Search

Copyright of Contaduría y Administración is the property of Facultad de Contaduria y Administracion-Universidad Nacional Autonoma de Mexico and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

In several research areas, ratings data and response times have been successfully used to unfold the stagewise process through which human raters provide their responses to questionnaires and social surveys. A limitation of the standard approach to analyze this type of data is that it requires the use of independent statistical models. Although this provides an effective way to simplify the data analysis, it could potentially involve difficulties with regard to statistical inference and interpretation. In this sense, a joint analysis could be more effective. In this research article, we describe a way to jointly analyze ratings and response times by means of fuzzy numbers. A probabilistic tree model framework has been adopted to fuzzify ratings data and four-parameters triangular fuzzy numbers have been used in order to integrate crisp responses and times. Finally, a real case study on psychometric data is discussed in order to illustrate the proposed methodology. Overall, we provide initial findings to the problem of using fuzzy numbers as abstract models for representing ratings data with additional information (i.e., response times). The results indicate that using fuzzy numbers leads to theoretically sound and more parsimonious data analysis methods, which limit some statistical issues that may occur with standard data analysis procedures. [ABSTRACT FROM AUTHOR]

Life time data analysis is regarded as one of the significant out-shoots of statistics. Classical statistical techniques reckon life time observations as precise numbers and solely cover variation among the observations. In fact, there are two types of uncertainty in data: variation among the observations and the fuzziness. To this effect, the analysis techniques, which do not consider fuzziness and are only based on precise life time observations, use incomplete information; hence lead to pseudo results. This study aimed at generalizing parameters estimation, survival functions, and hazard rates for fuzzy life time data. [ABSTRACT FROM AUTHOR]

Life time data are mainly used in medicine, public health, and engineering sciences. The classical statistics related to these fields are based on precise measurements. However, according to modern measurement science precise measurement of continuous phenomena is not possible. In addition the observed quantity is more or less precise. In order to obtain realistic results, in addition to classical and Bayesian inference, the most up to date model for this are fuzzy number approaches which are more suitable and realistic. In this study, I consider the classical and Bayesian inference criteria for the Pareto distribution to obtain more realistic results for fuzzy observations of life time. In addition to stochastic variation the proposed generalized estimators cover fuzziness of the life times as well. [ABSTRACT FROM AUTHOR]

LR-fuzzy numbers are widely used in Fuzzy Set Theory applications based on the standard definition of convex fuzzy sets. However, in some empirical contexts such as, for example, human decision making and ratings, convex representations might not be capable to capture more complex structures in the data. Moreover, non-convexity seems to arise as a natural property in many applications based on fuzzy systems (e.g., fuzzy scales of measurement). In these contexts, the usage of standard fuzzy statistical techniques could be questionable. A possible way out consists in adopting ad-hoc data manipulation procedures to transform non-convex data into standard convex representations. However, these procedures can artificially mask relevant information carried out by the non-convexity property. To overcome this problem, in this article we introduce a novel computational definition of non-convex fuzzy number which extends the traditional definition of LR-fuzzy number. Moreover, we also present a new fuzzy regression model for crisp input/non-convex fuzzy output data based on the fuzzy least squares approach. In order to better highlight some important characteristics of the model, we applied the fuzzy regression model to some datasets characterized by convex as well as non-convex features. Finally, some critical points are outlined in the final section of the article together with suggestions about future extensions of this work. [ABSTRACT FROM AUTHOR]

Abstract: When constructing the model of a word by collecting interval-valued data from a group of individuals, both interpersonal and intrapersonal uncertainties coexist. Similar to the interval type-2 fuzzy set (IT2 FS) used in the enhanced interval approach (EIA), the Cloud model characterized by only three parameters can manage both uncertainties. Thus, based on the Cloud model, this paper proposes a new representation model for a word from interval-valued data. In our proposed method, firstly, the collected data intervals are preprocessed to remove the bad ones. Secondly, the fuzzy statistical method is used to compute the histogram of the surviving intervals. Then, the generated histogram is fitted by a Gaussian curve function. Finally, the fitted results are mapped into the parameters of a Cloud model to obtain the parametric model for a word. Compared with eight or nine parameters needed by an IT2 FS, only three parameters are needed to represent a Cloud model. Therefore, we develop a much more parsimonious parametric model for a word based on the Cloud model. Generally a simpler representation model with less parameters usually means less computations and memory requirements in applications. Moreover, the comparison experiments with the recent EIA show that, our proposed method can not only obtain much thinner footprints of uncertainty (FOUs) but also capture sufficient uncertainties of words. [Copyright &y& Elsevier]

