scholarly journals Sub-exact sequence of rough groups

2021 ◽  
Vol 12 (2) ◽  
pp. 267-272
Author(s):  
Nevi Setyaningsih ◽  
Fitriani Fitriani ◽  
Ahmad Faisol

Rough Set Theory (RST) is an essential mathematical tool to deal with imprecise, inconsistent, incomplete information and knowledge Rough Some algebra structures, such as groups, rings, and modules, have been presented on rough set theory. The sub-exact sequence is a generalization of the exact sequence. In this paper, we introduce the notion of a sub-exact sequence of groups. Furthermore, we give some properties of the rough group and rough sub-exact sequence of groups. 

Author(s):  
JIYE LIANG ◽  
ZHONGZHI SHI

Rough set theory is a relatively new mathematical tool for use in computer applications in circumstances which are characterized by vagueness and uncertainty. In this paper, we introduce the concepts of information entropy, rough entropy and knowledge granulation in rough set theory, and establish the relationships among those concepts. These results will be very helpful for understanding the essence of concept approximation and establishing granular computing in rough set theory.


2011 ◽  
Vol 230-232 ◽  
pp. 625-628
Author(s):  
Lei Shi ◽  
Xin Ming Ma ◽  
Xiao Hong Hu

E-bussiness has grown rapidly in the last decade and massive amount of data on customer purchases, browsing pattern and preferences has been generated. Classification of electronic data plays a pivotal role to mine the valuable information and thus has become one of the most important applications of E-bussiness. Support Vector Machines are popular and powerful machine learning techniques, and they offer state-of-the-art performance. Rough set theory is a formal mathematical tool to deal with incomplete or imprecise information and one of its important applications is feature selection. In this paper, rough set theory and support vector machines are combined to construct a classification model to classify the data of E-bussiness effectively.


Author(s):  
JIYE LIANG ◽  
ZONGBEN XU

Rough set theory is emerging as a powerful tool for reasoning about data, knowledge reduction is one of the important topics in the research on rough set theory. It has been proven that finding the minimal reduct of an information system is a NP-hard problem, so is finding the minimal reduct of an incomplete information system. Main reason of causing NP-hard is combination problem of attributes. In this paper, knowledge reduction is defined from the view of information, a heuristic algorithm based on rough entropy for knowledge reduction is proposed in incomplete information systems, the time complexity of this algorithm is O(|A|2|U|). An illustrative example is provided that shows the application potential of the algorithm.


Complexity ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-10
Author(s):  
Jing Zhao ◽  
Ning Qi

Modern business judgment is mostly faced with complex, unclear nature, and not fully confirmed research objects and needs a lot of relevant data investigation, inherent contradiction retrieval, and the discovery and extraction of potential laws. Formulation of rules and evaluation of system uncertainty: Appropriate decisions can be made based on this. Rough set theory is a new mathematical tool to deal with uncertain knowledge. Therefore, the theory of rough set is helpful for decision-makers to solve the decision problems of complex systems. The simplification of knowledge of information systems and incomplete information systems and the theoretical and methodological study of rule acquisition are the central issues of rough set theory and applied research. A variety of simplified theories and methods have been proposed from a variety of viewpoints. However, there are still many theoretical problems that need to be investigated and solved in these aspects. In addition, the investment environment is a complex organic system that includes economic environment, social environment, resource environment, infrastructure, and other factors. There are a variety of data to measure these factors, which are mutually restrictive and interdependent. At present, domestic and foreign scholars have basically formed a series of assessment methods and models of investment environment assessment, but most of these assessment methods are affected by the differences in the degree of subjective factors of evaluators and the establishment of index weights in the assessment process. In most cases, more reliance is placed on subjective, artificial assignments and scoring loops. Therefore, it is an appropriate and reasonable method to evaluate the investment environment through data to evaluate all the factors affecting the investment environment and reach a comprehensive evaluation conclusion, which can effectively avoid human subjective factors to a certain extent.


Author(s):  
Kanchana. M ◽  
Rekha. S

Rough set theory is a new mathematical tool for dealing with vague, imprecise, inconsistent and uncertain knowledge. In recent years the research and applications on rough set theory have attracted more. In this paper, we have introduced and analyze the Rough set theory and also decide the factors for corona virus diagnosis by using Indiscernibility matrix.


2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
Feng Hu ◽  
Hang Li

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.


2017 ◽  
Vol 33 (2) ◽  
pp. 131-142
Author(s):  
Quang Minh Hoang ◽  
Vu Duc Thi ◽  
Nguyen Ngoc San

Rough set theory is useful mathematical tool developed to deal with vagueness and uncertainty. As an important concept of rough set theory, an attribute reduct is a subset of attributes that are jointly sufficient and individually necessary for preserving a particular property of the given information table. Rough set theory is also the most popular for generating decision rules from decision table. In this paper, we propose an algorithm finding object reduct of consistent decsion table. On the other hand, we also show an algorithm to find some attribute reducts and the correctness of our algorithms is proof-theoretically. These our algorithms have polynomial time complexity. Our finding object reduct helps other algorithms of finding attribute reducts become more effectively, especially as working with huge consistent decision table.


Author(s):  
JUNHONG WANG ◽  
JIYE LIANG ◽  
YUHUA QIAN ◽  
CHUANGYIN DANG

Rough set theory is a relatively new mathematical tool for computer applications in circumstances characterized by vagueness and uncertainty. In this paper, we address uncertainty of rough sets for incomplete information systems. An axiom definition of knowledge granulation for incomplete information systems is obtained, under which a measure of uncertainty of a rough set is proposed. This measure has some nice properties such as equivalence, maximum and minimum. Furthermore, we prove that the uncertainty measure is effective and suitable for measuring roughness and accuracy of rough sets for incomplete information systems.


2020 ◽  
Vol 191 ◽  
pp. 105251 ◽  
Author(s):  
Junfang Luo ◽  
Hamido Fujita ◽  
Yiyu Yao ◽  
Keyun Qin

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Hua Li ◽  
Deyu Li ◽  
Yanhui Zhai ◽  
Suge Wang ◽  
Jing Zhang

Owing to the high dimensionality of multilabel data, feature selection in multilabel learning will be necessary in order to reduce the redundant features and improve the performance of multilabel classification. Rough set theory, as a valid mathematical tool for data analysis, has been widely applied to feature selection (also called attribute reduction). In this study, we propose a variable precision attribute reduct for multilabel data based on rough set theory, calledδ-confidence reduct, which can correctly capture the uncertainty implied among labels. Furthermore, judgement theory and discernibility matrix associated withδ-confidence reduct are also introduced, from which we can obtain the approach to knowledge reduction in multilabel decision tables.


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