理利用直觉模糊数中的犹豫度确定专家客观权重,随后应用证据理论集结含有信息缺失的评价值,并构造了一可能度比较公式用于集结后方案排序。该法解决了决策问题中易出现的信息残缺和混合型信息等情况,具有更强的实用性。最后的实例分析证明了该方法的科学性、有效性。     

I-FIFOWA算子及其在群决策中的应用

对模糊数直觉模糊信息的集结算子进行了进一步研究,引入了模糊数直觉模糊的一些运算法则、模糊数直觉模糊的得分函数,并基于这些运算法则,提出了一些新算子:模糊数直觉模糊加权平均(FIFWA)算子、模糊数直觉模糊有序加权平均(FIFOWA)算子和诱导的模糊数直觉模糊有序加权平均(I-FIFOWA)算子,然后分析了它们的性质.针对属性权重和专家权重为实数,属性取值为模糊数直觉模糊数的多属性群决策问题,给出了一种基于FIFWA算子和I-FIFOWA算子的模糊数直觉模糊多属性群决策方法.最后,进行了实例分析,说明了该方法的实用性和有效性.     

权重信息未知情况下的多属性群决策方法及其拓展

本文针对群决策中专家权重及指标权重难以确定的问题,提出一种在权重信息完全未知情况下的基于证据距离和模糊熵权变换的多属性群决策方法,其核心在于如何仅通过决策矩阵客观地确定决策者权重及指标权重。通过信息熵和证据距离确定专家权重,并利用模糊变换原理,将专家权重向量与指标熵权矩阵合成,得到统一的群体决策指标权重;最后使用线性加权法集成所有专家对备选方案的评价信息,得到整个方案集的排序。实验结果及相关讨论表明,该方法概念清晰,计算量适中,具有较强的客观性,而且易于机器实现,是一种可行、有效的多属性群决策方法。最后将该方法推广到属性值由精确数、语言值、区间数、直觉模糊数等多种形式构成的混合型多属性群决策中。     

权重信息完全未知的灰色多属性群决策方法研究

基于灰色系统理论的思想和方法,探讨了决策方案的属性值为区间灰数、属性权重及各决策人的权威权重完全未知的灰色多属性群决策问题。通过分析,引入了个体理想最优方案向量、理想专家、方案间优势度和方案集中方案间优势比较矩阵等概念。根据区间灰数的本质特征,定义了两区间灰数的新的相离度,构建了基于两区间灰数相离度的灰色区间关联系数公式及灰色关联度。建立了基于投影的特征向量法和模糊互补判断矩阵排序方法的两种决策算法,给出的算法避免了权重的计算。文中实例分析说明了所提出的灰色多属性群决策方法的合理性及其算法的有效性。     

基于VIKOR和诱导广义直觉梯形模糊Choquet积分算子的多属性群决策方法

针对属性值为直觉梯形模糊数,决策者间和属性间存在相互关联的多属性群决策问题,引入模糊测度和Choquet积分的概念,在直觉梯形模糊数的运算法则基础上构建了诱导型广义直觉梯形模糊choquet积分平均(IG-ITFCA)算子和诱导型广义直觉梯形模糊choquet积分几何(IG-ITFCG)算子,探讨上述算子的若干性质及一些特例,进而提出了基于诱导型广义直觉梯形模糊Choquet积分算子和多准则妥协优化解(VIKOR)的直觉梯形模糊多属性群决策方法。实例分析验证该方法的有效性和合理性。     