Nonparametric statistical tests are a distribution-free method without any assumption that data are drawn from a particular probability distribution. In this paper, to identify the distribution difference between two populations of fuzzy data, we derive a function that can describe continuous fuzzy data. In particular, the Kolmogorov-Smirnov two-sample test is used for distinguishing two populations of fuzzy data. Empirical studies illustrate that the Kolmogorov-Smirnov two-sample test enables us to judge whether two independent samples of continuous fuzzy data are derived from the same population. The results show that the proposed function is successful in distinguishing two populations of continuous fuzzy data and useful in various applications. © 2013 Institute of Electrical Engineers of Japan. Published by John Wiley & Sons, Inc. [ABSTRACT FROM AUTHOR]

Abstract: Fuzzy rough sets, generalized from Pawlak''s rough sets, were introduced for dealing with continuous or fuzzy data. This model has been widely discussed and applied these years. It is shown that the model of fuzzy rough sets is sensitive to noisy samples, especially sensitive to mislabeled samples. As data are usually contaminated with noise in practice, a robust model is desirable. We introduce a new model of fuzzy rough set model, called soft fuzzy rough sets, and design a robust classification algorithm based on the model. Experimental results show the effectiveness of the proposed algorithm. [Copyright &y& Elsevier]

Abstract: In this paper, we establish a novel regard towards fuzzy clustering, showing it provides a sound framework for fitting finite mixture models. We propose a novel fuzzy clustering-type methodology for finite mixture model fitting, effected by utilizing a regularized form of the fuzzy c-means (FCM) algorithm, and introducing a proper dissimilarity functional for the algorithm with respect to the probabilistic properties of the model being treated. We apply the proposed methodology in a number of popular finite mixture models, and the corresponding expressions of the fuzzy model fitting algorithm are derived. We examine the efficacy of our novel approach in both clustering and classification applications of benchmark data sets, and we demonstrate the advantages of the proposed approach over maximum-likelihood. [ABSTRACT FROM AUTHOR]

Abstract: There is a family of well-known external clustering validity indexes to measure the degree of compatibility or similarity between two hard partitions of a given data set, including partitions with different numbers of categories. A unified, fully equivalent set-theoretic formulation for an important class of such indexes was derived and extended to the fuzzy domain in a previous work by the author [Campello, R.J.G.B., 2007. A fuzzy extension of the Rand index and other related indexes for clustering and classification assessment. Pattern Recognition Lett., 28, 833–841]. However, the proposed fuzzy set-theoretic formulation is not valid as a general approach for comparing two fuzzy partitions of data. Instead, it is an approach for comparing a fuzzy partition against a hard referential partition of the data into mutually disjoint categories. In this paper, generalized external indexes for comparing two data partitions with overlapping categories are introduced. These indexes can be used as general measures for comparing two partitions of the same data set into overlapping categories. An important issue that is seldom touched in the literature is also addressed in the paper, namely, how to compare two partitions of different subsamples of data. A number of pedagogical examples and three simulation experiments are presented and analyzed in details. A review of recent related work compiled from the literature is also provided. [Copyright &y& Elsevier]

Association rule mining is an important data analysis method that can discover associations within data. There are numerous previous studies that focus on finding fuzzy association rules from precise and certain data. Unfortunately, real-world data tends to be uncertain due to human errors, instrument errors, recording errors, and so on. Therefore, a question arising immediately is how we can mine fuzzy association rules from uncertain data. To this end, this paper proposes a representation scheme to represent uncertain data. This representation is based on possibility distributions because the possibility theory establishes a close connection between the concepts of similarity and uncertainty, providing an excellent framework for handling uncertain data. Then, we develop an algorithm to mine fuzzy association rules from uncertain data represented by possibility distributions. Experimental results from the survey data show that the proposed approach can discover interesting and valuable patterns with high certainty. [ABSTRACT FROM AUTHOR]

Abstract: Cluster analysis is one of the most crucial techniques in statistical data analysis. Among the clustering methods, density-based methods have great importance due to their ability to recognize clusters with arbitrary shape. In this paper, robustness of the clustering methods is handled. These methods use distance-based neighborhood relations between points. In particular, DBSCAN (density-based spatial clustering of applications with noise) algorithm and FN-DBSCAN (fuzzy neighborhood DBSCAN) algorithm are analyzed. FN-DBSCAN algorithm uses fuzzy neighborhood relation whereas DBSCAN uses crisp neighborhood relation. The main characteristic of the FN-DBSCAN algorithm is that it combines the speed of the DBSCAN and robustness of the NRFJP (noise robust fuzzy joint points) algorithms. It is observed that the FN-DBSCAN algorithm is more robust than the DBSCAN algorithm to datasets with various shapes and densities. [Copyright &y& Elsevier]

