scholarly journals Rough sets theory via new topological notions based on ideals and applications

2021 ◽  
Vol 7 (1) ◽  
pp. 869-902
Author(s):  
Mona Hosny ◽  
◽  
Keyword(s):  
Rough Set Theory ◽  
Boundary Region ◽  
Membership Functions ◽  
Rough Sets Theory ◽  
And Topology ◽  
Accuracy Measure ◽  
Essential Properties ◽  
Lower And Upper Approximations ◽  
Sets Theory ◽  
Better Than

<abstract><p>There is a close analogy and similarity between topology and rough set theory. As, the leading idea of this theory is depended on two approximations, namely lower and upper approximations, which correspond to the interior and closure operators in topology, respectively. So, the joined study of this theory and topology becomes fundamental. This theory mainly propose to enlarge the lower approximations by adding new elements to it, which is an equivalent goal for canceling elements from the upper approximations. For this intention, one of the primary motivation of this paper is the desire of improving the accuracy measure and reducing the boundary region. This aim can be achieved easily by utilizing ideal in the construction of the approximations as it plays an important role in removing the vagueness of concept. The emergence of ideal in this theory leads to increase the lower approximations and decrease the upper approximations. Consequently, it minimizes the boundary and makes the accuracy higher than the previous. Therefore, this work expresses the set of approximations by using new topological notions relies on ideals namely $ \mathcal{I} $-$ {\delta_{\beta}}_{J} $-open sets and $ \mathcal{I} $-$ {\bigwedge_{\beta}}_{J} $-sets. Moreover, these notions are also utilized to extend the definitions of the rough membership relations and functions. The essential properties of the suggested approximations, relations and functions are studied. Comparisons between the current and previous studies are presented and turned out to be more precise and general. The brilliant idea of these results is increased in importance by applying it in the chemical field as it is shown in the end of this paper. Additionally, a practical example induced from an information system is introduced to elucidate that the current rough membership functions is better than the former ones in the other studies.</p></abstract>

Feature Extraction from Engine's Data Based on Rough Sets Theory

2011 ◽  
Vol 120 ◽  
pp. 410-413
Author(s):  
Feng Wang ◽  
Li Xin Jia
Keyword(s):  
Feature Extraction ◽  
Set Theory ◽  
Rough Set ◽  
Rough Sets ◽  
Rough Set Theory ◽  
Technical Condition ◽  
Decision Table ◽  
Discernibility Matrix ◽  
Rough Sets Theory ◽  
Sets Theory

The speed signal of engine contains abundant information. This paper introduces rough set theory for feature extraction from engine's speed signals, and proposes a method of mining useful information from a mass of data. The result shows that the discernibility matrix algorithm can be used to reduce attributes in decision table and eliminate unnecessary attributes, efficiently extracted the features for evaluating the technical condition of engine.

Application of Rough Sets Theory in Graduate Enrollment

2014 ◽  
Vol 687-691 ◽  
pp. 1604-1607
Author(s):  
Juan Huang
Keyword(s):  
Set Theory ◽  
Rough Set ◽  
Rough Sets ◽  
Postgraduate Training ◽  
Rough Set Theory ◽  
Postgraduate Education ◽  
Rough Sets Theory ◽  
Graduate Enrollment ◽  
Enrollment Data ◽  
Sets Theory

Enrollment is the first step of the work of postgraduate education, and also a very crucial step. Therefore, in order to successfully carry out the postgraduate training work, be sure to do the enrollment work. In this paper, rough set theory is applied to the enrollment data of one college of a university. Then follow the general steps of data mining to research and analyze the enrollment data. Finally, draw some useful conclusions. These conclusions have a certain significance for graduate enrollment.

Product Function: Component Modeling Using Rough Sets

2009 ◽  
Author(s):  
Toshiharu Miwa ◽  
Hideki Aoyama
Keyword(s):  
Product Development ◽  
Rough Sets ◽  
Early Stage ◽  
Modeling Method ◽  
Rough Sets Theory ◽  
Development Cycle ◽  
Product Function ◽  
Lower And Upper Approximations ◽  
Sets Theory ◽  
Manufacturing Parameters

The acceleration of the product development cycle continues to be a significant challenge for manufacturing firms around the world. The misunderstanding of important relationships between product functions and components leads the delay of product development. The present paper describes an identification method of the relationships between product functions and components at the early stage of product development. The proposed product function-component modeling method using rough sets theory extracts the characteristic relationships between product functions and components from a small amount of the qualitative and linguistically-expressed knowledge data. The advantage of using the rough sets is that the combination of necessary and possible sets (lower and upper approximations) represents the vague knowledge. The present paper describes an example of a conventional cutting process with 6 manufacturing parameters that this method contributes to the identification of cutting mechanism from a small amount of sampling data (7% of whole event) compared to the conventional statistical modeling method.

