多品种集约生产计划问题的模糊方法

提出具有模糊需求量和模糊能力约束以及资本水平约束的多品种类集约生产计划问题 的模糊优化模型及模糊解方法. 通过对模糊需求量和模糊等式的描述,提出了模糊需求环境下 生产- 库存平衡方程的两种等价的描述方法, 并给出了模糊等式的实用解释. 建立了具有模 糊需求量和模糊能力约束集约生产计划问题的优化模型FMAPP ,并给出了求解模型的参数规 划方法.     

共识条件下最小最大妥协的直觉模糊数集结方法研究

直觉模糊集（IFS）理论是描述广泛模糊事物的重要工具。为减小决策过程中个体偏好值与群体偏好值的差异，协调个体与群体间矛盾，提升决策结果的执行效率，本文提出最小化最大妥协度（Minimize maximum compromise）的决策准则。给出直觉模糊环境下的，个体偏好值的集结算法及决策方法，并分别考虑了有无共识条件、有无决策主体权重的三类决策情景。最后给出算例，验证本文方法的有效性，结果表明，相较于I-IFOWG算子，本文方法能够有效降低群体决策中个体的妥协程度。     

R&D联盟条件下基于FMGTS评价的R&D项目合作成员选择

针对如何从多个候选R&D联盟成员中选择最理想的R&D项目合作成员问题,提出了一种操作性较强的选择方法。首先通过静态博弈得到了候选R&D联盟成员进行某R&D项目合作时竞标价格的可行区间,在考虑专家采用模糊多粒度语言(fuzzy multi-granularity term sets,FMGTS)进行期望获利度评价的状况下,运用基本语言转换函数将评价信息进行集结,据此确定候选R&D联盟成员的期望获利度和优化的竞标价格。在给出价格满意度与工期满意度公式的基础上,利用效用值法将基于不同满意度下的排名决策信息进行一致化处理,最后采用互补判断矩阵中的排序公式来选择理想的R&D项目合作成员。     

Fuzzy multi-attribute decision-making for evaluating manufacturing flexibility

Evaluation of manufacturing flexibility in operations management is important to determine the competitiveness of manufacturing system, and is being increasing discussed in the literature on manufacturing system. The objective of this research is to develop a multi-attribute decision-making model based on fuzzy set theory to improving the manufacturing flexibility evaluation process. Since most information available in this stage is not numerical, fuzzy linguistic assessment is used to represent the performance rating of all flexibility metrics under flexibility dimensions and importance grade of all flexibility dimensions. This paper proposes a modified LOWA operator, which uses the maximum entropy weights, and uses it to direct computation on linguistic terms. The developed model evaluates the degree of manufacturing flexibility that can assist decision-makers, when making capital investment decisions and measuring performance, in finding the need for improving manufacturing flexibility, and in determining the dimensions of flexibility as the best directions to improvement. Examples using a case study of leading Taiwan firm in the bicycle industry are used to illustrate the concept developed. In addition, sensitivity analysis can be performed to examine the solution reasonability.     

基于模糊判断矩阵的群决策方法研究

对多个决策者给出的偏好信息的有效集结是群决策过程的重要问题之一.不同类型的偏好信息有不同的集结方法.基于模糊判断矩阵一致性的定义,提出一种加权集结方法的最优化模型,从而得到群决策中一类模糊判断矩阵的集结方法,并进一步分析和研究群组判断矩阵与各决策者给出的判断矩阵之间关系的一些重要性质.     

基于犹豫直觉模糊语言集均值-标准差偏好距离的多属性决策研究

在犹豫直觉模糊语言集和语言尺度函数的基础上定义了均值-标准差偏好的Hamming距离，并提出了基于犹豫直觉模糊语言集距离TOPSIS和TODIM的多属性决策方法，进一步利用这两种方法对实例问题建筑商的招标方案进行排序，并讨论了偏好参数对排序结果的灵敏度分析。为验证上述方法的有效性，与已有方法对同一实例的排序结果进行了比较分析。     

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。     

EMPIRICAL TESTS OF CONSTRAINED NONLINEAR OPTIMIZATION ALGORITHMS

A major difficulty in practicing constrained nonlinear optimization is that different optimization algorithms are effective for different classes of problems. The search algorithms tested were selected because they seemingly had the capability of solving ill-defined problems. The emphasis of this research was on problems that are realistic and do not necessarily satisfy the classical assumptions of convexity, continuity, unimodality, etc. All algorithms were tested on a variety of problems. A problem was described by three types of attributes: the environmental attributes, the objective function attributes, and the constraint set attributes. The results of the study provide selective logic for choosing an effective search algorithm.     

