Methods of critical value reduction for type-2 fuzzy variables and their applications

A type-2 fuzzy variable is a map from a fuzzy possibility space to the real number space; it is an appropriate tool for describing type-2 fuzziness. This paper first presents three kinds of critical values (CVs) for a regular fuzzy variable (RFV), and proposes three novel methods of reduction for a type-2 fuzzy variable. Secondly, this paper applies the reduction methods to data envelopment analysis (DEA) models with type-2 fuzzy inputs and outputs, and develops a new class of generalized credibility DEA models. According to the properties of generalized credibility, when the inputs and outputs are mutually independent type-2 triangular fuzzy variables, we can turn the proposed fuzzy DEA model into its equivalent parametric programming problem, in which the parameters can be used to characterize the degree of uncertainty about type-2 fuzziness. For any given parameters, the parametric programming model becomes a linear programming one that can be solved using standard optimization solvers. Finally, one numerical example is provided to illustrate the modeling idea and the efficiency of the proposed DEA model.     

A short and mean-term automatic forecasting system––application to textile logistics

In order to reduce their stocks and to limit stock out, textile companies require specific and accurate sale forecasting systems. More especially, textile distribution involves different forecast lead times: mean-term (one year) and short-term (one week in average). This paper presents two new complementary forecasting models, appropriate to textile market requirements. The first model (AHFCCX) allows to automatically obtain mean-term forecasting by using fuzzy techniques to quantify influence of explanatory variables. The second one (SAMANFIS), based on a neuro-fuzzy method, performs short-term forecasting by readjusting mean-term model forecasts from load real sales. To evaluate forecasts accuracy, our models and classical ones are compared to 322 real items sales series of an important ready to wear distributor.     

Effects of Mis-Specification in Bivariate Extreme Value Problems

The need to incorporate the structure of complex problems in extreme value analyzes, and the requirement to exploit all the limited information that is available, has led to the increased use of advanced dependence models. When they are appropriate, these dependence models can lead to substantial benefits over simpler univariate extreme value methods. Here we explore some inference problems for the marginal and conditional distributions caused by model mis-specification. We find distinct differences in estimation characteristics when the dependence structure is asymptotically dependent or asymptotically independent, and that conditional models can be substantially improved if the variables are standardized to have common marginal distributions.     

Directional fuzzy clustering and its application to fuzzy modelling

The paradigm of clustering (unsupervised learning) viewed as a fundamental tool for data analysis has been found useful in fuzzy modelling. While the objective functions guiding the clustering mechanisms are by and large direction-free (namely, they do not distinguish between independent (input) and dependent (output) variables, for most of the models this discrimination becomes of vital importance. The method of directional clustering takes the directionality requirement into account by incorporating the nature of the functional relationships into the objective function guiding the formation of the clusters. The complete clustering algorithm is presented. The role of this method in a two-phase fuzzy identification scheme is also revealed in detail.     

FEATURES AND APPLICATIONS OF BERTALANFFY-RICHARDS‘ AND SCHNUTE'S GROWTH EQUATIONS

ABSTRACT. Based on various ranges of the parameter m (or b), the paper analyzes the features and the integral forms of the Schnute and the Bertalanffy-Richards growth equations as well as the two aspects of their special cases (such as Gompertz, logistic and monomolecular models). It is a first attempt to investigate all the corresponding relationships among parameters of the models derived from the Schnute and the Bertalanffy-Richards growth equations. All the models from the two are empirically fitted by different data sets for eucalypt plantations. Unlike earlier papers, the results of this paper show that either of the two growth equations can be considered as a model for estimating forest growth given a parameter range, and both can produce similar growth performances. Some other aspects of the two growth equations are discussed so that the two can be used correctly.     

