Grade of membership models in low dimensions

Grade of Membership (GoM) Models have always been presented by their inventors as statistical applications of fuzzy set theory. This paper develops an alternative formulation, recasting GoM as a geometric dimensionality-reduction technique in terms of an underlying family of metrics, exposing a close relationship with Principal Components. The geometric viewpoint facilitates intuitive understanding and guides an investigation into the robustness of GoM estimates to violations of assumption, with test cases drawn from the National Survey of Families and Households. Analysis is restricted to visualizable, low-dimensional cases with two pure types and 3 to 9 dichotomous variables, and to “conditional” GoM, the version more commonly used but less commonly studied. In these low-dimensional settings, I find GoM to be a successful technique for recovering an underlying gradient among individuals when such a gradient is actually present. GoM is only moderately sensitive to moderate violations in its assumptions. In the cases studied, GoM solutions turn out to be remarkably close to Principal Component solutions. This research has been supported by Grant R01 AG09781 from the Demography and Population Epidemiology Section of the U.S. National Institute on Aging under Richard Suzman's direction. I am grateful to Burton Singer for early suggestions and provision of the GoM3 program, and to Bryan Lincoln of the Berkeley NIA Center for the Economics and Demography of Aging.     

DESCRIBING DISABILITY THROUGH INDIVIDUAL-LEVEL MIXTURE MODELS FOR MULTIVARIATE BINARY DATA

Data on functional disability are of widespread policy interest in the United States, especially with respect to planning for Medicare and Social Security for a growing population of elderly adults. We consider an extract of functional disability data from the National Long Term Care Survey (NLTCS) and attempt to develop disability profiles using variations of the Grade of Membership (GoM) model. We first describe GoM as an individual-level mixture model that allows individuals to have partial membership in several mixture components simultaneously. We then prove the equivalence between individual-level and population-level mixture models, and use this property to develop a Markov Chain Monte Carlo algorithm for Bayesian estimation of the model. We use our approach to analyze functional disability data from the NLTCS.     

Fuzzy K-means clustering models for triangular fuzzy time trajectories

We focus our attention on the classification of fuzzy time trajectories with triangular membership function, described by a given set of individuals. To this purpose, we adopt a fullyinformational approach, explicitly recognizing the informational nature shared by the ingredients of the classification procedure: the observed data (Empirical Information) and the classification model (Theoretical Information). In particular, by supposing that the informational paradigm has a fuzzy nature, we suggest three fuzzy clustering models allowing the classification of the triangular fuzzy time trajectories, based on the analysis of the cross sectional and/or longitudinal characteristics of their components (centers and spreads). Two applicative examples are illustrated.     

Correlation with Fuzzy Data and Its Applications in the 12-year Compulsory Education in Taiwan

In the study, we developed a new model of fuzzy correlation and empirically examined the fuzzy correlation with student test scores in subjects of Chinese and Mathematics. Our sample comprised 419 Taiwanese students in the 12-year compulsory education. We applied fuzzy theory and conducted simulations with the data from Normal, Uniform, and Cauchy distributions to illustrate the efficiency of our proposed methods.     

Causal inference in outcome-dependent two-phase sampling designs

Summary.  We consider estimation of the causal effect of a treatment on an outcome from observational data collected in two phases. In the first phase, a simple random sample of individuals is drawn from a population. On these individuals, information is obtained on treatment, outcome and a few low dimensional covariates. These individuals are then stratified according to these factors. In the second phase, a random subsample of individuals is drawn from each stratum, with known stratum-specific selection probabilities. On these individuals, a rich set of covariates is collected. In this setting, we introduce five estimators: simple inverse weighted; simple doubly robust; enriched inverse weighted; enriched doubly robust; locally efficient. We evaluate the finite sample performance of these estimators in a simulation study. We also use our methodology to estimate the causal effect of trauma care on in-hospital mortality by using data from the National Study of Cost and Outcomes of Trauma.     

Fuzzy p-value in testing fuzzy hypotheses with crisp data

In testing statistical hypotheses, as in other statistical problems, we may be confronted with fuzzy concepts. This paper deals with the problem of testing hypotheses, when the hypotheses are fuzzy and the data are crisp. We first introduce the notion of fuzzy p-value, by applying the extension principle and then present an approach for testing fuzzy hypotheses by comparing a fuzzy p-value and a fuzzy significance level, based on a comparison of two fuzzy sets. Numerical examples are also provided to illustrate the approach.     

Survival estimation and the effects of dependency among animals

Survival models assume that fates of individuals are independent, yet the robustness of this assumption has been poorly quantified. We examine how empirically derived estimates of the variance of survival rates are affected by dependency in survival probability among individuals. We used Monte Carlo simulations to generate known amounts of dependency among pairs of individuals and analyzed these data with Kaplan-Meier and Cormack-Jolly-Seber models. Dependency significantly increased these empirical variances as compared to theoretically derived estimates of variance from the same populations. Using resighting data from 168 pairs of black brant ( Branta bernicla nigricans ), we used a resampling procedure and program RELEASE to estimate empirical and mean theoretical variances. We estimated that the relationship between paired individuals caused the empirical variance of the survival rate to be 155% larger than the empirical variance for unpaired individuals. Monte Carlo simulations and use of this resampling strategy can provide investigators with information on how robust their data are to this common assumption of independent survival probabilities.     