Concepts,Theory, and Techniques A NEW METHODOLOGY FOR ORDINAL MULTIOBJECTIVE DECISIONS BASED ON FUZZY SETS

Using the structural forms supplied by fuzzy set theory and approximate reasoning, a new method is presented for solving multiple-objective decision problems for which the decision maker can supply only ordinal information on his preferences and the importance of the individual objectives.     

Fuzzy LINMAP approach to heterogeneous MADM considering comparisons of alternatives with hesitation degrees

Multiattribute decision making (MADM) with multiple formats of information, which is called heterogeneous MADM for short, is very complex and interesting in applications. The purpose of this paper is to extend the Linear Programming Technique for Multidimensional Analysis of Preference (LINMAP) for solving heterogeneous MADM problems which involve intuitionistic fuzzy (IF) sets (IFSs), trapezoidal fuzzy numbers (TrFNs), intervals and real numbers. In this method, DM's preference is given through pair-wise comparisons of alternatives with hesitation degrees which are represented as IFSs. The IF consistency and inconsistency indices are defined on the basis of pair-wise comparisons of alternatives. Each alternative is assessed on the basis of its distance to a fuzzy ideal solution (FIS) unknown a priori. Based on the defined IF consistency and inconsistency indices, we construct a new fuzzy mathematical programming model, which is solved by the developed method of fuzzy mathematical programming with IFSs. Once the FIS and the attribute weights are obtained, we can calculate the distances of all alternatives to the FIS, which are used to determine the ranking order of the alternatives. A supplier selection example is presented to demonstrate the validity and applicability of the proposed method.     

Fuzzy LINMAP approach to heterogeneous MADM considering comparisons of alternatives with hesitation degrees

Multiattribute decision making (MADM) with multiple formats of information, which is called heterogeneous MADM for short, is very complex and interesting in applications. The purpose of this paper is to extend the Linear Programming Technique for Multidimensional Analysis of Preference (LINMAP) for solving heterogeneous MADM problems which involve intuitionistic fuzzy (IF) sets (IFSs), trapezoidal fuzzy numbers (TrFNs), intervals and real numbers. In this method, DM's preference is given through pair-wise comparisons of alternatives with hesitation degrees which are represented as IFSs. The IF consistency and inconsistency indices are defined on the basis of pair-wise comparisons of alternatives. Each alternative is assessed on the basis of its distance to a fuzzy ideal solution (FIS) unknown a priori. Based on the defined IF consistency and inconsistency indices, we construct a new fuzzy mathematical programming model, which is solved by the developed method of fuzzy mathematical programming with IFSs. Once the FIS and the attribute weights are obtained, we can calculate the distances of all alternatives to the FIS, which are used to determine the ranking order of the alternatives. A supplier selection example is presented to demonstrate the validity and applicability of the proposed method.     

Matrix games with fuzzy goals and fuzzy payoffs

A two person zero sum matrix game with fuzzy goals and fuzzy payoffs is considered and its solution is conceptualized using a suitable defuzzification function. Also, it is proved that such a game is equivalent to a primal–dual pair of certain fuzzy linear programming problems in which both goals as well as parameters are fuzzy.     

An extension of the Electre I method for group decision-making under a fuzzy environment

Many real-world decision problems involve conflicting systems of criteria, uncertainty and imprecise information. Some also involve a group of decision makers (DMs) where a reduction of different individual preferences on a given set to a single collective preference is required. Multi-criteria decision analysis (MCDA) is a widely used decision methodology that can improve the quality of group multiple criteria decisions by making the process more explicit, rational and efficient. One family of MCDA models uses what is known as “outranking relations” to rank a set of actions. The Electre method and its derivatives are prominent outranking methods in MCDA. In this study, we propose an alternative fuzzy outranking method by extending the Electre I method to take into account the uncertain, imprecise and linguistic assessments provided by a group of DMs. The contribution of this paper is fivefold: (1) we address the gap in the Electre literature for problems involving conflicting systems of criteria, uncertainty and imprecise information; (2) we extend the Electre I method to take into account the uncertain, imprecise and linguistic assessments; (3) we define outranking relations by pairwise comparisons and use decision graphs to determine which action is preferable, incomparable or indifferent in the fuzzy environment; (4) we show that contrary to the TOPSIS rankings, the Electre approach reveals more useful information including the incomparability among the actions; and (5) we provide a numerical example to elucidate the details of the proposed method.     