基于CI-TOPSIS的梯形直觉模糊多准则群决策分类方法

模糊群决策分类方法广泛应用于政治、经济与社会生活各个领域，可有效避免个人知识与经验局限性所导致的决策失误。针对信息不完备的多准则群决策问题，提出基于CI-TOPSIS的梯形直觉模糊多准则群决策分类方法。首先，给出梯形直觉模糊集及广义梯形直觉模糊几何聚类算子，兼顾考虑群决策中相应依赖属性与决策者的决策偏好。其次，给出基于离散Choquet积分的TOPSIS算子（CI-TOPSIS），以此为基础，进一步给出基于CI-TOPSIS的梯形直觉模糊多准则群决策分类步骤，用于确定具有最大可信度群体一致案例比较信息集，并逐步引导决策者给出部分及全部方案的精确分类，充分考虑模糊决策环境下决策者偏好与案例比较信息的级别关系。最后，通过一个投资决策实例对所提出的多准则分类方法进行验证。实例分析表明：该方法克服了决策过程中信息的遗漏，充分保留了决策过程中信息的完备性，更适用于直觉模糊群决策环境下的决策实践，是一种非常有效和科学的方法，可应用推广到更多决策领域。本文所得结论，对于有效解决多人多投资方案的群决策问题，具有一定的借鉴意义。     

基于后悔理论的混合型多属性案例决策方法

本文针对决策者的后悔规避行为对案例决策的影响,提出了一种基于后悔理论的混合型多属性案例决策方法。首先,针对案例属性的相似度测算,将案例属性的范围拓展到定性数据、清晰数、区间数、语言变量和区间直觉模糊数五种类型;然后,在案例原有效用基础上考虑决策者的后悔-欣喜值来测算各案例的感知效用;进一步,通过案例相似度对感知效用加权求和得到备选方案的综合感知效用,并依据综合感知效用大小对备选方案进行排序;最后通过一个实例,验证了上述方法的可行性和有效性。     

基于对偶犹豫模糊几何Heronian平均算子的多属性决策方法及其应用

针对需要同时考虑变量隶属度、非隶属度以及关联性的融合问题，本文将对偶犹豫模糊集与Heronian平均算子相结合，定义了对偶犹豫模糊几何Heronian平均算子和对偶犹豫模糊几何加权Heronian平均算子，讨论了新算子的一些优良特性，包括幂等性、置换不变性、有界性、单调性等性质，并针对属性值为对偶犹豫模糊语言信息关联系的多属性决策问题，建立了基于对偶犹豫模糊几何加权Heronian平均算子的多属性决策模型，基于所定义的算子和建立的数学模型，提出了一种新的基于对偶犹豫模糊Heronian平均算子的多属性决策方法。最后，通过多属性决策算例验证了方法的有效性和可行性。     

Evaluation of the results of multi-attribute group decision-making with linguistic information

Multi-attribute group decision-making (MAGDM) has received increasing attentions in both engineering and economy fields. Correspondingly, many valuable methods have been developed to solve various MAGDM problems, but relatively, very few research results focus on the evaluation of the effect of MAGDM. In this paper, based on the existing MAGDM methods with linguistic information, three key evaluation indices, consistency, closeness and uniformity, are proposed to measure the results of MAGDM from different aspects. By comparing the individual overall preference values with the collective ones, the three indices cannot only provide a reference for judging the decision-making effect of each decision maker, but also reflect the effect of group decision-making to a certain extent. The practicality and effectiveness of the proposed method are shown by two heuristic examples. Furthermore, the proposed method will be helpful for setting and adjusting the weights of both attributes and decision makers, as well as for selecting and comparing various aggregation operators and methods in dynamic or interactive group decision-making.     

On qualitative multi-attribute group decision making and its consensus measure: A probability based perspective

This paper focuses on qualitative multi-attribute group decision making (MAGDM) with linguistic information in terms of single linguistic terms and/or flexible linguistic expressions. To do so, we propose a new linguistic decision rule based on the concepts of random preference and stochastic dominance, by a probability based interpretation of weight information. The importance weights and the concept of fuzzy majority are incorporated into both the multi-attribute and collective decision rule by the so-called weighted ordered weighted averaging operator with the input parameters expressed as probability distributions over a linguistic term set. Moreover, a probability based method is proposed to measure the consensus degree between individual and collective overall random preferences based on the concept of stochastic dominance, which also takes both the importance weights and the fuzzy majority into account. As such, our proposed approaches are based on the ordinal semantics of linguistic terms and voting statistics. By this, on one hand, the strict constraint of the uniform linguistic term set in linguistic decision making can be released; on the other hand, the difference and variation of individual opinions can be captured. The proposed approaches can deal with qualitative MAGDM with single linguistic terms and flexible linguistic expressions. Two application examples taken from the literature are used to illuminate the proposed techniques by comparisons with existing studies. The results show that our proposed approaches are comparable with existing studies.     

