Clustering of fuzzy data using credibilistic expected and critical values
01 Feb 2014-pp 176-181
TL;DR: A new approach for handling fuzzy data sets in producing crisp clusters using the notion of expectation of discrete fuzzy variables is introduced and compared with another approach through fuzzy critical values pursued by Sampath and Kalaivani (2010).
Abstract: This paper introduces a new approach for handling fuzzy data sets in producing crisp clusters. The proposed method uses the notion of expectation of discrete fuzzy variables. The proposed method has been compared with another approach through fuzzy critical values pursued by Sampath and Kalaivani (2010). Comparative experimental study has been carried out with the help of data sets simulated from multivariate normal populations where fuzziness has been induced using a well defined procedure. In the process of comparison two partitioning clustering methods, namely, k-means and k-medoids algorithm have been considered.
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09 Apr 2019
TL;DR: In this article, a fuzzy expected value model is designed through the concept of credibility expected value criterion, and an iteration programming model is developed to calculate the expected value of the fuzzy credibility function.
Abstract: In this present study, a single period inventory problem is inquired with the aid of fuzzy numbers and credibility theory. A fuzzy expected value model is designed through the concept of credibility expected value criterion. The necessity of fuzzy expected value model is to determine the optimal order quantity so that the total cost becomes minimal. An iteration programming model is developed to calculate the expected value of the fuzzy credibility function. Moreover, a numerical illustration is also provided to strengthen the validity of the proposed algorithm.
01 Jan 2017
TL;DR: In this paper, the authors considered the problem of developing test procedures for testing credibility hypotheses about the variance of fuzzy normal distribution assuming the expected values of the distributions mentioned under null and alternative credibility hypotheses are known and equal.
Abstract: This paper considers the problem of developing test procedures for testing credibility hypotheses about the variance of fuzzy normal distribution assuming the expected values of the distributions mentioned under null and alternative credibility hypotheses are known and equal. The cases where the underlying hypothesis is simple and composite (one sided) are considered. Tests have been derived with the help of the membership ratio criterion. Properties possessed by the developed tests, like best credibility rejection region and uniformly best rejection region have been studied. Examples are also given to illustrate the usage of the derived tests.
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01 Jan 1967
TL;DR: The k-means algorithm as mentioned in this paper partitions an N-dimensional population into k sets on the basis of a sample, which is a generalization of the ordinary sample mean, and it is shown to give partitions which are reasonably efficient in the sense of within-class variance.
Abstract: The main purpose of this paper is to describe a process for partitioning an N-dimensional population into k sets on the basis of a sample. The process, which is called 'k-means,' appears to give partitions which are reasonably efficient in the sense of within-class variance. That is, if p is the probability mass function for the population, S = {S1, S2, * *, Sk} is a partition of EN, and ui, i = 1, 2, * , k, is the conditional mean of p over the set Si, then W2(S) = ff=ISi f z u42 dp(z) tends to be low for the partitions S generated by the method. We say 'tends to be low,' primarily because of intuitive considerations, corroborated to some extent by mathematical analysis and practical computational experience. Also, the k-means procedure is easily programmed and is computationally economical, so that it is feasible to process very large samples on a digital computer. Possible applications include methods for similarity grouping, nonlinear prediction, approximating multivariate distributions, and nonparametric tests for independence among several variables. In addition to suggesting practical classification methods, the study of k-means has proved to be theoretically interesting. The k-means concept represents a generalization of the ordinary sample mean, and one is naturally led to study the pertinent asymptotic behavior, the object being to establish some sort of law of large numbers for the k-means. This problem is sufficiently interesting, in fact, for us to devote a good portion of this paper to it. The k-means are defined in section 2.1, and the main results which have been obtained on the asymptotic behavior are given there. The rest of section 2 is devoted to the proofs of these results. Section 3 describes several specific possible applications, and reports some preliminary results from computer experiments conducted to explore the possibilities inherent in the k-means idea. The extension to general metric spaces is indicated briefly in section 4. The original point of departure for the work described here was a series of problems in optimal classification (MacQueen [9]) which represented special
24,320Â citations
Book•
01 Jan 1990TL;DR: An electrical signal transmission system, applicable to the transmission of signals from trackside hot box detector equipment for railroad locomotives and rolling stock, wherein a basic pulse train is transmitted whereof the pulses are of a selected first amplitude and represent a train axle count.
