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.     

Global supplier development considering risk factors using fuzzy extended AHP-based approach

Global supplier development is a multi-criterion decision problem which includes both qualitative and quantitative factors. The global supplier selection problem is more complex than domestic one and it needs more critical analysis. The aim of this paper is to identify and discuss some of the important and critical decision criteria including risk factors for the development of an efficient system for global supplier selection. Fuzzy extended analytic hierarchy process (FEAHP) based methodology will be discussed to tackle the different decision criteria like cost, quality, service performance and supplier's profile including the risk factors involved in the selection of global supplier in the current business scenario. FEAHP is an efficient tool to handle the fuzziness of the data involved in deciding the preferences of different decision variables. The linguistic level of comparisons produced by the customers and experts for each comparison are tapped in the form triangular fuzzy numbers to construct fuzzy pair-wise comparison matrices. The implementation of the system is demonstrated by a problem having four stages of hierarchy which contains different criteria and attributes at wider perspective. The proposed model can provide not only a framework for the organization to select the global supplier but also has the capability to deploy the organization's strategy to its supplier.     

An integrated method for cognitive complex multiple experts multiple criteria decision making based on ELECTRE III with weighted Borda rule

The ELECTRE (ELimination Et Choix Traduisant la REalité, in French) is an effective multiple criteria decision making method based on comparative analysis. Among the family of the ELECTRE methods and their extensions, the ELECTRE III is widely used since it can tackle uncertain and imprecise information. The hesitant fuzzy linguistic term set can represent people's perceptions more comprehensively and flexibly than exact numbers especially in cognitive complex decision-making process. In this paper, we develop an integrated method based on the ELECTRE III to handle the cognitive complex multiple experts multiple criteria decision making problems in which the cognitive complex information is represented by hesitant fuzzy linguistic term sets and the outranking relations between alternatives are calculated by a novel score-function-based distance measure between hesitant fuzzy linguistic elements. A combinative weight-determining method involving both subjective and objective opinions of experts is introduced to derive the weights of criteria. After obtaining the ranking of alternatives from each experts’ decision matrix by the distillation algorithm, the weighted Borda rule is implemented to aggregate the rankings of alternatives regarding different experts. Some ordinal consensus measures are introduced to identify the reliability of the final ranking result. An application of hospital ranking in China is provided to validate the efficiency of the proposed method.     

A multi-criteria ranking algorithm (MCRA) for determining breast cancer therapy

Breast cancer is the leading cause of cancer deaths among women. The selection of an effective, patient-specific treatment plan for breast cancer has been a challenge for physicians because the decision process involves a vast number of treatment alternatives as well as treatment decision criteria, such as the stage of the cancer (e.g., in situ, invasive, metastasis), tumor characteristics, biomarker-related risks, and patient-related risks. Furthermore, every patient's case is unique, requiring a patient-specific treatment plan, while there is no standard procedure even for a particular stage of the breast cancer. In this paper, we first determine a comprehensive set of criteria for selecting the best breast cancer therapy by interviewing medical oncologists and reviewing the literature. We then present two analytical hierarchy process (AHP) models for quantifying the weights of criteria for breast cancer treatment in two sequential steps: primary and secondary treatment therapy. Using the weights of criteria from the AHP model, we propose a new multi-criteria ranking algorithm (MCRA), which evaluates a large variety of patient scenarios and provides the best patient-tailored breast cancer treatment alternatives based on the input of nine medical oncologists. We then validate the predictions of the multi-criteria ranking algorithm by comparing treatment ranks of the algorithm with ranks of five different oncologists, and show that algorithm rankings match or are statistically significantly correlated with the overall expert ranking in most cases. Our multi-criteria ranking algorithm could be used as an accessible decision-support tool to aid oncologists and educate patients for determining appropriate and effective treatment alternatives for breast cancer. Our approach is also general in the sense that it could be adapted to solve other complex decision-making problems in medicine, healthcare, as well as other service and manufacturing industries.     

