A Study on Bayesian Decision Theoretic Rough Set

2014 ◽  
Vol 1 (1) ◽  
pp. 1-14 ◽  
Author(s):  
Sharmistha Bhattacharya Halder
Keyword(s):  
Set Theory ◽  
Rough Set ◽  
Rough Set Theory ◽  
Boundary Region ◽  
Data Sets ◽  
Bayesian Decision ◽  
Minimum Risk ◽  
Useful Knowledge ◽  
Research Fields ◽  
Hybrid Development

The concept of rough set was first developed by Pawlak (1982). After that it has been successfully applied in many research fields, such as pattern recognition, machine learning, knowledge acquisition, economic forecasting and data mining. But the original rough set model cannot effectively deal with data sets which have noisy data and latent useful knowledge in the boundary region may not be fully captured. In order to overcome such limitations, some extended rough set models have been put forward which combine with other available soft computing technologies. Many researchers were motivated to investigate probabilistic approaches to rough set theory. Variable precision rough set model (VPRSM) is one of the most important extensions. Bayesian rough set model (BRSM) (Slezak & Ziarko, 2002), as the hybrid development between rough set theory and Bayesian reasoning, can deal with many practical problems which could not be effectively handled by original rough set model. Based on Bayesian decision procedure with minimum risk, Yao (1990) puts forward a new model called decision theoretic rough set model (DTRSM) which brings new insights into the probabilistic approaches to rough set theory. Throughout this paper, the concept of decision theoretic rough set is studied and also a new concept of Bayesian decision theoretic rough set is introduced. Lastly a comparative study is done between Bayesian decision theoretic rough set and Rough set defined by Pawlak (1982).

The Incremental Knowledge Acquisition Based on Hash Algorithm

2016 ◽  
Vol 24 (03) ◽  
pp. 347-366 ◽  
Author(s):  
Qing-Hua Zhang ◽  
Long-Yang Yao ◽  
Guan-Sheng Zhang ◽  
Yu-Ke Xin
Keyword(s):  
Knowledge Acquisition ◽  
Set Theory ◽  
Rough Set ◽  
Granular Computing ◽  
Rough Set Theory ◽  
Attribute Reduction ◽  
Algorithm Analysis ◽  
Data Sets ◽  
Hash Algorithm ◽  
Acquisition Method

In this paper, a new incremental knowledge acquisition method is proposed based on rough set theory, decision tree and granular computing. In order to effectively process dynamic data, describing the data by rough set theory, computing equivalence classes and calculating positive region with hash algorithm are analyzed respectively at first. Then, attribute reduction, value reduction and the extraction of rule set by hash algorithm are completed efficiently. Finally, for each new additional data, the incremental knowledge acquisition method is proposed and used to update the original rules. Both algorithm analysis and experiments show that for processing the dynamic information systems, compared with the traditional algorithms and the incremental knowledge acquisition algorithms based on granular computing, the time complexity of the proposed algorithm is lower due to the efficiency of hash algorithm and also this algorithm is more effective when it is used to deal with the huge data sets.

Application of Rough Set Theory to Data Mining of Condenser Diagnosis in Power Plants

2003 ◽  
Author(s):  
Zhongguang Fu ◽  
Tao Jin ◽  
Kun Yang
Keyword(s):  
Data Mining ◽  
Set Theory ◽  
Rough Set ◽  
Power Plants ◽  
Rough Set Theory ◽  
A Priori ◽  
Reduction Algorithm ◽  
Useful Knowledge ◽  
Fault Features ◽  
Basic Concepts

Rough set theory is a powerful tool in deal with vagueness and uncertainty. It is particularly suitable to discover hidden and potentially useful knowledge in data and can be used to reduce features and extract rules. This paper introduces the basic concepts and fundamental elements of the rough set theory. A reduction algorithm that integrates a priori with significance is proposed to illustrate how the rough set theory could be used to extract fault features of the condenser in a power plant. Two testing examples are then presented to demonstrate the effectiveness of the theory in fault diagnosis.

scholarly journals δ-Cut Decision-Theoretic Rough Set Approach: Model and Attribute Reductions

2014 ◽  
Vol 2014 ◽  
pp. 1-12 ◽  
Author(s):  
Hengrong Ju ◽  
Huili Dou ◽  
Yong Qi ◽  
Hualong Yu ◽  
Dongjun Yu ◽  
...  
Keyword(s):  
Set Theory ◽  
Rough Set ◽  
Rough Set Theory ◽  
Original Data ◽  
Boundary Region ◽  
Research Trends ◽  
Data Set ◽  
Lower Approximation ◽  
New Research ◽  
Decision Cost