A hybrid model for selection of an outsourcing provider

Outsourcing is a good strategy for firms that need to reduce operating costs and improve competitiveness and it is important that firms scientifically select appropriate outsourcing providers. Some efforts have been made to find systematic ways to deal with outsourcing problems, but these efforts incorrectly assumed that the criteria used in the decision process are independent, which is not true in the real world. In this study, we propose a new hybrid multiple criteria decision-making (MCDM) model, which addresses the dependent relationships between the various criteria. The relations-structure among the criteria is built with the aid of the decision-making trial and evaluation laboratory (DEMATEL) method. Decision-makers tend to hold diverse opinions about their preferences due to incomplete information and knowledge, or inherent conflict between various departments. We further used the fuzzy preference programming and the analytic network process (ANP) to form a model for the selection of partners for outsourcing providers. The proposed model can help practitioners improve their decision making process, especially when criteria are numerous and inter-related. The method is demonstrated using data from a Taiwanese airline.     

Solving a multiobjective possibilistic problem through compromise programming

Real decision problems usually consider several objectives that have parameters which are often given by the decision maker in an imprecise way. It is possible to handle these kinds of problems through multiple criteria models in terms of possibility theory.Here we propose a method for solving these kinds of models through a fuzzy compromise programming approach.To formulate a fuzzy compromise programming problem from a possibilistic multiobjective linear programming problem the fuzzy ideal solution concept is introduced. This concept is based on soft preference and indifference relationships and on canonical representation of fuzzy numbers by means of their α-cuts. The accuracy between the ideal solution and the objective values is evaluated handling the fuzzy parameters through their expected intervals and a definition of discrepancy between intervals is introduced in our analysis.     

Updating a credit-scoring model based on new attributes without realization of actual data

Funding small and medium-sized enterprises (SMEs) to support technological innovation is critical for national competitiveness. Technology credit scoring models are required for the selection of appropriate funding beneficiaries. Typically, a technology credit-scoring model consists of several attributes and new models must be derived every time these attributes are updated. However, it is not feasible to develop new models until sufficient historical evaluation data based on these new attributes will have accumulated. In order to resolve this limitation, we suggest the framework to update the technology credit scoring model. This framework consists of ways to construct new technology credit-scoring model by comparing alternative scenarios for various relationships between existing and new attributes based on explanatory factor analysis, analysis of variance, and logistic regression. Our approach can contribute to find the optimal scenario for updating a scoring model.     

Bayesian analysis of non-linear structural equation models with non-ignorable missing outcomes from reproductive dispersion models

Non-linear structural equation models are widely used to analyze the relationships among outcomes and latent variables in modern educational, medical, social and psychological studies. However, the existing theories and methods for analyzing non-linear structural equation models focus on the assumptions of outcomes from an exponential family, and hence can’t be used to analyze non-exponential family outcomes. In this paper, a Bayesian method is developed to analyze non-linear structural equation models in which the manifest variables are from a reproductive dispersion model (RDM) and/or may be missing with non-ignorable missingness mechanism. The non-ignorable missingness mechanism is specified by a logistic regression model. A hybrid algorithm combining the Gibbs sampler and the Metropolis–Hastings algorithm is used to obtain the joint Bayesian estimates of structural parameters, latent variables and parameters in the logistic regression model, and a procedure calculating the Bayes factor for model comparison is given via path sampling. A goodness-of-fit statistic is proposed to assess the plausibility of the posited model. A simulation study and a real example are presented to illustrate the newly developed Bayesian methodologies.     

Optimal and efficient designs for Gompertz regression models

Gompertz functions have been widely used in characterizing biological growth curves. In this paper we consider D-optimal designs for Gompertz regression models. For homoscedastic Gompertz regression models with two or three parameters, we prove that D-optimal designs are minimally supported. Considering that minimally supported designs might not be applicable in practice, alternative designs are proposed. Using the D-optimal designs as benchmark designs, these alternative designs are found to be efficient in general.     

