Fuzzy multi-criteria decision-making based on positive and negative extreme solutions

To encompass decision data vagueness, many researchers generalized multi-criteria decision-making (MCDM) methods in certain environment into fuzzy multi-criteria decision-making (FMCDM) methods under fuzzy environment. In these FMCDM methods, ranking fuzzy numbers based on fuzzy pair-wise comparison is normally essential, but the comparison is a complexity work. To avoid fuzzy pair-wise comparison, we propose a FMCDM method based on positive and negative extreme solutions of alternatives. In the proposed method, two extreme solutions of alternatives are obtained by MAX and MIN operations of fuzzy TOPSIS. Then weakness and strength matrices between alternatives and extreme solutions are derived by a difference function revised from fuzzy preference relation of Lee, and multiplied with weight matrix to be weighted weakness and strength indices. The two weighted indices are respectively transferred into positive and negative indices, and then the two indices integrated into a total performance index. Finally, alternatives can be sorted according to their related performance indices, and FMCDM problems are easily solved, not by fuzzy pair-wise comparison.     

A method for solving fuzzy multicriteria decision problems with dependent criteria

We propose a new multi-criteria decision making (MCDM) method based on fuzzy pair-wise comparisons and a feedback between the criteria. The evaluation of the weights of criteria, the variants as well as the feedback between the criteria is based on the data given in pair-wise comparison matrices. Extended arithmetic operations with fuzzy numbers are used as well as ordering fuzzy relations to compare fuzzy outcomes. An illustrating numerical example is presented to clarify the methodology. A special SW-Microsoft Excel add-in named FVK was developed for applying the proposed method. Comparing to other software products, FVK is free, able to work with fuzzy data and utilizes capabilities of widespread spreadsheet Microsoft Excel.     

基于犹豫毕达哥拉斯模糊环境下的TODIM方法

在决策过程中TODIM方法能有效的捕捉决策者的心理行为。犹豫毕达哥拉斯模糊集不但能反映正反两个方面的不确定性,而且能反映决策者的犹豫程度。本文将TODIM方法扩展到犹豫毕达哥拉斯模糊集。首先定义了犹豫毕达哥拉斯模糊环境下的测量函数,用于比较两个犹豫毕达哥拉斯模糊数的大小,其次计算每个备选方案相对其它备选方案的相对优势度,然后根据相对优势度选出最佳方案。最后,用航空公司服务质量的评估来说明本文给出方法的可行性和有效性。     

How to generate regularly behaved production data? A Monte Carlo experimentation on DEA scale efficiency measurement

Monte Carlo experimentation is a well-known approach used to test the performance of alternative methodologies under different hypotheses. In the frontier analysis framework, whatever the parametric or non-parametric methods tested, experiments to date have been developed assuming single output multi-input production functions. The data generated have mostly assumed a Cobb–Douglas technology. Among other drawbacks, this simple framework does not allow the evaluation of DEA performance on scale efficiency measurement. The aim of this paper is twofold. On the one hand, we show how reliable two-output two-input production data can be generated using a parametric output distance function approach. A variable returns to scale translog technology satisfying regularity conditions is used for this purpose. On the other hand, we evaluate the accuracy of DEA technical and scale efficiency measurement when sample size and output ratios vary. Our Monte Carlo experiment shows that the correlation between true and estimated scale efficiency is dramatically low when DEA analysis is performed with small samples and wide output ratio variations.     