Accident Causation Factor Analysis of Traffic Accidents using Rough Relational Analysis

2016 ◽  
Vol 3 (3) ◽  
pp. 60-71 ◽  
Author(s):  
Caner Erden ◽  
Numan Çelebi
Keyword(s):  
Big Data ◽  
Rough Sets ◽  
Traffic Accidents ◽  
Rough Set Theory ◽  
Decision Rules ◽  
Decision Makers ◽  
Rough Sets Theory ◽  
Relational Analysis ◽  
Accident Causation ◽  
Sets Theory

The aim of this study is to show that the decision rules generated from Rough Sets Theory can be used for a new relational analysis. Rough Sets Theory generally works with small datasets more than big data. If we can deal with the decision rules and its complexities, it is still possible to analyze big data with Rough Set Theory. That is why in this study the authors offer a statistical method to overdue problems which belongs to big data. According statistical methods, a lots of decision rules generated from rough sets theory become useful information. Using a real case data on the traffic accident which were taken place in USA in 2013, this paper finds the relationships between accident causation factors which may be referred to decision makers in the field of traffic.

Generalized Rough Sets

2016 ◽  
pp. 223-246
Author(s):  
Mona Hosny ◽  
Ali Kandil ◽  
Osama A. El-Tantawy ◽  
Sobhy A. El-Sheikh
Keyword(s):  
Rough Set ◽  
Rough Set Theory ◽  
Order Relation ◽  
Boundary Region ◽  
Current Approach ◽  
Partially Order ◽  
Lower Approximation ◽  
Upper Approximation ◽  
Relation Ideal ◽  
Lower And Upper Approximations

This chapter concerns construction of a new rough set structure for an ideal ordered topological spaces and ordered topological filters. The approximation space approached depend on general binary relation, partially order relation, ideal and filter concepts. Properties of lower and upper approximation are extended to an ideal order topological approximation spaces. The main aim of the rough set theory is reducing the bouwndary region by increasing the lower approximation and decreasing the upper approximation. So, in this chapter different methods are proposed to reduce the boundary region. Comparisons between the current approximations and the previous approximations (El-Shafei et al.,2013) are introduced. It's therefore shown that the current approximations are more generally and reduce the boundary region by increasing the lower approximation and decreasing the upper approximation. The lower and upper approximations satisfy some properties in analogue of Pawlak's spaces (Pawlak, 1982). Moreover, we give several examples for comparison between the current approach and (El-Shafei et al., 2013).

A NUMERICAL APPROACH TO UNCERTAINTY IN ROUGH LOGIC

2013 ◽  
Vol 21 (03) ◽  
pp. 391-413
Author(s):  
YAN-HONG SHE ◽  
XIAO-LI HE
Keyword(s):  
Rough Set ◽  
Rough Set Theory ◽  
Numerical Approach ◽  
Boundary Region ◽  
Approximate Reasoning ◽  
Mathematical Tool ◽  
Inclusion Degree ◽  
Accuracy Measure ◽  
Reasoning Mechanism ◽  
Accuracy Degree

Rough set theory, initiated by Pawlak, is a mathematical tool in dealing with inexact and incomplete information. Numerical characterizations of rough sets such as accuracy measure, roughness measure, etc, which aim to quantify the imprecision of a rough set caused by its boundary region, have been extensively studied in the existing literatures. However, very few of them are explored from the viewpoint of rough logic, which, however, helps to establish a kind of approximate reasoning mechanism. For this purpose, we introduce a kind of numerical approach to the study of rough logic in this paper. More precisely, we propose the notions of accuracy degree and roughness degree for each formula in rough logic with the intension of measuring the extent to which any formula is accurate and rough, respectively. Then, to measure the degree to which any two formulae are roughly included in each other and roughly similar, respectively, the concepts of rough inclusion degree and rough similarity degree are also proposed and their properties are investigated in detail. Lastly, by employing the proposed notions, we develop two types of approximate reasoning patterns in the framework of rough logic.

Application of MMAS and Rough Sets in Compound-Fault Diagnosis of Bearing

2012 ◽  
Vol 433-440 ◽  
pp. 6319-6324 ◽  
Author(s):  
Hai Ying Kang ◽  
Ren Fa Shen ◽  
Yan Jie Qi ◽  
Wen Yan ◽  
Hai Qi Zheng
Keyword(s):  
Fault Diagnosis ◽  
Rough Set ◽  
Rough Sets ◽  
Rough Set Theory ◽  
Decision Rules ◽  
Ant System ◽  
Fisher Criterion ◽  
Rough Sets Theory ◽  
Np Hard Problem ◽  
Sets Theory