Quantifying CFSE label decay in flow cytometry data

We developed a series of models for the label decay in cell proliferation assays when the intracellular dye carboxyfluorescein succinimidyl ester (CFSE) is used as a staining agent. Data collected from two healthy patients were used to validate the models and to compare the models with the Akiake Information Criteria. The distinguishing features of multiple decay rates in the data are readily characterized and explained via time dependent decay models such as the logistic and Gompertz models.     

Error analysis: a tool for selecting travel demand models

In developing travel demand models it is generally assumed that the base-year data used in developing the parameters, as well as the forecasted data to be used as independent variables for the design year, are of acceptable quality. The purpose of this paper is to present the application of error propagation theory in assesing the predictive quality of one type of travel demand forecasting model (multinomial logit models) and to demonstrate how error considerations can be used as a tool for identifying the optimal model. The general conclusions of this study are that: (1) it is indeed possible to quantify errors in dependent variables in logit models as a consequence of errors in independent variables; and (2) error consideration can be used as a tool for identifying the optimal model from a set of candidate models. Further research is recommended to develop better insights into the phenomenon of error propagation so that the consideration of errors can be a factor in decisions on model selection.     

Fuzzy minimum weight edge covering problem

Minimum weight edge covering problem, known as a classic problem in graph theory, is employed in many scientific and engineering applications. In the applications, the weight may denote cost, time, or opponent’s payoff, which can be vague in practice. This paper considers the edge covering problem under fuzzy environment, and formulates three models which are expected minimum weight edge cover model, α-minimum weight edge cover model, and the most minimum weight edge cover model. As an extension for the models, we respectively introduce the crisp equivalent of each model in the case that the weights are independent trapezoidal fuzzy variables. Due to the complexity of the problem, a hybrid intelligent algorithm is employed to solve the models, which can deal with the problem with any type of fuzzy weights. At last, some numerical experiments are given to show the application of the models and the robustness of the algorithm.     

基于可信性理论的模糊广义指派问题研究

鉴于广义指派问题的参数确定上通常包含不确定性,因此,将模型的主要参数,即单位费用、资源消耗量,用梯形模糊变量来刻画,从而建立模糊广义指派模型.在模型求解过程中,结合到决策者的实际要求,利用可信性理论将目标函数和约束条件进行清晰化处理,进而通过参数分解法求解.最后,通过数值例子说明模糊广义指派问题的应用,并检验所提方法的有效性.     

高速公路交通事件影响范围的模糊预测

高速公路交通事件的影响范围预测主要包括两个方面:排队长度预测和延误预测.在对排队长度和延误进行实时预测时,需精确预测出事件发生期间的交通流量和通行能力、事件持续时间及车辆到达事件点的时间等参数,而事实上,用于确定这些参数的信息是非常复杂的,得到的这些参数值是模糊的,但是其变化范围是可以精确确定的.充分考虑上述参数的模糊特性,及事件发生期间的交通流量和通行能力的模糊关系,运用α截集表示了车辆到达离去曲线,建立了交通事件排队长度模糊预测模型和延误模糊预测模型.利用2001年6月16日发生在美国210-E高速公路的交通事件验证了该模型的可行性,并分析了事件发生期间交通流量和通行能力及事件持续时间的模糊度变化对排队长度和延误预测结果的影响.     

Modelling life tables with advanced ages: An extreme value theory approach

We propose a new model – we call it a smoothed threshold life table (STLT) model – to generate life tables incorporating information on advanced ages. Our method allows a smooth mortality transition from non-extreme to extreme ages, and provides objectively determined highest attained ages with which to close the life table.We proceed by modifying the threshold life table (TLT) model developed by Li et al. (2008). In the TLT model, extreme value theory (EVT) is used to make optimal use of the relatively small number of observations at high ages, while the traditional Gompertz distribution is assumed for earlier ages. Our novel contribution is to constrain the hazard function of the two-part lifetime distribution to be continuous at the changeover point between the Gompertz and EVT models. This simple but far-reaching modification not only guarantees a smooth transition from non-extreme to extreme ages, but also provides a better and more robust fit than the TLT model when applied to a high quality Netherlands dataset. We show that the STLT model also compares favourably with other existing methods, including the Gompertz–Makeham model, logistic models, Heligman–Pollard model and Coale–Kisker method, and that a further generalisation, a time-dependent dynamic smooth threshold life table (DSTLT) model, generally has superior in-sample fitting as well as better out-of-sample forecasting performance, compared, for example, with the Cairns et al. (2006) model.     