The interval efficiency based on the optimistic and pessimistic points of view

Data envelopment analysis (DEA) is a data-oriented approach for evaluating the performances of a set of peer entities called decision-making units (DMUs), whose performance is determined based on multiple measures. The traditional DEA, which is based on the concept of efficiency frontier (output frontier), determines the best efficiency score that can be assigned to each DMU. Based on these scores, DMUs are classified into DEA-efficient (optimistic efficient) or DEA-non-efficient (optimistic non-efficient) units, and the DEA-efficient DMUs determine the efficiency frontier. There is a comparable approach which uses the concept of inefficiency frontier (input frontier) for determining the worst relative efficiency score that can be assigned to each DMU. DMUs on the inefficiency frontier are specified as DEA-inefficient or pessimistic inefficient, and those that do not lie on the inefficient frontier, are declared to be DEA-non-inefficient or pessimistic non-inefficient. In this paper, we argue that both relative efficiencies should be considered simultaneously, and any approach that considers only one of them will be biased. For measuring the overall performance of the DMUs, we propose to integrate both efficiencies in the form of an interval, and we call the proposed DEA models for efficiency measurement the bounded DEA models. In this way, the efficiency interval provides the decision maker with all the possible values of efficiency, which reflect various perspectives. A numerical example is presented to illustrate the application of the proposed DEA models.     

An equilibrium efficiency frontier data envelopment analysis approach for evaluating decision-making units with fixed-sum outputs

Based on the minimal reduction strategy, Yang et al. (2011) developed a fixed-sum output data envelopment analysis (FSODEA) approach to evaluate the performance of decision-making units (DMUs) with fixed-sum outputs. However, in terms of such a strategy, all DMUs compete over fixed-sum outputs with “no memory” that will result in differing efficient frontiers’ evaluations. To address the problem, in this study, we propose an equilibrium efficiency frontier data envelopment analysis (EEFDEA) approach, by which all DMUs with fixed-sum outputs can be evaluated based on a common platform (or equilibrium efficient frontier). The proposed approach can be divided into two stages. Stage 1 constructs a common evaluation platform via two strategies: an extended minimal adjustment strategy and an equilibrium competition strategy. The former ensures that original efficient DMUs are still efficient, guaranteeing the existence of a common evaluation platform. The latter makes all DMUs achieve a common equilibrium efficient frontier. Then, based on the common equilibrium efficient frontier, Stage 2 evaluates all DMUs with their original inputs and outputs. Finally, we illustrate the proposed approach by using two numerical examples.     

基于直觉模糊集的突发事件应急预案评估

提出了一种基于直觉模糊集理论的突发事件应急预案评价的新方法.首先,定义了直觉模糊集和两个直觉模糊集之间的距离;然后,建立了应急预案评价指标体系,给出了直觉模糊正理想点和负理想点的概念,提出了基于直觉模糊集和TOPS IS法的应急预案评估方法.最后通过实例说明了该方法的有效性.     

A new fuzzy multiple attributive group decision making methodology and its application to propulsion/manoeuvring system selection problem

In this paper, a new fuzzy multiple attribute decision-making (FMADM) method, which is suitable for multiple attributive group decision making (GDM) problems in fuzzy environment, is proposed to deal with the problem of ranking and selection of alternatives. Since the subjectivity, imprecision and vagueness in the estimates of a performance rating enter into multiple attribute decision-making (MADM) problems, fuzzy set theory provides a mathematical framework for modelling vagueness and imprecision. In the proposed approach, an attribute based aggregation technique for heterogeneous group of experts is employed and used for dealing with fuzzy opinion aggregation for the subjective attributes of the decision problem. The propulsion/manoeuvring system selection as a real case study is used to demonstrate the versatility and potential of the proposed method for solving fuzzy multiple attributive group decision-making problems. The proposed method is a generalised model, which can be applied to great variety of practical problems encountered in the naval architecture from propulsion/manoeuvring system selection to warship requirements definition.     

Ranking efficient decision making units in data envelopment analysis based on reference frontier share

Data envelopment analysis (DEA) is a powerful technique for performance evaluation of decision making units (DMUs). Ranking efficient DMUs based on a rational analysis is an issue that yet needs further research. The impact of each efficient DMU in evaluation of inefficient DMUs can be considered as additional information to discriminating among efficient DMUs. The concept of reference frontier share is introduced in which the share of each efficient DMU in construction of the reference frontier for evaluating inefficient DMUs is considered. For this purpose a model for measuring the reference frontier share of each efficient DMU associated with each inefficient one is proposed and then a total measure is provided based on which the ranking is made. The new approach has the capability for ranking extreme and non-extreme efficient DMUs. Further, it has no problem in dealing with negative data. These facts are verified by theorems, discussions and numerical examples.     

