Characteristics of Rough SetC-Means Clustering

2018 ◽  
Vol 22 (4) ◽  
pp. 551-564 ◽  
Author(s):  
Seiki Ubukata ◽  
◽  
Keisuke Umado ◽  
Akira Notsu ◽  
Katsuhiro Honda
Keyword(s):  
Set Theory ◽  
Rough Set ◽  
Malignant Disease ◽  
Rough Set Theory ◽  
Fuzzy Theory ◽  
Classification Performance ◽  
Approximation Space ◽  
Clustering Model ◽  
Positive Region ◽  
Medical Dataset

HardC-means (HCM), which is one of the most popular clustering techniques, has been extended by using soft computing approaches such as fuzzy theory and rough set theory. FuzzyC-means (FCM) and roughC-means (RCM) are respectively fuzzy and rough set extensions of HCM. RCM can detect the positive and the possible regions of clusters by using the lower and the upper areas which are respectively analogous to the lower and the upper approximations in rough set theory. RCM-type methods have the problem that the original definitions of the lower and the upper approximations are not actually used. In this paper, rough setC-means (RSCM), which is an extension of HCM based on the original rough set definition, is proposed as a rough set-based counterpart of RCM. Specifically, RSCM is proposed as a clustering model on an approximation space considering a space granulated by a binary relation and uses the lower and the upper approximations of temporal clusters. For this study, we investigated the characteristics of the proposed RSCM through basic considerations, visual demonstrations, and comparative experiments. We observed the geometric characteristics of the examined methods by using visualizations and numerical experiments conducted for the problem of classifying patients as having benign or malignant disease based on a medical dataset. We compared the classification performance by viewing the trade-off between the classification accuracy in the positive region and the fraction of objects classified as being in the positive region.

Measures of uncertainty for a fuzzy probabilistic approximation space

2021 ◽  
pp. 1-24
Author(s):  
Lijun Chen ◽  
Damei Luo ◽  
Pei Wang ◽  
Zhaowen Li ◽  
Ningxin Xie
Keyword(s):  
Set Theory ◽  
Rough Set ◽  
Rough Set Theory ◽  
Fuzzy Relation ◽  
Point Of View ◽  
Approximation Space ◽  
Fuzzy Approximation ◽  
Entropy Measurement ◽  
Fuzzy Relation Matrix ◽  
Relation Matrix

 An approximation space (A-space) is the base of rough set theory and a fuzzy approximation space (FA-space) can be seen as an A-space under the fuzzy environment. A fuzzy probability approximation space (FPA-space) is obtained by putting probability distribution into an FA-space. In this way, it combines three types of uncertainty (i.e., fuzziness, probability and roughness). This article is devoted to measuring the uncertainty for an FPA-space. A fuzzy relation matrix is first proposed by introducing the probability into a given fuzzy relation matrix, and on this basis, it is expanded to an FA-space. Then, granularity measurement for an FPA-space is investigated. Next, information entropy measurement and rough entropy measurement for an FPA-space are proposed. Moreover, information amount in an FPA-space is considered. Finally, a numerical example is given to verify the feasibility of the proposed measures, and the effectiveness analysis is carried out from the point of view of statistics. Since three types of important theories (i.e., fuzzy set theory, probability theory and rough set theory) are clustered in an FPA-space, the obtained results may be useful for dealing with practice problems with a sort of uncertainty.

scholarly journals AN OVERVIEW OF ROUGH SET SEMANTICS FOR MODAL AND QUANTIFIER LOGICS

2000 ◽  
Vol 08 (01) ◽  
pp. 93-118 ◽  
Author(s):  
CHURN-JUNG LIAU
Keyword(s):  
Set Theory ◽  
Rough Set ◽  
Possible Worlds ◽  
Rough Set Theory ◽  
Modal Logics ◽  
The Other ◽  
Approximation Space ◽  
The Universe

In this paper, we would like to present some logics with semantics based on rough set theory and related notions. These logics are mainly divided into two classes. One is the class of modal logics and the other is that of quantifier logics. For the former, the approximation space is based on a set of possible worlds, whereas in the latter, we consider the set of variable assignments as the universe of approximation. In addition to surveying some well-known results about the links between logics and rough set notions, we also develop some new applied logics inspired by rough set theory.

Facial Expression Recognition Based on RS-SVM

2014 ◽  
Vol 543-547 ◽  
pp. 2329-2332
Author(s):  
Dong Li
Keyword(s):  
Facial Expression ◽  
Set Theory ◽  
Rough Set ◽  
Facial Expression Recognition ◽  
Rough Set Theory ◽  
Rapid Development ◽  
Classification Performance ◽  
Svm Classifier ◽  
Expression Recognition

In Recent years, with the rapid development of facial expression recognition technology, processing and classification of facial expression recognition has become a hotspot in application studies of remote sensing. Rough set theory (RS) and SVM have unique advantages in information processing and classification. This paper applies RS-SVM to facial expression recognition, briefly introduce the concepts of RS and principle of SVM, attributes reduction in RS theory as preposing system to get rid of redundancy attributes. Meanwhile, the SVM classifier works as postposing system helps training and classifying the facial expression recognition. Experimental results indicate this model not only raise the operating speed, but also improve classification performance, providing a new effective way in facial expression recognition technology.