Multi-objective simulation optimization using data envelopment analysis and genetic algorithm: Specific application to determining optimal resource levels in surgical services

Simulation is a powerful tool for modeling complex systems with intricate relationships between various entities and resources. Simulation optimization refers to methods that search the design space (i.e., the set of all feasible system configurations) to find a system configuration (also called a design point) that gives the best performance. Since simulation is often time consuming, sampling as few design points from the design space as possible is desired. However, in the case of multiple objectives, traditional simulation optimization methods are ineffective to uncover the efficient frontier. We propose a framework for multi-objective simulation optimization that combines the power of genetic algorithm (GA), which can effectively search very large design spaces, with data envelopment analysis (DEA) used to evaluate the simulation results and guide the search process. In our framework, we use a design point's relative efficiency score from DEA as its fitness value in the selection operation of GA. We apply our algorithm to determine optimal resource levels in surgical services. Our numerical experiments show that our algorithm effectively furthers the frontier and identifies efficient design points.     

Developing a supplier selection system through integrating fuzzy AHP and fuzzy DEA: a case study on an auto lighting system company in Taiwan

Supplier selection plays a very important role in supply chain management. This study intends to develop a novel performance evaluation method, which integrates both fuzzy analytical hierarchy process (AHP) method and fuzzy data envelopment analysis (DEA) for assisting organisations to make the supplier selection decision. Fuzzy AHP method is first applied to find the indicators’ weights through expert questionnaire survey. Then, these weights are integrated with fuzzy DEA. We use α -cut set and extension principle of fuzzy set theory to simplify the fuzzy DEA as a pair of traditional DEA model. Finally, fuzzy ranking using maximising and minimising set method is able to rank the evaluation samples. A case study on an internationally well-known auto lighting OEM company shows that the proposed method is very suitable for practical applications.     

Data envelopment analysis: Prior to choosing a model

In this paper, we address several issues related to the use of data envelopment analysis (DEA). These issues include model orientation, input and output selection/definition, the use of mixed and raw data, and the number of inputs and outputs to use versus the number of decision making units (DMUs). We believe that within the DEA community, researchers, practitioners, and reviewers may have concerns and, in many cases, incorrect views about these issues. Some of the concerns stem from what is perceived as being the purpose of the DEA exercise. While the DEA frontier can rightly be viewed as a production frontier, it must be remembered that ultimately DEA is a method for performance evaluation and benchmarking against best-practice. DEA can be viewed as a tool for multiple-criteria evaluation problems where DMUs are alternatives and each DMU is represented by its performance in multiple criteria which are coined/classified as DEA inputs and outputs. The purpose of this paper is to offer some clarification and direction on these matters.     

INFLUENCE OF MISSING ATTRIBUTES ON SELECTING A BEST MULTIATTRIBUTED ALTERNATIVE

Alternatives involving many factors arc difficult to evaluate because of multiple underlying competing objectives. If evaluation is based on an incomplete set of factors, and if the purpose of the evaluation is to select a single overall best alternative, inferior alternatives may be selected with surprising frequency and/or severe negative impact. At the same time, sensitivity analysis of evaluation scores based on statistical criteria can easily mask the impact and the frequency of selection of inferior alternatives. In this paper, criteria appropriate to reflect the decision impact are developed and both the frequency and impact of the selection of inferior alternatives are demonstrated empirically. Previous studies based on statistical criteria [1] [9] indicated minimal impact on overall evaluation and selection. This paper demonstrates that high statistical criterion values coexist with frequent and/or serious errors of selection.     