Survival estimation and the effects of dependency among animals

Survival models assume that fates of individuals are independent, yet the robustness of this assumption has been poorly quantified. We examine how empirically derived estimates of the variance of survival rates are affected by dependency in survival probability among individuals. We used Monte Carlo simulations to generate known amounts of dependency among pairs of individuals and analyzed these data with Kaplan-Meier and Cormack-Jolly-Seber models. Dependency significantly increased these empirical variances as compared to theoretically derived estimates of variance from the same populations. Using resighting data from 168 pairs of black brant ( Branta bernicla nigricans ), we used a resampling procedure and program RELEASE to estimate empirical and mean theoretical variances. We estimated that the relationship between paired individuals caused the empirical variance of the survival rate to be 155% larger than the empirical variance for unpaired individuals. Monte Carlo simulations and use of this resampling strategy can provide investigators with information on how robust their data are to this common assumption of independent survival probabilities.     

An Approach of Stocks Substitution Strategy Using Fuzzy Interval Correlation Coefficient

The classical Pearson's correlation coefficient has been widely adopted in various fields of application. However, when the data are composed of fuzzy interval values, it is not feasible to use such a traditional approach to evaluate the correlation coefficient. In this study, we propose the specific calculation of fuzzy interval correlation coefficient with fuzzy interval data to measure the relationship between various stocks. As such, the study is able to offer an improving measure of investment strategy for stocks substitution via the analysis of the fuzzy interval correlation. In addition, we use empirical studies to verify the validity of our proposal on fuzzy interval correlation coefficient using data from companies in electric machinery and plastic sectors in Taiwan.     

人力资源管理胜任能力构成因素实证研究

人力资源管理胜任能力研究是组织对人力资源从业者进行管理和开发的基础,而目前中国在该领域的研究较少,且尚无形成一致的认识。鉴此,根据国内外人力资源管理胜任能力相关研究成果,结合专家访谈设计的人力资源从业者胜任素质构成问卷调研结果,运用因子分析法进行数据处理并对人力资源管理工作胜任能力的构成因素进行分析识别,构建了人力资源管理胜任能力模型,并应用结构方程模型研究各构成因素对其胜任能力的影响程度得出了相关研究结论。     

Multi-objective fuzzy flexible job shop scheduling using memetic algorithm

Multi-objective flexible job shop scheduling problem with fuzzy processing time and fuzzy due date is a complicated combinatorial optimization problem. In this paper, a genetic global optimization is combined with a local search method to construct an effective memetic algorithm (MA) for simultaneously optimizing fuzzy makespan, average agreement index and minimal agreement index. First, a hybridization of different machine assignment methods with different operation sequence rules is proposed to generate a high-performance initial population. Second, the algorithm framework similar to the non-dominated sorting genetic algorithm II (NSGA-II) is adopted, in which a well-designed chromosome decoding method and two effective genetic operators are used. Then, a novel fuzzy Pareto dominance relationship based on the possibility degree and a modified crowding distance measure are defined and further employed to modify the fast non-dominated sorting. Next, a novel local search is incorporated into NSGA-II, where some candidate individuals are selected from the offspring population to experience variable neighbourhood local search by using the selection mechanism. In the experiment, the influence of four key parameters is investigated based on the Taguchi method of design of experiment. Finally, some comparisons are carried out with other existing algorithms on benchmark instances, and demonstrate the effectiveness of the proposed MA.     

The minimum inaccuracy estimates in χ2 tests for goodness of fit with fuzzy observations

A relevant problem in Statistics relates to obtaining conclusions about the shape of the distribution of an experiment from which a sample is drawn. We will consider this problem when the available information from the experimental performance cannot be exactly perceived, but that rather it may be assimilated with fuzzy information (as defined by L.A. Zadeh, and H. Tanaka, T. Okuda and K. Asai).If the hypothetical distribution is completely specified, the extension of the chi-square goodness of fit test on the basis of some concepts in Fuzzy Sets Theory does not entail difficulties. Nevertheless, if the hypothetical distribution involves unknown parameters, the extension of the chi- square goodness of fit test requires the estimation of those parameters from the fuzzy data. The aim of the present paper is to prove that, under certain natural assumptions, the minimum inaccuracy principle of estimation from fuzzy observations (which we have suggested in a previous paper as an operative extension of the maximum likelihood principle) supplies a suitable method for the above requirement.     