The Application of Fuzzy Theory and Gray-Based Rough Set Theory in the Supplier Selection Decision Making

2010 ◽  
Vol 26-28 ◽  
pp. 559-563 ◽  
Author(s):  
Kai Jun Leng ◽  
Shu Hong Zhang
Keyword(s):  
Set Theory ◽  
Rough Set ◽  
Supplier Selection ◽  
Rough Set Theory ◽  
Fuzzy Theory ◽  
Decision Makers ◽  
Location Selection ◽  
Integrated Method ◽  
Selection Decision ◽  
Selection Of

This work presents the combination of fuzzy theory and rough set theory to solve facility location selection problems under the condition of involving different objective/subjective attributes. We try to utilize individual merits for each method and combine it to form a reliable selection of alternative suppliers. An empirical example is illustrated to show the effectiveness of the integrated method. Our results showed that the integrated method can allow decision makers to get the best candidate of supplier location, and is recommended in the practice therefore.

scholarly journals An Attribute Reduction Method using Neighborhood Entropy Measures in Neighborhood Rough Sets

Entropy ◽  
2019 ◽  
Vol 21 (2) ◽  
pp. 155 ◽  
Author(s):  
Lin Sun ◽  
Xiaoyu Zhang ◽  
Jiucheng Xu ◽  
Shiguang Zhang
Keyword(s):  
Set Theory ◽  
Rough Set ◽  
Rough Sets ◽  
Rough Set Theory ◽  
Attribute Reduction ◽  
Classification Performance ◽  
Data Sets ◽  
Complex Data ◽  
Decision Systems ◽  
Neighborhood Rough Sets

Attribute reduction as an important preprocessing step for data mining, and has become a hot research topic in rough set theory. Neighborhood rough set theory can overcome the shortcoming that classical rough set theory may lose some useful information in the process of discretization for continuous-valued data sets. In this paper, to improve the classification performance of complex data, a novel attribute reduction method using neighborhood entropy measures, combining algebra view with information view, in neighborhood rough sets is proposed, which has the ability of dealing with continuous data whilst maintaining the classification information of original attributes. First, to efficiently analyze the uncertainty of knowledge in neighborhood rough sets, by combining neighborhood approximate precision with neighborhood entropy, a new average neighborhood entropy, based on the strong complementarity between the algebra definition of attribute significance and the definition of information view, is presented. Then, a concept of decision neighborhood entropy is investigated for handling the uncertainty and noisiness of neighborhood decision systems, which integrates the credibility degree with the coverage degree of neighborhood decision systems to fully reflect the decision ability of attributes. Moreover, some of their properties are derived and the relationships among these measures are established, which helps to understand the essence of knowledge content and the uncertainty of neighborhood decision systems. Finally, a heuristic attribute reduction algorithm is proposed to improve the classification performance of complex data sets. The experimental results under an instance and several public data sets demonstrate that the proposed method is very effective for selecting the most relevant attributes with great classification performance.

Discretization of Attributes Based on Relative Positive Region of Decision Attribute

2011 ◽  
Vol 271-273 ◽  
pp. 253-257
Author(s):  
Chang Jie Zhou ◽  
Xiao Li ◽  
Dong Wen Zhang ◽  
Ji Qing Qiu
Keyword(s):  
Set Theory ◽  
Rough Set ◽  
Rough Set Theory ◽  
Real Life ◽  
New Method ◽  
Life Data ◽  
Positive Region ◽  
Real Life Data ◽  
Discrete Methods ◽  
Continuous Attribute

Traditional rough set theory can hardly handle the real-life data which contains continuous attribute. In order to solve this problem, a new method for discretization of continuous attributes based on relative positive region of decision attribute is presented. The method which distinguishes from traditional discrete methods firstly gets the relative positive region of decision attribute, and then discrete continuous attributes with the theorem proved in this paper. Finally, the result of an example shows that our method is efficient and feasible.

Uncertainty Measures for Multigranulation Approximation Space

2015 ◽  
Vol 23 (03) ◽  
pp. 443-457 ◽  
Author(s):  
Guoping Lin ◽  
Jiye Liang ◽  
Yuhua Qian
Keyword(s):  
Set Theory ◽  
Rough Set ◽  
Information Entropy ◽  
Rough Set Theory ◽  
Mathematical Tool ◽  
Approximation Space ◽  
Uncertainty Measures ◽  
Multigranulation Rough Set ◽  
Essential Properties ◽  
The Relationship

Multigranulation rough set theory is a relatively new mathematical tool for solving complex problems in the multigranulation or distributed circumstances which are characterized by vagueness and uncertainty. In this paper, we first introduce the multigranulation approximation space. According to the idea of fusing uncertain, imprecise information, we then present three uncertainty measures: fusing information entropy, fusing rough entropy, and fusing knowledge granulation in the multigranulation approximation space. Furthermore, several essential properties (equivalence, maximum, minimum) are examined and the relationship between the fusion information entropy and the fusion rough entropy is also established. Finally, we prove these three measures are monotonously increasing as the partitions become finer. These results will be helpful for understanding the essence of uncertainty measures in multigranulation rough space and enriching multigranulation rough set theory.

scholarly journals Multiset concepts in two-universe approximation spaces

2020 ◽  
Vol 28 (1) ◽  
Author(s):  
O. A. Embaby ◽  
Nadya A. Toumi
Keyword(s):  
Decision Making ◽  
Information Systems ◽  
Set Theory ◽  
Rough Set ◽  
Rough Set Theory ◽  
Approximation Space ◽  
Approximation Spaces ◽  
Lower And Upper Approximations ◽  
Two Universes ◽  
Basic Sets

Abstract Rough set theory over two universes is a generalization of rough set model to find accurate approximations for uncertain concepts in information systems in which uncertainty arises from existence of interrelations between the three basic sets: objects, attributes, and decisions. In this work, multisets are approximated in a crisp two-universe approximation space using binary ordinary relation and multi relation. The concept of two universe approximation is applied for defining lower and upper approximations of multisets. Properties of these approximations are investigated, and the deviations between them and corresponding notions are obtained; some counter examples are given. The suggested notions can help in the modification of the decision-making for events in which objects have repetitions such as patients visiting a doctor more than one time; an example for this case is given.

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