Heuristics for prioritizing pair-wise elicitation questions with additive multi-attribute value models

Additive value models are widely used in Multiple Criteria Decision Analysis. Direct elicitation of the value model preference parameters can impose excessive cognitive burden on the decision maker. Indirect techniques that employ pair-wise questions have been proposed for lowering the elicitation effort. In all practically relevant problems, more than a single question needs to be answered for arriving at a sufficiently precise outcome. The selection and ordering of questions affects the number of answers required for ranking the decision alternatives. However, evaluating all possible questions and answers is intractable due to the search space being, in the worst case, of factorial size. This paper develops heuristics for prioritizing pair-wise elicitation questions based on (1) necessary preference relations, (2) extreme ranks attained by the alternatives, (3) pair-wise preference indices, and (4) rank acceptability indices. We also introduce three metrics for assessing quality of a question prioritization heuristic. Numerical results allow us to identify a subset of heuristics that score well on our metrics in a variety of problem settings. This conclusion was validated in a real-world experiment where 101 subjects answered pair-wise questions to rank 10 mobile phone packages evaluated in terms of four criteria.     

Productivity Growth in the Lisbon Police Force

This paper estimates total productivity change with regard to the Lisbon Police Force and decomposes it into technically efficient change and technological change with data envelopment analysis (DEA). The benchmarking procedure implemented is an internal benchmarking, in which police precincts are compared against each other. The aim of this procedure is to seek out those best practices that will lead to improved performance throughout the whole force. We rank the precincts according to their total productivity change for the period 2000–2001, concluding that some precincts experienced productivity growth while a small number experienced productivity decrease. Economic implications arising from the study are considered.     

RANK GENERATION,PRESERVATION, AND REVERSAL IN THE ANALYTIC HIERARCHY DECISION PROCESS

Decision making has the objective of finding the best alternative or set of alternatives by considering a number of goals, objectives, criteria, competitors, and other important factors. The analytic hierarchy process is a decision aid used to assist a decision maker in sorting out the complexity of a decision problem and making use of his or her judgments. A decision maker must be assured that the arithmetic operations of any such decision process are the right ones—that they surface the correct ranking and values of the alternatives and preserve or alter ranks appropriately when new alternatives are added or deleted. In this paper it will be shown that with absolute measurement, rank always is preserved, with relative measurement, rank changes with nspect to scveral criteria only because of the structural dependence (involving both numbers and measurements) of criteria on alternatives. A discussion of the effect on rank of replicas and near replicas of the alternatives also is given.     

基于DEA理论的ANP/BOCR方案评价值综合集成新方法

网络分析法(ANP)是一种能够有效处理复杂决策问题的多准则决策方法。然而现有ANP文献在对收益、机会、成本、风险(统称为BOCR)评价值综合集成时会因评价值之间的不匹配而可能得出错误的方案排序结果和绩效表示。为克服上述缺陷,本文基于数据包络分析理论提出一种新的针对ANP/BOCR评价值的综合集成方法,使用摆幅置权区间估计方式反映出了决策者在判断BOCR相对权重时所面临的不精确性和模糊性。实例验证结果表明,所提方法对BOCR评价值的处理更符合实际情况。     

存在保证域的模糊超效率DEA模型

模糊DEA模型是用于解决存在模糊数据的决策单元(DMUs)效率评价问题的,然而现有的模糊DEA模型分辨率低,本文构建了存在保证域的模糊超效率DEA模型,并给出了一种基于截集的求解方法并进行了证明,该模型有效地解决了输入和输出全部或部分为模糊数的决策单元全排序问题。最后给出了一个银行效率评价的实例说明了方法的有效性。     

Decision Making Under Uncertainty—An Example for Seismic Risk Management

Decision-making techniques are used to select the "best" alternatives under multiple and often conflicting criteria. Multicriteria decision making (MCDM) necessitates to incorporate uncertainties in the decision-making process. The major thrust of this article is to extend the framework proposed by Yager^{( 1 )} for multiple decisionmakers and fuzzy utilities (payoffs). In addition, the concept of expert credibility factor is introduced. The proposed approach is demonstrated for an example of seismic risk management using a heuristic hierarchical structure. A step-by-step formulation of the proposed approach is illustrated using a hypothetical example and a three-story reinforced concrete building.     