A key challenge in pattern recognition is how to scale the computational efficiency of clustering algorithms on large data sets. The extension of non-Euclidean relational fuzzy c-means (NERF) clustering to very large (VL = unloadable) relational data is called the extended NERF (eNERF) clustering algorithm, which comprises four phases: (i) finding distinguished features that monitor progressive sampling; (ii) progressively sampling from a N × N relational matrix RN to obtain a n × n sample matrix Rn; (iii) clustering Rn with literal NERF; and (iv) extending the clusters in Rn to the remainder of the relational data. Previously published examples on several fairly small data sets suggest that eNERF is feasible for truly large data sets. However, it seems that phases (i) and (ii), i.e., finding Rn, are not very practical because the sample size n often turns out to be roughly 50% of n, and this over-sampling defeats the whole purpose of eNERF. In this paper, we examine the performance of the sampling scheme of eNERF with respect to different parameters. We propose a modified sampling scheme for use with eNERF that combines simple random sampling with (parts of) the sampling procedures used by eNERF and a related algorithm sVAT (scalable visual assessment of clustering tendency). We demonstrate that our modified sampling scheme can eliminate over-sampling of the original progressive sampling scheme, thus enabling the processing of truly VL data. Numerical experiments on a distance matrix of a set of 3,000,000 vectors drawn from a mixture of 5 bivariate normal distributions demonstrate the feasibility and effectiveness of the proposed sampling method. We also find that actually running eNERF on a data set of this size is very costly in terms of computation time. Thus, our results demonstrate that further modification of eNERF, especially the extension stage, will be needed before it is truly practical for VL data. © 2008 Wiley Periodicals, Inc. [ABSTRACT FROM AUTHOR]

This paper constitutes a first step towards an extension of correspondence analysis with fuzzy data (FCA). At this stage, our main objective is to lay down the algebraic foundations for this fuzzy extension of the usual correspondence analysis. A two-step method is introduced to convert the fuzzy eigenvalue problem to an ordinary one. We consider a fuzzy matrix as the set of its cuts. Each such cut is an interval-valued matrix viewed as a line-segment in the matrix space. In this way, line-segments of cut-matrices are transformed into intervals of eigenvalues. Therefore, the two-step method is essentially a reduction of the fuzzy eigenvalue problem to an ordinary one. We illustrate the FCA-fuzzy eigenvalue problem with a simple numerical example. We hope upon the completion of this project in near future, to be able to supply the necessary tools for the end user of the correspondence analysis with fuzzy data. [Copyright &y& Elsevier]

In the fuzzy clustering literature, two main types of membership are usually considered: A relative type, termed probabilistic, and an absolute or possibilistic type, indicating the strength of the attribution to any cluster independent from the rest. There are works addressing the unification of the two schemes. Here, we focus on providing a model for the transition from one schema to the other, to exploit the dual information given by the two schemes, and to add flexibility for the interpretation of results. We apply an uncertainty model based on interval values to memberships in the clustering framework, obtaining a framework that we term graded possibility. We outline a basic example of graded possibilistic clustering algorithm and add some practical remarks about its implementation. The experimental demonstrations presented highlight the different properties attainable through appropriate implementation of a suitable graded possibilistic model. An interesting application is found in automated segmentation of diagnostic medical images, where the model provides an interactive visualization tool for this task. [ABSTRACT FROM AUTHOR]

The learning algorithm and multivariable data analysis (LAMDA) is an algorithm to group quantitative and qualitative data, applying self-learning and/or directed learning. Usually, LAMDA automatically generates classes by assigning the best data partition to a class. To evaluate the data partitions generated by LAMDA, the internal evaluation is used to find the optimal number of clusters. For the LAMDA algorithm, the cluster validity (CV) is the most popular index which is based on inter-class contrast (ICC). However, other indices have not been defined for LAMDA and a comparative analysis is required to evaluate its performance. In this paper, two metrics called cluster validity index based on granulation error and the ratio of the distance (CVGED) and cluster validity index based on the ratios of covariance and distance (CVCOD) are proposed. Such indices are compared with the CV and ICC indices for two experiments: using a databases repository and selected open data and experimental laboratory data. According to the main results, CVGED and CVCOD have a better performance in compactness, separation, and coefficient of variation than ICC and CV for most of the selected repository databases but the accuracy is limited for the four indices. Nevertheless, CVCOD improves the quality of data partition when the open data and experimental laboratory data are used. • The paper proposes two cluster validity indices for the LAMDA clustering algorithm. • The CVGED index is based on the granulation error and the ratio of the distance. • The CVCOD index is based on the ratio of the distances and the ratio of compactness. • CVGED and CVCOD have a better performance than ICC and CV. • CVCOD can find the best parameter values and to increase the quality of partition. [ABSTRACT FROM AUTHOR]