Decision-theoretic rough set is a quite useful rough set by introducing the decision cost into probabilistic approximations of the target. However, Yao’s decision-theoretic rough set is based on the classical indiscernibility relation; such a relation may be too strict in many applications. To solve this problem, aδ-cut decision-theoretic rough set is proposed, which is based on theδ-cut quantitative indiscernibility relation. Furthermore, with respect to criterions of decision-monotonicity and cost decreasing, two different algorithms are designed to compute reducts, respectively. The comparisons between these two algorithms show us the following: (1) with respect to the original data set, the reducts based on decision-monotonicity criterion can generate more rules supported by the lower approximation region and less rules supported by the boundary region, and it follows that the uncertainty which comes from boundary region can be decreased; (2) with respect to the reducts based on decision-monotonicity criterion, the reducts based on cost minimum criterion can obtain the lowest decision costs and the largest approximation qualities. This study suggests potential application areas and new research trends concerning rough set theory.

scholarly journals A Novel Boundary Oversampling Algorithm Based on Neighborhood Rough Set Model: NRSBoundary-SMOTE

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
Feng Hu ◽  
Hang Li
Keyword(s):  
Set Theory ◽  
Rough Set ◽  
Rough Set Theory ◽  
Boundary Region ◽  
Mathematical Tool ◽  
Decision Space ◽  
Minority Class ◽  
Original Dataset ◽  
Neighborhood Rough Set ◽  
Powerful Mathematical Tool

Rough set theory is a powerful mathematical tool introduced by Pawlak to deal with imprecise, uncertain, and vague information. The Neighborhood-Based Rough Set Model expands the rough set theory; it could divide the dataset into three parts. And the boundary region indicates that the majority class samples and the minority class samples are overlapped. On the basis of what we know about the distribution of original dataset, we only oversample the minority class samples, which are overlapped with the majority class samples, in the boundary region. So, the NRSBoundary-SMOTE can expand the decision space for the minority class; meanwhile, it will shrink the decision space for the majority class. After conducting an experiment on four kinds of classifiers, NRSBoundary-SMOTE has higher accuracy than other methods when C4.5, CART, and KNN are used but it is worse than SMOTE on classifier SVM.

scholarly journals Rough Set Theory and its Applications: A recent Survey

2020 ◽  
pp. 548-552
Keyword(s):  
Set Theory ◽  
Rough Set ◽  
Intelligent Agents ◽  
Rough Set Theory ◽  
Boundary Region ◽  
Process Industry ◽  
Decision Making Process ◽  
Upper Approximation ◽  
Analysis Process ◽  
The Universe

Rough set theory is a mathematical method proposed by Pawlak . Rough set theory has been developed to manage uncertainties in information that presents missing and noises. Rough set theory is an expansion of the conventional set theory that supports approximations in decision making process. Fundamental of assumption of rough set theory is that with every object of the universe has some information associated it. Rough set theory is correlate two crisp sets, called lower and upper approximation. The lower approximation of a set consists of all elements that surely belong to the set, and the upper approximation of the set constitutes of all elements that possibly belong to the set. The boundary region of the set consists of all elements that cannot be classified uniquely as belonging to the set or as belonging to its complement, with respect to the available knowledge Rough sets are applied in several domains, such as, pattern recognition, medicine, finance, intelligent agents, telecommunication, control theory ,vibration analysis, conflict resolution, image analysis, process industry, marketing, banking risk assessment etc. This paper gives detail survey of rough set theory and its properties and various applications of rough set theory.

scholarly journals An Efficient Classification Model using Fuzzy Rough Set Theory and Random Weight Neural Network

2021 ◽  
Vol 5 (3) ◽  
pp. 92-108
Author(s):  
Rana Aamir Raza
Keyword(s):  
Neural Network ◽  
Predictive Model ◽  
Set Theory ◽  
Rough Set ◽  
Large Scale ◽  
Rough Set Theory ◽  
Classification Model ◽  
Data Sets ◽  
Fuzzy Rough Set ◽  
Random Weight

In the area of fuzzy rough set theory (FRST), researchers have gained much interest in handling the high-dimensional data. Rough set theory (RST) is one of the important tools used to pre-process the data and helps to obtain a better predictive model, but in RST, the process of discretization may loss useful information. Therefore, fuzzy rough set theory contributes well with the real-valued data. In this paper, an efficient technique is presented based on Fuzzy rough set theory (FRST) to pre-process the large-scale data sets to increase the efficacy of the predictive model. Therefore, a fuzzy rough set-based feature selection (FRSFS) technique is associated with a Random weight neural network (RWNN) classifier to obtain the better generalization ability. Results on different dataset show that the proposed technique performs well and provides better speed and accuracy when compared by associating FRSFS with other machine learning classifiers (i.e., KNN, Naive Bayes, SVM, decision tree and backpropagation neural network).