一种基于TOPSIS的混合型多属性群决策方法

本文针对具有语言型和直觉模糊数两种评价信息的混合型多属性群决策问题,提出了一种基于TOPSIS的决策方法。首先,定义了新的函数,可将不同粒度的语言评价信息转换成直觉模糊数。其次,在直觉模糊数熵值的基础上,提出了一种新的专家权重确定模型。再次,利用IFWA算子在把个体决策矩阵集结为群体决策矩阵后,基于TOPSIS分别计算群体评价值到正理想解和负理想解的距离,从而得到方案集的排序。最后,在ERP选优问题中的应用,验证了方法的有效性。     

Best-worst multi-criteria decision-making method

In this paper, a new method, called best-worst method (BWM) is proposed to solve multi-criteria decision-making (MCDM) problems. In an MCDM problem, a number of alternatives are evaluated with respect to a number of criteria in order to select the best alternative(s). According to BWM, the best (e.g. most desirable, most important) and the worst (e.g. least desirable, least important) criteria are identified first by the decision-maker. Pairwise comparisons are then conducted between each of these two criteria (best and worst) and the other criteria. A maximin problem is then formulated and solved to determine the weights of different criteria. The weights of the alternatives with respect to different criteria are obtained using the same process. The final scores of the alternatives are derived by aggregating the weights from different sets of criteria and alternatives, based on which the best alternative is selected. A consistency ratio is proposed for the BWM to check the reliability of the comparisons. To illustrate the proposed method and evaluate its performance, we used some numerical examples and a real-word decision-making problem (mobile phone selection). For the purpose of comparison, we chose AHP (analytic hierarchy process), which is also a pairwise comparison-based method. Statistical results show that BWM performs significantly better than AHP with respect to the consistency ratio, and the other evaluation criteria: minimum violation, total deviation, and conformity. The salient features of the proposed method, compared to the existing MCDM methods, are: (1) it requires less comparison data; (2) it leads to more consistent comparisons, which means that it produces more reliable results.     

Screening alternatives graphically by an extended case-based distance approach

Screening is a helpful process of multiple criteria decision aid (MCDA) to reduce a larger set of alternatives into a smaller one containing the best alternatives; thereby, decision makers are able to concentrate on evaluating alternatives within a smaller set. Therefore, determining how to assist decision makers in screening is an important issue for MCDA. This study proposes an extended case-based distance approach incorporating the advantages of a case-based distance method, a mixed-integer programming approach of discriminant analysis, and a multidimensional scaling technique to help decision makers screen alternatives visually in MCDA. The proposed approach can screen alternatives by evaluating sets of cases selected by decision makers, providing visual aids to observe decision context, reducing the number of misclassifications, and improving multiple solution problems. An interactive screening procedure is also developed to provide flexibility so that decision makers can check and adjust screening results iteratively.     

AGGREGATING EXPERT OPINION IN DECISION-MAKING

In using nominal groups for decision making, it is necessary to use some mechanical procedure for combining the evaluations. A simulation model is used to compare procedures for the case where a nominal group of m evaluators must select the best of n alternatives and where the evaluations are subject to random errors. Criteria are the probability of making a correct selection and the relative quality of the choice.     

A Flexible Evaluative Framework for Order Picking Systems

This paper develops a novel framework to evaluate the integral performance of order picking systems with different combinations of storage and order picking policies. The warehousing literature on order picking mostly considers minimizing either elapsed time or distance as the sole objective, whereas warehouse managers in a supply chain have to look beyond single‐dimensional performance and consider trade‐offs among different criteria. Thus managers still need a unified and efficient framework to select a portfolio of appropriate order picking policies from a multi‐criteria and contextual perspective. Our framework—combining data envelopment analysis, ranking and selection, and multiple comparisons—provides an efficient methodology to simultaneously analyze several interrelated problems in order picking systems with multiple performance attributes, such as service levels and operational costs. We demonstrate our approach through comprehensive evaluations of order picking policies in three low‐level, picker‐to‐parts rectangular warehouses facing demand variations.