Credit scoring with macroeconomic variables using survival analysis

Survival analysis can be applied to build models for time to default on debt. In this paper, we report an application of survival analysis to model default on a large data set of credit card accounts. We explore the hypothesis that probability of default (PD) is affected by general conditions in the economy over time. These macroeconomic variables (MVs) cannot readily be included in logistic regression models. However, survival analysis provides a framework for their inclusion as time-varying covariates. Various MVs, such as interest rate and unemployment rate, are included in the analysis. We show that inclusion of these indicators improves model fit and affects PD yielding a modest improvement in predictions of default on an independent test set.     

A hybrid method to evaluate pure endowment policies: Crédit Agricole and ERGO Index linked policies

An empirical method to evaluate pure endowment policies is proposed. The financial component of the policies is described using the time dependent Black Scholes model and making a suitable choice for its time dependent parameter functions. Specifically, the integral of the time dependent risk free interest rate is modeled using an extension of the Nelson and Siegel yield curve (see Dielbold and Li, 2006). The time dependent volatility is expressed using two different models. One of these is based on an extension of the Nelson and Siegel model (Dielbold and Li, 2006), while the other assumes that the volatility is a piecewise function with respect to the time variable. The demographic component is modeled using a generalization of the geometric Brownian mean reverting Gompertz model while an asymptotic formula for survival probability is derived when the mortality risk volatility is small. The method has been tested on two policies. In these the risk free interest rate parameters are calibrated using the one-month, three-month, six-month, one-year, three-year and five-year US treasury constant maturity yields and the parameters of the volatility are calibrated using the VSTOXX volatility indices. The choice of the data employed in the calibration depends on the policy to be evaluated. The performance of the method is established comparing the observed values of the policies with the values obtained using this method.     

A production-repairing inventory model with fuzzy rough coefficients under inflation and time value of money

In this paper, a production-repairing inventory model in fuzzy rough environment is proposed incorporating inflationary effects where a part of the produced defective units are repaired and sold as fresh units. Here, production and repairing rates are assumed as dynamic control variables. Due to complexity of environment, different costs and coefficients are considered as fuzzy rough type and these are reduced to crisp ones using fuzzy rough expectation. Here production cost is production rate dependent, repairing cost is repairing rate dependent and demand of the item is stock-dependent. Goal of the research work is to find decisions for the decision maker (DM) who likes to maximize the total profit from the above system for a finite time horizon. The model is formulated as an optimal control problem and solved using a gradient based non-linear optimization method. Some particular cases of the general model are derived. The results of the models are illustrated with some numerical examples.     

Stress testing network reconstruction via graphical causal model

An resilience optimal evaluation of financial portfolios implies having plausible hypotheses about the multiple interconnections between the macroeconomic variables and the risk parameters. In this article, we propose a graphical model for the reconstruction of the causal structure that links the multiple macroeconomic variables and the assessed risk parameters, it is this structure that we call stress testing network. In this model, the relationships between the macroeconomic variables and the risk parameter define a “relational graph” among their time‐series, where related time‐series are connected by an edge. Our proposal is based on the temporal causal models, but unlike, we incorporate specific conditions in the structure which correspond to intrinsic characteristics this type of networks. Using the proposed model and given the high‐dimensional nature of the problem, we used regularization methods to efficiently detect causality in the time‐series and reconstruct the underlying causal structure. In addition, we illustrate the use of model in credit risk data of a portfolio. Finally, we discuss its uses and practical benefits in stress testing.