基于模糊环境下的最大偏差法和TODIM法的多属性应急选址决策

犹豫模糊集(HFS)是一个元素的隶属度可以用多个实数值表示的集合.该方法通常用于处理决策者在具有多个评价指标、方案、变量等多个值时犹豫不决的情况.本文基于犹豫不决的模糊环境,提出了一种新的混合方法.首先,基于最大偏差法确定属性权重;其次,利用TODIM方法计算各方案的优势度.通过对这些优势度的聚合,可以进一步得到每个方...     

A robust nonparametric approach to evaluate and explain the performance of mutual funds

The topic of the measurement of mutual funds’ performance is receiving an increasing interest both from an applied and a theoretical perspective. Beside the traditional financial literature, a growing body of studies has started to apply the tools of frontier analysis for benchmarking comparisons in portfolio analysis. Our paper contributes to this literature proposing a robust nonparametric approach for analysing mutual funds. It is based on the concept of order-m frontier [Cazals, C., Florens, J.P., Simar, L., 2002. Nonparametric frontier estimation: A robust approach. Journal of Econometrics 106, 1–25] and on a probabilistic approach [Daraio, C., Simar, L., 2005. Introducing environmental variables in nonparametric frontier models: A probabilistic approach. Journal of Productivity Analysis 24 (1), 93–121] to find out the factors explaining mutual funds’ performance. Within this framework, a decomposition of conditional efficiency is proposed, and its usefulness for economic interpretation analysed. Our approach is illustrated by using US mutual funds data, grouped for category by objective. Economies of scale, slacks and market risks are investigated. A comparison of traditional, nonparametric and robust performance measures is also offered.     

Collaborative production planning of supply chain under price and demand uncertainty

This research is motivated by an automobile manufacturing supply chain network. It involves a multi-echelon production system with material supply, component fabrication, manufacturing, and final product distribution activities. We address the production planning issue by considering bill of materials and the trade-offs between inventories, production costs and customer service level. Due to its complexity, an integrated solution framework which combines scatter evolutionary algorithm, fuzzy programming and stochastic chance-constrained programming are combined to jointly take up the issue. We conduct a computational study to evaluate the model. Numerical results using the proposed algorithm confirm the advantage of the integrated planning approach. Compared with other solution methodologies, the supply chain profits from the proposed approach consistently outperform, in some cases up to 13% better. The impacts of uncertainty in demand, material price, and other parameters on the performance of the supply chain are studied through sensitivity analysis. We found the proposed model is effective in developing robust production plans under various market conditions.     

基于直觉模糊软集的煤矿应急救援决策方法

在煤矿突发事故初期,时间的紧迫性和环境的复杂性导致应急救援决策中的评估信息存在不确定性,传统基于确数的决策方法难以适用,对此本文提出了一种基于直觉模糊软集(IFSSs)的煤矿应急救援决策方法。首先对现有IFSSs熵公理化定义中的不合理之处进行修正,进而据此构造新的IFSSs熵计算公式,并通过与既有IFSSs熵公式的对比算例表现了新公式的合理性和有效性。然后基于新熵公式给出属性综合权重的确定方法,再利用推广的TOPSIS方法对预案进行排序以确定最优煤矿应急救援预案。最后将本文提出的方法应用于某煤矿应急救援实例。结果表明,基于IFSSs的煤矿应急救援决策方法能充分利用和有效处理不确定性的信息,具有更好的决策分辨效果,可以为煤矿突发事故的应急救援提供决策支持。     

On fuzzy linear projection equation and applications

This paper introduces the concept of fuzzy projection of a fuzzy number on a set of fuzzy numbers based on r-cut approach. It is proved that the projection of a fuzzy number on the set of all fuzzy numbers is itself and under a special metric, the proposed fuzzy projection is a non-expansive mapping. By using this definition, the concept of fuzzy linear projection equation is defined and to solve it, a numerical method is applied. Based on the proposed algorithm and as an important application, two different types of system of fuzzy linear equations with fuzzy variables are solved. Numerical results illustrate the applicabilities of proposed approach.     