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.

scholarly journals Uncertainty Analysis of Knowledge Reductions in Rough Sets

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Ying Wang ◽  
Nan Zhang
Keyword(s):  
Uncertainty Analysis ◽  
Set Theory ◽  
Rough Set ◽  
Rough Set Theory ◽  
Boundary Region ◽  
Relative Reduction ◽  
Uncertainty Measure ◽  
Intelligent Information Processing ◽  
Intelligent Information ◽  
Analysis Of Knowledge

Uncertainty analysis is a vital issue in intelligent information processing, especially in the age of big data. Rough set theory has attracted much attention to this field since it was proposed. Relative reduction is an important problem of rough set theory. Different relative reductions have been investigated for preserving some specific classification abilities in various applications. This paper examines the uncertainty analysis of five different relative reductions in four aspects, that is, reducts’ relationship, boundary region granularity, rules variance, and uncertainty measure according to a constructed decision table.

scholarly journals Seleksi Fitur Pada Klasifikasi Multi-label Menggunakan Proportional Feature Rough Selector

2021 ◽  
Vol 8 (4) ◽  
pp. 2084-2094
Author(s):  
Vilat Sasax Mandala Putra Paryoko
Keyword(s):  
Set Theory ◽  
Rough Set ◽  
Rough Set Theory ◽  
Boundary Region ◽  
Lower Approximation ◽  
Upper Approximation ◽  
Tv Shows

Proportional Feature Rough Selector (PFRS) merupakan sebuah metode seleksi fitur yang dikembangkan berdasarkan Rough Set Theory (RST). Pengembangan ini dilakukan dengan merinci pembagian wilayah dalam set data menjadi beberapa bagian penting yaitu lower approximation, upper approximation dan boundary region. PFRS memanfaatkan boundary region untuk menemukan wilayah yang lebih kecil yaitu Member Section (MS) dan Non-Member Section (NMS). Namun PFRS masih hanya digunakan dalam seleksi fitur pada klasifikasi biner dengan tipe data teks. PFRS ini juga dikembangkan tanpa memperhatikan hubungan antar fitur, sehingga PFRS memiliki potensi untuk ditingkatkan dengan mempertimbangkan korelasi antar fitur dalam set data. Untuk itu, penelitian ini bertujuan untuk melakukan penyesuaian PFRS untuk bisa diterapkan pada klasifikasi multi-label dengan data campuran yakni data teks dan data bukan teks serta mempertimbangkan korelasi antar fitur untuk meningkatkan performa klasifikasi multi-label. Pengujian dilakukan pada set data publik yaitu 515k Hotel Reviews dan Netflix TV Shows. Set data ini diuji dengan menggunakan empat metode klasifikasi yaitu DT, KNN, NB dan SVM. Penelitian ini membandingkan penerapan seleksi fitur PFRS pada data multi-label dengan pengembangan PFRS yaitu dengan mempertimbangkan korelasi. Hasil penelitian menunjukkan bahwa penggunaan PFRS berhasil meningkatkan performa klasifikasi. Dengan mempertimbangkan korelasi, PFRS menghasilkan peningkatan akurasi hingga 23,76%. Pengembangan PFRS juga menunjukkan peningkatan kecepatan yang signifikan pada semua metode klasifikasi sehingga pengembangan PFRS dengan mempertimbangkan korelasi mampu memberikan kontribusi dalam meningkatkan performa klasifikasi.

scholarly journals Neighborhood Based Multi-Granularity Attribute Reduction: An Acceleration Approach

2020 ◽  
Author(s):  
Jingjing Song ◽  
Huili Dou ◽  
Xiansheng Rao ◽  
Xiaojing Luo ◽  
Xuan Yan
Keyword(s):  
Set Theory ◽  
Rough Set ◽  
Rough Set Theory ◽  
Attribute Reduction ◽  
Superior Performance ◽  
Data Sets ◽  
Feature Selection Technique ◽  
Elapsed Time ◽  
Multiple Granularities ◽  
Naive Approach

As a feature selection technique in rough set theory, attribute reduction has been extensively explored from various viewpoints especially the aspect of granularity, and multi-granularity attribute reduction has attracted much attention. Nevertheless, it should be pointed out that multiple granularities require to be considered simultaneously to evaluate the significance of candidate attribute in the corresponding process of computing reduct, which may result in high elapsed time of searching reduct. To alleviate such a problem, an acceleration strategy for neighborhood based multi-granularity attribute reduction is proposed in this paper, which aims to improve the computational efficiency of searching reduct. Our proposed approach is actually realized through the positive approximation mechanism, and the processes of searching qualified attributes are executed through evaluating candidate attributes over the gradually reduced sample space rather than all samples. The experimental results over 12 UCI data sets demonstrate that the acceleration strategy can provide superior performance to the naive approach of deriving multi-granularity reduct in the elapsed time of computing reduct without generating different reducts.

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