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.

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 Topologies Generated by Two Ideals and the Corresponding j -Approximations Spaces with Applications

2021 ◽  
Vol 2021 ◽  
pp. 1-13
Author(s):  
Mona Hosny
Keyword(s):  
Rough Set ◽  
Rough Set Theory ◽  
Boundary Region ◽  
Original Model ◽  
Topological Spaces ◽  
Powerful Method ◽  
Chemical Application ◽  
Accuracy Measure ◽  
Common Vision ◽  
Do So

Ideal is a fundamental concept in topological spaces and plays an important role in the study of topological problems. This motivated us to use two ideals to generate different topologies to take the advantage of the two ideals at the same time. Two ideals represent two opinions instead of one opinion which is very useful for using the insights of two groups of experts to study the problem and elicit decisions based on their common vision. Topology is a rich source for constructs that is helpful to enrich the original model of approximations spaces. Rough set theory has inbuilt topological concepts. Hence, the main purpose of this paper is to point out that the concept of rough sets has a purely topological aspects nature. To do so, new approximations spaces are introduced and defined based on the topologies generated by two ideals. The results in this paper show that the topological concepts can be a powerful method to study rough set models. The basic properties of these approximations are studied and compared to the previous ones and shown to be more general. The importance of the current paper is not only introducing a new kind of rough set based on bi-ideals, increasing the accuracy measure, and reducing the boundary region of the sets which is the main aim of rough set but also introducing a chemical application to explain the concepts.

THE INFORMATION ENTROPY, ROUGH ENTROPY AND KNOWLEDGE GRANULATION IN ROUGH SET THEORY

2004 ◽  
Vol 12 (01) ◽  
pp. 37-46 ◽  
Author(s):  
JIYE LIANG ◽  
ZHONGZHI SHI
Keyword(s):  
Set Theory ◽  
Rough Set ◽  
Information Entropy ◽  
Granular Computing ◽  
Rough Set Theory ◽  
Computer Applications ◽  
Mathematical Tool

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.

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).

Combination with Machine Learning Algorithms for the Classification in E-Bussiness

2011 ◽  
Vol 230-232 ◽  
pp. 625-628
Author(s):  
Lei Shi ◽  
Xin Ming Ma ◽  
Xiao Hong Hu
Keyword(s):  
Machine Learning ◽  
Support Vector Machines ◽  
Set Theory ◽  
Rough Set ◽  
Rough Set Theory ◽  
Machine Learning Algorithms ◽  
Classification Model ◽  
Support Vector ◽  
Mathematical Tool ◽  
Vector Machines

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.

scholarly journals Analysis of International Competitiveness of Multinational Corporations Based on Rough Sets

Complexity ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-10
Author(s):  
Jing Zhao ◽  
Ning Qi
Keyword(s):  
Information Systems ◽  
Multinational Corporations ◽  
Set Theory ◽  
Rough Set ◽  
Rough Set Theory ◽  
Assessment Methods ◽  
Assessment Process ◽  
Mathematical Tool ◽  
Investment Environment ◽  
Organic System

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.

scholarly journals Decision Making Using Rough Topology and Indiscernibility Matrix for Corona Virus Diagnosis

2020 ◽  
pp. 31-33
Author(s):  
Kanchana. M ◽  
Rekha. S
Keyword(s):  
Decision Making ◽  
Set Theory ◽  
Rough Set ◽  
Rough Set Theory ◽  
Mathematical Tool ◽  
Virus Diagnosis ◽  
Corona Virus ◽  
Uncertain Knowledge

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.

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).

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.

Uncertainty Measurement for Covering Rough Sets

2014 ◽  
Vol 22 (02) ◽  
pp. 217-233 ◽  
Author(s):  
Jianhua Dai ◽  
Debiao Huang ◽  
Huashi Su ◽  
Haowei Tian ◽  
Tian Yang
Keyword(s):  
Set Theory ◽  
Rough Set ◽  
Rough Sets ◽  
Rough Set Theory ◽  
Accuracy Measure ◽  
Uncertainty Measurement ◽  
Covering Rough Set ◽  
Measure Entropy ◽  
Theoretical Results ◽  
Generalized Rough Sets

Covering rough set theory is an important generalization of traditional rough set theory. So far, the studies on covering generalized rough sets mainly focus on constructing different types of approximation operations. However, little attention has been paid to uncertainty measurement in covering cases. In this paper, a new kind of partial order is proposed for coverings which is used to evaluate the uncertainty measures. Consequently, we study uncertain measures like roughness measure, accuracy measure, entropy and granularity for covering rough set models which are defined by neighborhoods and friends. Some theoretical results are obtained and investigated.

Sign in / Sign up

Export Citation Format

Share Document