基于不确定纯语言混合调和平均算子的多属性群决策方法

在现实生活中,由于决策者对一些特定领域问题的熟悉度和时间限制等因素制约,决策信息一般以不确定纯语言的形式给出,即专家权重、属性权重及属性值均为语言标度的形式. 本文研究了不确定纯语言环境下的多属性群决策问题,给出了不确定环境下的纯语言有序加权调和平均(UPLOWHA)算子,纯语言混合调和平均(UPLHHA)算子等,研究了基于这些算子的纯语言多属性群决策问题,提出了相应的多属性群决策方法. 该方法计算方便且能充分利用已有语言决策信息. 同时,将该方法应用于解决虚拟企业中的合作伙伴选择问题,并通过与其他方法的比较分析,说明此方法的有效性.     

基于理想解和灰关联度的动态评价方法及其应用研究

为了对多个多属性（指标）待评价对象（方案）在多个时间点的发展状态和该时间段内的总体发展水平进行比较分析，根据理想解法和灰关联度法优缺点，提出基于理想解和灰关联度的动态评价方法。该方法基于三维数据，将欧氏距离和灰色关联度相结合，提出一种新贴近度，同时反映了位置关系和数据曲线的相似性差异，兼顾评价指标值差异程度和增长程度。最后将该方法应用于"十二五"期间省域循环经济生态效益评价，通过实例验证该方法实际应用上的有效性。     

Carbon price forecasting with a novel hybrid ARIMA and least squares support vector machines methodology

In general, due to inherently high complexity, carbon prices simultaneously contain linear and nonlinear patterns. Although the traditional autoregressive integrated moving average (ARIMA) model has been one of the most popular linear models in time series forecasting, the ARIMA model cannot capture nonlinear patterns. The least squares support vector machine (LSSVM), a novel neural network technique, has been successfully applied in solving nonlinear regression estimation problems. Therefore, we propose a novel hybrid methodology that exploits the unique strength of the ARIMA and LSSVM models in forecasting carbon prices. Additionally, particle swarm optimization (PSO) is used to find the optimal parameters of LSSVM in order to improve the prediction accuracy. For verification and testing, two main future carbon prices under the EU ETS were used to examine the forecasting ability of the proposed hybrid methodology. The empirical results obtained demonstrate the appeal of the proposed hybrid methodology for carbon price forecasting.     

A robust ranking method extending ELECTRE III to hierarchy of interacting criteria,imprecise weights and stochastic analysis

A great majority of methods designed for Multiple Criteria Decision Aiding (MCDA) assume that all assessment criteria are considered at the same level, however, decision problems encountered in practice often impose a hierarchical structure of criteria. The hierarchy helps to decompose complex decision problems into smaller and manageable subtasks, and thus, it is very attractive for computational efficiency and explanatory purposes. To handle the hierarchy of criteria in MCDA, a methodology called Multiple Criteria Hierarchy Process (MCHP), has been recently proposed. MCHP permits to consider preference relations with respect to a subset of criteria at any level of the hierarchy. Here, we propose to apply MCHP to the ELECTRE III ranking method adapted to handle three types of interaction effects between criteria: mutual-weakening, mutual-strengthening and antagonistic effect. We also involve in MCHP an imprecise elicitation of criteria weights, generalizing a technique called the SRF method. In order to explore the plurality of rankings obtained by the ELECTRE III method for possible sets of criteria weights, we apply the Stochastic Multiobjective Acceptability Analysis (SMAA) that permits to draw robust conclusions in terms of rankings and preference relations at each level of the hierarchy of criteria. The novelty of the whole methodology consists of a joint consideration of hierarchical assessments of alternatives performances on interacting criteria, imprecise criteria weights, and robust analysis of ranking recommendations resulting from ELECTRE III. An example regarding the multiple criteria ranking of some European universities will show how to apply the proposed methodology on a decision problem.     

