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Proceedings ArticleDOI

Approximating fuzzy membership functions from clustered raw data

TL;DR: Two heuristic algorithms are presented for the estimation of parameterized family of membership functions, namely, triangular and trapezoidal for fuzzy c-means clustering and practical application is given.
Abstract: Clustering is the process of identifying groups of similar data fulfilling certain criteria. Fuzzy c-means clustering algorithm generates cluster centers and degree of memberships of each pattern to each fuzzy cluster. However, this clustered raw data is not of much benefit for the symbolic representation of fuzzy rule base which can be generated using standard algorithms like fuzzy decision trees and others. Also human interpretability is improved when clustered raw data is represented by Triangular, Trapezoidal, or Gaussian kind of membership functions, rather than representing as matrix of raw membership values. The convex hull method for the estimation of trapezoidal membership functions from the clustered raw data is of limited use and many a times generates membership functions that are either highly overlapped or highly separated. In this article, two heuristic algorithms are presented for the estimation of parameterized family of membership functions, namely, triangular and trapezoidal. Each of these algorithms has been explained formally and then stated in pseudo code form and illustrated with a sample dataset. Finally, the practical application of these algorithms is given in the context of our recent research.
Citations
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Journal ArticleDOI
TL;DR: This study shows that the accuracy levels of FDT generated using FCM clustered raw data, bypassing the approximation step, is acceptable and this method has several advantages too.
Abstract: This paper investigates the Triangular, Trapezoidal and Gaussian approximation methods for the purpose of induction of Fuzzy Decision Trees FDT. The generation of FDT is done using a Fuzzy ID3 induction algorithm. In this work three fuzzy partitioning techniques which form the basis for our investigation are given attention, namely Fuzzy C Means clustering FCM, Grid partitioning and Subtractive clustering Subclust. Our contribution lies in studying the effect of various approximations on the generation of FDT giving specific attention to the classification accuracy of FDT. In this study we show that the accuracy levels of FDT generated using FCM clustered raw data, bypassing the approximation step, is acceptable and this method has several advantages too. Several computational experiments are conducted and non parametric statistical tests are performed to find if any significant differences exist between the method of bypassing the approximation step and the other methods which include approximation. Ten FDTs are developed and used in this study. These FDT's differ in their fuzzy partitioning techniques and the approximation methods used.

17 citations


Cites methods from "Approximating fuzzy membership func..."

  • ...To overcome these limitations we introduced two heuristic approximation algorithms [13]....

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  • ...The symbols used in the pseudo code [13] are:...

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  • ...Approximation methods for FCM and subtractive clustered data Two efficient heuristic algorithms proposed in our earlier work [13] are used for converting FCM clustered raw data and subtractive clustered Gaussian data to parameterized family of fuzzy membership functions, like Triangular MF and Trapezoidal MF....

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Journal ArticleDOI
TL;DR: Firefly colony and fuzzy firefly colony optimization algorithms are proposed to apply to solve two key issues of datacenters, namely, server consolidation and multiobjective virtual machine placement problem.
Abstract: Managing cloud datacenters is the most prevailing challenging task ahead for the IT industries. The data centers are considered to be the main source for resource provisioning to the cloud users. Managing these resources to handle large number of virtual machine requests has created the need for heuristic optimization algorithms to provide the optimal placement strategies satisfying the objectives and constraints formulated. In this paper, we propose to apply firefly colony and fuzzy firefly colony optimization algorithms to solve two key issues of datacenters, namely, server consolidation and multiobjective virtual machine placement problem. The server consolidation aims to minimize the count of physical machines used and the virtual machine placement problem is to obtain optimal placement strategy with both minimum power consumption and resource wastage. The proposed techniques exhibit better performance than the heuristics and metaheuristic approaches considered in terms of server consolidation and finding optimal placement strategy.

17 citations

Journal ArticleDOI
31 Jan 2021-Symmetry
TL;DR: In this article, a structured literature review on generating triangular and trapezoidal Interval Fuzzy Type-2 membership functions using fuzzy C-means is presented, with the aim to motivate the future works of constructing the methods to generate Interval FF-type-2 triangular membership functions.
Abstract: Clustering is more popular than the expert knowledge approach in Interval Fuzzy Type-2 membership function construction because it can construct membership function automatically with less time consumption Most research proposed a two-fuzzifier fuzzy C-Means clustering method to construct Interval Fuzzy Type-2 membership function which mainly focused on producing Gaussian membership function The other two important membership functions, triangular and trapezoidal, are constructed using the grid partitioning method However, the method suffers a drawback of not being able to represent actual data composition in the underlying dataset Some research proposed triangular and trapezoidal membership functions construction using readily formed Fuzzy Type-1 membership functions, which means it remains unclear how the membership functions are heuristically constructed using fuzzy C-Means outputs The triangular and trapezoidal membership functions are important because previous works have shown that they may produce superior performance than Gaussian membership function in some applications Therefore, this paper presents a structured literature review on generating triangular and trapezoidal Interval Fuzzy Type-2 membership functions using fuzzy C-Means Initially, 110 related manuscripts were collected from Web of Science, Scopus, and Google Scholar These manuscripts went through the identification, screening, eligibility, and inclusion processes, and as a result, 21 manuscripts were reviewed and discussed in this paper To ensure that the review also covers the important components of fuzzy logic, this paper also reviews and discusses another 49 manuscripts on fuzzy calculation and operation Furthermore, this paper also discusses the contributions of the conducted review to the body of knowledge, future research directions and challenges, with the aim to motivate the future works of constructing the methods to generate Interval Fuzzy Type-2 triangular and trapezoidal membership functions using fuzzy C-Means The methods imply flexibility in choosing membership function type, hence increasing the effectiveness of fuzzy applications through leveraging the advantages that each of the three membership function types could provide

