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.

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.

Comparative Analysis of Hybrid Soft Set Methods

2014 ◽  
pp. 360-383
Author(s):  
Debadutta Mohanty
Keyword(s):  
Information System ◽  
Comparative Analysis ◽  
Set Theory ◽  
Rough Set ◽  
Rough Set Theory ◽  
Soft Set ◽  
Mathematical Tool ◽  
Soft Rough Set ◽  
Definition Of ◽  
The Relationship

The whole mathematical scenario has changed with the advent of the Rough Set Theory, a powerful tool to deal with uncertainty and incompleteness of knowledge in information system. With the advancement of research, the Soft Set Theory has emerged as an advanced mathematical tool to deal with data associated with uncertainty. The present chapter endeavors to forge a connection between soft set and rough set and maps a new model rough soft set to address the challenges of vagueness and impreciseness. Although the research contribution of M. Irfan Ali, Dan Meng, et al. and Feng Feng et al. had given distinct definition of rough soft set and soft rough set, the analysis explaining the genesis of these sets is not appropriate. This chapter is a new attempt to construct the relationship between a rough set, soft set, and fuzzy set to form a hybrid soft set giving a concrete comprehensive definition of rough soft set in border perspective.

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.

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.

The Discretization Algorithm Based on Rough Set and its Application

2013 ◽  
Vol 416-417 ◽  
pp. 1399-1403 ◽  
Author(s):  
Zhi Cai Shi ◽  
Yong Xiang Xia ◽  
Chao Gang Yu ◽  
Jin Zu Zhou
Keyword(s):  
Intrusion Detection ◽  
Set Theory ◽  
Rough Set ◽  
Information Entropy ◽  
Rough Set Theory ◽  
Information Loss ◽  
Intrusion Detection Systems ◽  
Detection Systems ◽  
Discretization Algorithm ◽  
Response Performance

The discretization is one of the most important steps for the application of Rough set theory. In this paper, we analyzed the shortcomings of the current relative works. Then we proposed a novel discretization algorithm based on information loss and gave its mathematical description. This algorithm used information loss as the measure so as to reduce the loss of the information entropy during discretizating. The algorithm was applied to different samples with the same attributes from KDDcup99 and intrusion detection systems. The experimental results show that this algorithm is sensitive to the samples only for parts of all attributes. But it dose not compromise the effect of intrusion detection and it improves the response performance of intrusion detection remarkably.

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.

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