The diagnosis of compound-fault is always a difficult point, and there is not an effective method in equipment diagnosis field. Rough set theory is a relatively new soft computing tool to deal with vagueness and uncertainty. Condition attribute reduce algorithm is the key point of rough set research. However, it has been proved that finding the best reduction is the NP-hard problem. For the purpose of getting the reduction of systems effectively, an improved algorithm is put forward. The worst Fisher criterion was adopted as heuristic information to improve the searching efficiency and Max-Min Ant System was selected. Simplify the fault diagnosis decision table, then clear and concise decision rules can be obtained by rough sets theory. This method raises the accuracy and efficiency of fault diagnosis of bearing greatly.

scholarly journals Modified Uncertainty Measure of Rough Fuzzy Sets from the Perspective of Fuzzy Distance

2018 ◽  
Vol 2018 ◽  
pp. 1-11 ◽  
Author(s):  
Jie Yang ◽  
Taihua Xu ◽  
Fan Zhao
Keyword(s):  
Fuzzy Sets ◽  
Rough Sets ◽  
Boundary Region ◽  
Uncertainty Measure ◽  
Approximation Spaces ◽  
Rough Sets Theory ◽  
Fuzzy Distance ◽  
Rough Approximation ◽  
Sets Theory

As an extension of Pawlak’s rough sets, rough fuzzy sets are proposed to deal with fuzzy target concept. As we know, the uncertainty of Pawlak’s rough sets is rooted in the objects contained in the boundary region, while the uncertainty of rough fuzzy sets comes from three regions (positive region, boundary region, and negative region). In addition, in the view of traditional uncertainty measures, the two rough approximation spaces with the same uncertainty are not necessarily equivalent, and they cannot be distinguished. In this paper, firstly, a fuzziness-based uncertainty measure is proposed. Meanwhile, the essence of the uncertainty for rough fuzzy sets and its three regions in a hierarchical granular structure is revealed. Then, from the perspective of fuzzy distance, we introduce a modified uncertainty measure based on the fuzziness-based uncertainty measure and present that our method not only is strictly monotonic with finer approximation spaces, but also can distinguish the two rough approximation spaces with the same uncertainty. Finally, a case study is introduced to demonstrate that the modified uncertainty measure is more suitable for evaluating the significance of attributes. These works are useful for further study on rough sets theory and promote the development of uncertain artificial intelligence.

Research on Intelligent Fault Diagnosis Method Based on Rough Set Theory and Fuzzy Petri Nets

2010 ◽  
Vol 26-28 ◽  
pp. 77-82 ◽  
Author(s):  
Lan Yun Li ◽  
Zhuan Zhao Yang ◽  
Zhi He
Keyword(s):  
Fault Diagnosis ◽  
Petri Nets ◽  
Rough Set Theory ◽  
Rough Sets Theory ◽  
Fault Features ◽  
Fuzzy Petri Nets ◽  
Diagnosis Method ◽  
Sets Theory ◽  
Complementary Strategy ◽  
Fault Information

Rough sets theory (RST) and Fuzzy Petri nets (FPN) have been widely used in fault diagnosis. However, RST has the weakness of over-rigidity decision, and FPN has the dimensional disaster problem. In order to solve these shortcomings, according to complementary strategy, a new fault diagnosis method based on integration of RST and FPN was presented. Firstly, RST was applied to remove redundant fault features and simply fault information, so that the minimal diagnostic rules can be obtained and the fault was roughly diagnosed. Secondly, the optimal FPN structure was built and the fault diagnosis was finally realized through matrix operation of FPN. Finally, a diesel engine fault diagnosis example was analyzed, and the results show that the proposed method not only holds the ability of RST for analyzing and reducing data, but also has the advantage of FPN for parallel reasoning, so it has strong engineering practicability and validity.

New Approaches of Rough Sets via Ideals

2016 ◽  
pp. 247-264 ◽  
Author(s):  
Ali Kandil ◽  
M. M. Yakout ◽  
A. Zakaria
Keyword(s):  
Rough Sets ◽  
Present Method ◽  
Boundary Region ◽  
Topological Spaces ◽  
Membership Functions ◽  
New Approaches ◽  
Approximation Operators ◽  
Definition Of ◽  
Lower And Upper Approximations

An ideal I on a nonempty set X is a subfamily of P(X) which is closed under finite unions and subsets. In this chapter, a new definition of approximation operators and rough membership functions via ideal has been introduced. The concepts of lower and upper approximations via ideals have been mentioned. These new definitions are comparing with Pawlak's, Yao's and Allam's definitions. It's therefore shown that the current definitions are more generally. Also, it's shown that the present method decreases the boundary region. In addition to these points, the topology generated via present method finer than Allam's one which is a generalization of that obtained by Yao's method. Finally, T1 topological spaces are obtained by relations and ideals which are not discrete.

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