Efficiency measurement in the stochastic frontier model

Deterministic models of technical efficiency assume that all deviations from the production frontier are due to inefficiency. Critics argue that no allowance is made for measurement error and other statistical noise so that the resulting efficiency measure will be contaminated. The stochastic frontier model is an alternative that allows both inefficiency and measurement error. Advocates argue that the stochastic frontier models should be used despite other potential limitations because of the superior conceptual treatment of noise. As will be demonstrated in this paper, however, the assumed shape of the error distributions is used to identify a key production function parameter. Therefore, the stochastic frontier models, like the deterministic models, cannot produce absolute measures of efficiency. Moreover, we show that rankings for firm-specific inefficiency estimates produced by traditional stochastic frontier models do not change from the rankings of the composed errors. As a result, the performance of the deterministic models is qualitatively similar to that of the stochastic frontier models.     

A new fuzzy comprehensive evaluation model based on the support vector machine

In this paper, focused on a proper weight distribution vector of a fuzzy comprehensive evaluation method, a new fuzzy comprehensive evaluation model based on the supper vector machine (SVM) is proposed for overcoming the subjective limitation in traditional fuzzy comprehensive evaluation model. Furthermore, a multilevel fuzzy comprehensive evaluation model based on SVM of network learning has also been designed, and the improved algorithm is used to make an instant computation. This method gives good performance on determination of the weight distribution vector and improves the evaluation accuracy and generalization with an example.     

Adaptive fuzzy sliding mode control for synchronization of uncertain fractional order chaotic systems

This paper deals with chaos synchronization between two different uncertain fractional order chaotic systems based on adaptive fuzzy sliding mode control (AFSMC). With the definition of fractional derivatives and integrals, a fuzzy Lyapunov synthesis approach is proposed to tune free parameters of the adaptive fuzzy controller on line by output feedback control law and adaptive law. Moreover, chattering phenomena in the control efforts can be reduced. The sliding mode design procedure not only guarantees the stability and robustness of the proposed AFSMC, but also the external disturbance on the synchronization error can be attenuated. The simulation example is included to confirm validity and synchronization performance of the advocated design methodology.     

Fuzzy clusterwise quasi-likelihood generalized linear models

The quasi-likelihood method has emerged as a useful approach to the parameter estimation of generalized linear models (GLM) in circumstances where there is insufficient distributional information to construct a likelihood function. Despite its flexibility, the quasi-likelihood approach to GLM is currently designed for an aggregate-sample analysis based on the assumption that the entire sample of observations is taken from a single homogenous population. Thus, this approach may not be suitable when heterogeneous subgroups exist in the population, which involve qualitatively distinct effects of covariates on the response variable. In this paper, the quasi-likelihood GLM approach is generalized to a fuzzy clustering framework which explicitly accounts for such cluster-level heterogeneity. A simple iterative estimation algorithm is presented to optimize the regularized fuzzy clustering criterion of the proposed method. The performance of the proposed method in recovering parameters is investigated based on a Monte Carlo analysis involving synthetic data. Finally, the empirical usefulness of the proposed method is illustrated through an application to actual data on the coupon usage behaviour of a sample of consumers.     

Dominance-based fuzzy rough set analysis of uncertain and possibilistic data tables

In this paper, we propose a dominance-based fuzzy rough set approach for the decision analysis of a preference-ordered uncertain or possibilistic data table, which is comprised of a finite set of objects described by a finite set of criteria. The domains of the criteria may have ordinal properties that express preference scales. In the proposed approach, we first compute the degree of dominance between any two objects based on their imprecise evaluations with respect to each criterion. This results in a valued dominance relation on the universe. Then, we define the degree of adherence to the dominance principle by every pair of objects and the degree of consistency of each object. The consistency degrees of all objects are aggregated to derive the quality of the classification, which we use to define the reducts of a data table. In addition, the upward and downward unions of decision classes are fuzzy subsets of the universe. Thus, the lower and upper approximations of the decision classes based on the valued dominance relation are fuzzy rough sets. By using the lower approximations of the decision classes, we can derive two types of decision rules that can be applied to new decision cases.