模糊随机不确定环境下考虑决策者主观判断的亚式期权定价

考虑金融市场的不确定性包含随机性和模糊性两个方面,把标的资产价格视作一个模糊随机过程,以连续几何平均亚式看涨期权为例运用随机分析和模糊集理论研究了模糊随机不确定环境下的亚式期权定价问题。首先,推导出了亚式期权模糊价格的任意水平截集,并将如何计算给定任一个参考价格的置信度问题转化为求解最优化问题。然后,研究了两种考虑决策者主观判断的亚式期权定价,一是引入模糊目标表示决策者对期权预期价格的满意度,给出可靠度大于决策者满意度的亚式期权预期价格的范围;二是引入悲观-乐观指数表示决策者的悲观程度,基于加权函数和可能性估计测度定义模糊数的可能性均值,得到可能性均值意义下的亚式期权定价公式。最后,给出了一个数值例子说明了模型的可行性和实用性。     

基于证据推理和广义Shapley值的扩展概率语言多属性群决策方法

扩展概率语言词集通过语言变量概率分布的调整能够转化为多种语言信息表示模型,是语言变量、不确定语言信息、扩展犹豫模糊语言词集、分布语言评估信息、概率语言词集等的一般化,具有较强的通用性和实用性,是处理不确定性信息的重要工具。鉴于此,本文针对扩展概率语言环境下的多属性群决策问题,提出基于证据推理和广义Shapley值的多属性群决策方法。首先,提出扩展概率语言词集的定义和相关基础理论。其次,将广义Shapley值和证据推理相结合用于专家信息融合,并将广义Shapley值和TODIM方法相结合用于备选方案排序。再次,提出基于灰色关联法的权重确定模型来处理专家/属性权重部分未知的情况。最后,以绿色供应商选择为例进行分析,通过对比分析验证所提方法的有效性和优越性。     

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Mo-RVIKOR的混合多属性决策方法

针对复杂性和不确定性多属性决策问题,考虑定量和定性融合的属性形式,提出了模块化随机多准则妥协解排序法（Modular Random VlseKriterijumska Opti-mizacija I Kompromisno Resenje,Mo-RVIKOR）,该方法无需将信息统一,就能处理多种信息形式存在的多属性决策问题。采用精确数、随机变量处理定量评价信息,用概率语义术语集处理定性评价信息;通过改进离差最大化法确定属性权重;根据Mo-RVIKOR对决策对象进行排序;最后以某公司C2B定制化服务质量评测项目为例,验证了所提方法的有效性。     

Power planning in ICT infrastructure: A multi-criteria operational performance evaluation approach

It is critical for information and communications technology (ICT) companies to carry our effective power planning, in order to support the growing number of services they provide, and this traditionally relies on the tacit knowledge and experience of senior staff. The loss of such domain knowledge resulting from the retirement of staff is an important issue for organizations such as Chunghwa Telecom (CHT), the largest ICT operator in Taiwan. This study thus develops a systematic power planning model using a multi-criteria operational performance evaluation. A group version of the fuzzy repertory grid and fuzzy TOPSIS approaches is applied to elicit a set of evaluation criteria that senior staff agree on, and then the priorities of the telecom rooms are evaluated against this. In addition, a new factor, reflecting the attitudes of the decision makers with respect to the degree of strictness, is defined to determine the superiority and inferiority of each alternative compared to the others. Furthermore, a novel decision aggregation strategy regarding the degree of variation among decision makers is proposed, and a quantitative assessment is carried out to analyze its impact on the ranking results in an objective manner. The proposed model may help ICT organizations to more effectively manage their power resources, and thus obtain competitive advantages.     

一类序贯决策方法的提出:透镜与直觉模糊信息的视角

与大多数关注经典秘书问题的序贯决策研究不同,本文针对决策对象不变而其状态更新的一类序贯决策问题,提供决策方法。相较已有研究而言,本文从透镜与直觉模糊信息的视角提出这类序贯决策的一般方法,更加具有普适性,可应用于应急管理、风险投资等多个方向。该决策方法具有如下特点：1）借鉴透镜模型,通过当期可观测的线索,预测这类序贯决策问题的下一期状态;2）考虑到决策环境具有不确定性,采用直觉模糊数对决策者获取的信息线索进行刻画;3）为最大化模拟现实决策者,在前景理论框架下提出状态更新的序贯决策方法。本文提出的决策方法依据在于决策者对决策对象的预测"前景"值和预测绩效,基于此提出了具体的决策步骤,并辅以案例进行分析。通过对不同决策情形下决策结果的比较分析和对案例的稳健性检验,验证了该决策方法的适用性和有效性。     

群组决策中三角模糊数互补判断矩阵的相容性及方案排序研究

针对专家偏好信息为三角模糊数互补判断矩阵的群组决策问题,研究偏好信息的相容性及方案排序问题。基于Hamming 距离的概念,首先给出了衡量两个三角模糊数相容性的一个指标,并研究了该指标的相关性质;其次,根据三角模糊数互补判断矩阵的特点,给出了三角模糊数互补判断矩阵的相容性指标;以相容性指标为依据设定专家权重,进而给出了一种方案排序方法。最后,算例验证了方法的有效性。