Robustness analysis methodology for multi-objective combinatorial optimization problems and application to project selection

Multi-objective combinatorial optimization (MOCO) problems, apart from being notoriously difficult and complex to solve in reasonable computational time, they also exhibit high levels of instability in their results in case of uncertainty, which often deviate far from optimality. In this work we propose an integrated methodology to measure and analyze the robustness of MOCO problems, and more specifically multi-objective integer programming ones, given the imperfect knowledge of their parameters. We propose measures to assess the robustness of each specific Pareto optimal solution (POS), as well as the robustness of the entire Pareto set (PS) as a whole. The approach builds upon a synergy of Monte Carlo simulation and multi-objective optimization, using the augmented ε-constraint method to generate the exact PS for the MOCO problems under examination. The usability of the proposed framework is justified through the identification of the most robust areas of the Pareto front, and the characterization of every POS with a robustness index. This index indicates a degree of certainty that a specific POS sustains its efficiency. The proposed methodology communicates in an illustrative way the robustness information to managers/decision makers and provides them with an additional supplement/tool to guide and support their final decision. Numerical examples focusing on a multi-objective knapsack problem and an application to academic capital budgeting problem for project selection, are provided to verify the efficacy and added value of the methodology.     

具有时变自由度的t-copula蒙特卡罗组合收益风险研究

应用时变条件t-copula函数描述股票指数收益序列之间的时变相依结构。时变条件t-copula模型的难点在于如何设定时变相依参数的演化方程,本文建立了用于描述包含时变自由度在内的所有时变相依模型参数的演化方程。进而采用蒙特卡洛仿真方法计算了各种指数组合的VaR,分析了道琼斯指数与标准普尔指数组合风险的演化趋势,并对结果进行后验测试,结果表明,时变条件t-copula函数仿真估计VaR可以覆盖最大损失风险。     

A heuristic approach to n/ m job shop scheduling: fuzzy dynamic scheduling algorithms

n/m shop scheduling is a ‘ NP-Hard’ problem. Using conventional heuristic algorithms ( priority rules) only, it is almost impossible to achieve an optimal solution. Research has been carried out to improve the heuristic algorithms to give a near-optimal solution. This paper advocates a fuzzy logic based, dynamic scheduling algoridim aimed at achieving this goal. The concept of new membership functions is discussed in die algorithm as a link to connect several priority rules. The constraints to determine the membership function of jobs for a particular priority rule are established, and three membership functions are developed. In order to decide the weight vector of priority rules, an aggregate performance measure is suggested. The methodology for constructing the weight vector is discussed in detail. Experiments have been carried out using a simulation technique to validate the proposed scheduling algorithm.     

Development of Economic Consequence Methodology for Process Risk Analysis

A comprehensive methodology for economic consequence analysis with appropriate models for risk analysis of process systems is proposed. This methodology uses loss functions to relate process deviations in a given scenario to economic losses. It consists of four steps: definition of a scenario, identification of losses, quantification of losses, and integration of losses. In this methodology, the process deviations that contribute to a given accident scenario are identified and mapped to assess potential consequences. Losses are assessed with an appropriate loss function (revised Taguchi, modified inverted normal) for each type of loss. The total loss is quantified by integrating different loss functions. The proposed methodology has been examined on two industrial case studies. Implementation of this new economic consequence methodology in quantitative risk assessment will provide better understanding and quantification of risk. This will improve design, decision making, and risk management strategies.