Abstract: 1. Introduction. 2. Partitioning Around Medoids (Program PAM). 3. Clustering large Applications (Program CLARA). 4. Fuzzy Analysis. 5. Agglomerative Nesting (Program AGNES). 6. Divisive Analysis (Program DIANA). 7. Monothetic Analysis (Program MONA). Appendix 1. Implementation and Structure of the Programs. Appendix 2. Running the Programs. Appendix 3. Adapting the Programs to Your Needs. Appendix 4. The Program CLUSPLOT. References. Author Index. Subject Index.
10,537Â citations
01 Jan 1990
TL;DR: In this article, an electrical signal transmission system for railway locomotives and rolling stock is proposed, where a basic pulse train is transmitted whereof the pulses are of a selected first amplitude and represent a train axle count, and a spike pulse of greater selected amplitude is transmitted, occurring immediately after the axle count pulse to which it relates, whenever an overheated axle box is detected.
Abstract: An electrical signal transmission system, applicable to the transmission of signals from trackside hot box detector equipment for railroad locomotives and rolling stock, wherein a basic pulse train is transmitted whereof the pulses are of a selected first amplitude and represent a train axle count, and a spike pulse of greater selected amplitude is transmitted, occurring immediately after the axle count pulse to which it relates, whenever an overheated axle box is detected. To enable the signal receiving equipment to determine on which side of a train the overheated box is located, the spike pulses are of two different amplitudes corresponding, respectively, to opposite sides of the train.
9,011Â citations
TL;DR: This book make understandable the cluster analysis is based notion of starsmodern treatment, which efficiently finds accurate clusters in data and discusses various types of study the user set explicitly but also proposes another.
Abstract: The Wiley-Interscience Paperback Series consists of selected books that have been made more accessible to consumers in an effort to increase In both the increasingly important and distribution we show how these methods. Our experiments demonstrate that together can deal with most applications technometrics. In an appropriate visualization technique is to these new. The well written and efficiently finds accurate clusters in data including. Of applied value for several preprocessing tasks discontinuity preserving smoothing feature clusters! However the model based notion of domain knowledge from real data repositories in data. Discusses various types of study the user set explicitly but also propose another. This book make understandable the cluster analysis is based notion of starsmodern treatment.
7,423Â citations
"Clustering of fuzzy data using cred..." refers methods in this paper
...B. k -medoids Algorithm k-medoids algorithm due to Kaufmann and Rousseeuw [7] is also a partitioning and prototype based algorithm....
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...k - medoidsAlgorithm k-medoids algorithm due to Kaufmann and Rousseeuw [7] is also a partitioning and prototype based algorithm....
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...QCris p [clustering algoflullllS lIke Tt-means algorlullll ot JVrac ueefl :>J and kmedoids algorithm of Kaufmann and Rousseeuw [7] produce disjoint and exhaustive partition of the given data set....
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...QCrisp [clustering algoflullllS lIke Tt-means algorlullll ot JVrac ueefl :>J and kmedoids algorithm of Kaufmann and Rousseeuw [7] produce disjoint and exhaustive partition of the given data set....
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...Keeping these points in mind Kaufmann and Rousseeuw [7] proposed k-medoids algorithm in order to create a robust partitioning of the data set which is not easily affected by extreme values....
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01 Jul 2004
TL;DR: A variation of the K-means clustering algorithm based on properties of rough sets is proposed, which represents clusters as interval or rough sets.
Abstract: Data collection and analysis in web mining faces certain unique challenges. Due to a variety of reasons inherent in web browsing and web logging, the likelihood of bad or incomplete data is higher than conventional applications. The analytical techniques in web mining need to accommodate such data. Fuzzy and rough sets provide the ability to deal with incomplete and approximate information. Fuzzy set theory has been shown to be useful in three important aspects of web and data mining, namely clustering, association, and sequential analysis. There is increasing interest in research on clustering based on rough set theory. Clustering is an important part of web mining that involves finding natural groupings of web resources or web users. Researchers have pointed out some important differences between clustering in conventional applications and clustering in web mining. For example, the clusters and associations in web mining do not necessarily have crisp boundaries. As a result, researchers have studied the possibility of using fuzzy sets in web mining clustering applications. Recent attempts have used genetic algorithms based on rough set theory for clustering. However, the genetic algorithms based clustering may not be able to handle the large amount of data typical in a web mining application. This paper proposes a variation of the K-means clustering algorithm based on properties of rough sets. The proposed algorithm represents clusters as interval or rough sets. The paper also describes the design of an experiment including data collection and the clustering process. The experiment is used to create interval set representations of clusters of web visitors.
493Â citations
"Clustering of fuzzy data using cred..." refers background in this paper
...For recent developments on rough clustering one can refer Lingras, Yan and West [8], Lingras and West [9], Peters [2], Peters [3], Peters, Lampart and Weber [4] and Sampath and Ramya [11]....
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