16 citations

Journal ArticleDOI
TL;DR: This work restricts the values of certainty factor to lie within theoretical bounds using the concept of gradient projection over neuro fuzzy decision tree and the model is named as Gradient Projected-Neuro-Fuzzy Decision Tree (GP-N-FDT).
Abstract: Fuzzy decision tree (FDT) induction is a powerful methodology to extract human interpretable classification rules. Due to the greedy nature of FDT, there is a chance of FDT resulting in poor classification accuracy. To improve the accuracy of FDT, Bhatt and Gopal (2006) have proposed a back propagation strategy, where the interpretability of derived fuzzy rules is affected, as the certainty factor of the rules does not lie within the theoretical bounds of 0 and 1. To retain the human interpretability of fuzzy rules, and to make rules consistent with fuzzy set theory, we restrict the values of certainty factor to lie within theoretical bounds using the concept of gradient projection over neuro fuzzy decision tree and the model is named as Gradient Projected-Neuro-Fuzzy Decision Tree (GP-N-FDT). Here, the parameters of FDT developed using Fuzzy ID3 algorithm are fine tuned using GP-N-FDT strategy to improve the classification accuracy.

9 citations

Journal ArticleDOI
TL;DR: This work considers locating the users as a pattern classification problem and uses Fuzzy decision tree (FDT) as a knowledge discovery method to locate the users based on the wireless signal strength observed by their handheld devices to increase the FDT accuracy and to achieve faster convergence.

8 citations

References
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Book
31 Jul 1981
TL;DR: Books, as a source that may involve the facts, opinion, literature, religion, and many others are the great friends to join with, becomes what you need to get.
Abstract: New updated! The latest book from a very famous author finally comes out. Book of pattern recognition with fuzzy objective function algorithms, as an amazing reference becomes what you need to get. What's for is this book? Are you still thinking for what the book is? Well, this is what you probably will get. You should have made proper choices for your better life. Book, as a source that may involve the facts, opinion, literature, religion, and many others are the great friends to join with.

15,662 citations

Journal ArticleDOI
TL;DR: A FORTRAN-IV coding of the fuzzy c -means (FCM) clustering program is transmitted, which generates fuzzy partitions and prototypes for any set of numerical data.

5,287 citations

Journal ArticleDOI
TL;DR: A general approach to quali- tative modeling based on fuzzy logic is discussed, which proposes to use a fuzzy clustering method (fuzzy c-means method) to identify the structure of a fuzzy model.
Abstract: This paper discusses a general approach to quali- tative modeling based on fuzzy logic. The method of qualitative modeling is divided into two parts: fuzzy modeling and linguistic approximation. It proposes to use a fuzzy clustering method (fuzzy c-means method) to identify the structure of a fuzzy model. To clarify the advantages of the proposed method, it also shows some examples of modeling, among them a model of a dynamical process and a model of a human operator's control action.

2,447 citations

Journal ArticleDOI
TL;DR: An appropriate objective function whose minimum will characterize a good possibilistic partition of the data is constructed, and the membership and prototype update equations are derived from necessary conditions for minimization of the criterion function.
Abstract: The clustering problem is cast in the framework of possibility theory. The approach differs from the existing clustering methods in that the resulting partition of the data can be interpreted as a possibilistic partition, and the membership values can be interpreted as degrees of possibility of the points belonging to the classes, i.e., the compatibilities of the points with the class prototypes. An appropriate objective function whose minimum will characterize a good possibilistic partition of the data is constructed, and the membership and prototype update equations are derived from necessary conditions for minimization of the criterion function. The advantages of the resulting family of possibilistic algorithms are illustrated by several examples. >

2,388 citations

Journal ArticleDOI
TL;DR: Limitation analysis indicates, and numerical experiments confirm, that the Fukuyama-Sugeno index is sensitive to both high and low values of m and may be unreliable because of this, and calculations suggest that the best choice for m is probably in the interval [1.5, 2.5], whose mean and midpoint, m=2, have often been the preferred choice for many users of FCM.
Abstract: Many functionals have been proposed for validation of partitions of object data produced by the fuzzy c-means (FCM) clustering algorithm We examine the role a subtle but important parameter-the weighting exponent m of the FCM model-plays in determining the validity of FCM partitions The functionals considered are the partition coefficient and entropy indexes of Bezdek, the Xie-Beni (1991), and extended Xie-Beni indexes, and the Fukuyama-Sugeno index (1989) Limit analysis indicates, and numerical experiments confirm, that the Fukuyama-Sugeno index is sensitive to both high and low values of m and may be unreliable because of this Of the indexes tested, the Xie-Beni index provided the best response over a wide range of choices for the number of clusters, (2-10), and for m from 101-7 Finally, our calculations suggest that the best choice for m is probably in the interval [15, 25], whose mean and midpoint, m=2, have often been the preferred choice for many users of FCM >

1,724 citations