模糊数据均值方法及应用研究

提出一种＂Zadeh＂式模糊数据,并探讨这种模糊数据的模糊样本均值及其统计检验问题,给出模糊等于、模糊属于的定义,提出离散型和连续型模糊总体均值检验方法,并利用一些实例阐述了此类统计方法的应用。     

On Bayes' theorem for fuzzy data

There are some ideas concerning a generalization of Bayes' theorem to the situation of fuzzy data. Some of them are given in the references [1], [5], and [7]. But the proposed methods are not generalizations in the sense of the probability content of Bayes' theorem for precise data. In the present paper a generalization of Bayes' theorem to the case of fuzzy data is described which contains Bayes' theorem for precise data as a special case and allows to use the information in fuzzy data in a coherent way. Moreover a generalization of the concept of HPD-regions is explained which makes it possible to model and analyze the situation of fuzzy data. Also a generalization of the concept of predictive distributions is given in order to calculate predictive densities based on fuzzy sample information.     

A fuzzy robust regression approach applied to bedload transport data

Fuzzy least-square regression can be very sensitive to unusual data (e.g., outliers). In this article, we describe how to fit an alternative robust-regression estimator in fuzzy environment, which attempts to identify and ignore unusual data. The proposed approach concerns classical robust regression and estimation methods that are insensitive to outliers. In this regard, based on the least trimmed square estimation method, an estimation procedure is proposed for determining the coefficients of the fuzzy regression model for crisp input-fuzzy output data. The investigated fuzzy regression model is applied to bedload transport data forecasting suspended load by discharge based on a real world data. The accuracy of the proposed method is compared with the well-known fuzzy least-square regression model. The comparison results reveal that the fuzzy robust regression model performs better than the other models in suspended load estimation for the particular dataset. This comparison is done based on a similarity measure between fuzzy sets. The proposed model is general and can be used for modeling natural phenomena whose available observations are reported as imprecise rather than crisp.     

Monitoring imprecise fraction of nonconforming items using p control charts

The quality characteristics, which are known as attributes, cannot be conveniently and numerically represented. Generally, the attribute data can be regarded as the fuzzy data, which are ubiquitous in the manufacturing process and cannot be measured precisely and often be collected by visual inspection. In this paper, we construct a p control chart for monitoring the fraction of nonconforming items in the process in which fuzzy sample data are collected from the manufacturing process. The resolution identity – a well-known theorem in the fuzzy set theory – is invoked to construct the control limits of fuzzy-p control charts using fuzzy data. In order to determine whether the plotted imprecise fraction of nonconforming items is within the fuzzy lower and upper control limits, we also propose a ranking method for a set of fuzzy numbers. Using the fuzzy-p control charts and the proposed acceptability function to classify the manufacturing process allows the decision-maker to make linguistic decisions such as rather in control or rather out of control. A practical example is provided to describe the applicability of the fuzzy set theory to a conventional p control chart.     

Fuzzy prior information and minimax estimation in the linear regression model

We consider the linear regression modely=Xβ+u with prior information on the unknown parameter vector β. The additional information on β is given by a fuzzy set. Using the mean squared error criterion we derive linear estimators that optimally combine the data with the fuzzy prior information. Our approach generalizes the classical minimax procedure firstly proposed by Kuks and Olman.     

Construction of Fuzzy Control Charts Based on Weighted Possibilistic Mean

The problem of constructing control charts for fuzzy data has been considered in literature. The proposed transformation approaches and direct fuzzy approaches have their advantages and disadvantages. The representative values charts based on transformation methods are often recommended in practical application. For representing a fuzzy set by a crisp value, the weight of importance of the members assigned with some membership levels in a fuzzy set should be considered, and the possibility theory can be employed to deal with such problem. In this article, we propose to employ the weighted possibilistic mean (WPM), weighted interval valued possibilistic mean (WIVPM) of fuzzy number as a sort of representative values for the fuzzy attribute data, and establish new fuzzy control charts with WPM and WIVPM. The performance of the charts is compared to the existing fuzzy charts with a fuzzy c-chart example via newly defined average number of inspection for variation of control state.     

Reducing Periodicity of Fuzzy Markov Chains Based on Simulation Using Halton Sequence

We first introduce fuzzy finite Markov chains and present some of their fundamental properties based on possibility theory. We also bring in a way to convert fuzzy Markov chains to classic Markov chains. In addition, we simulate fuzzy Markov chain using different sizes. It is observed that the most of fuzzy Markov chains not only do have an ergodic behavior, but also they are periodic. Finally, using Halton quasi-random sequence we generate some fuzzy Markov chains, which are compared with the ones generated by the RAND function of MATLAB. Therefore, we improve the periodicity behavior of fuzzy Markov chains.     

The Development and Use of the NASIG Core Competencies for Electronic Resources Librarians

The Core Competencies for Electronic Resources Librarians was adopted by NASIG in 2013 and provides a framework to assess skills needed for electronic resources management. In this column, Sarah Sutton, whose graduate dissertation research led to the creation of the NASIG task force responsible for developing the core competencies, describes the development and adoption of the core competencies. Paula Sullenger describes the application of the core competencies at two institutions: Auburn University and Texas A&M University. The competencies have supported libraries in reorganization efforts as well as assessing current staff to identify gaps in skills and more effectively manage electronic resources. They have also been used to assess Library and Information Science (LIS) curricula. It is important that the core competencies be reviewed and revised to ensure their enduring relevancy within the profession.