Rough Set Theory, Granular Computing on Partition

2009 ◽  
pp. 2453-2453
Keyword(s):  
Set Theory ◽  
Rough Set ◽  
Granular Computing ◽  
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.

Multi-Granular Computing through Rough Sets

2014 ◽  
pp. 1-34 ◽  
Author(s):  
B. K. Tripathy
Keyword(s):  
Set Theory ◽  
Rough Set ◽  
Equivalence Relation ◽  
Rough Sets ◽  
Intelligent Systems ◽  
Granular Computing ◽  
Rough Set Theory ◽  
Point Of View ◽  
Information Granules ◽  
Computing Platform

Granular Computing has emerged as a framework in which information granules are represented and manipulated by intelligent systems. Granular Computing forms a unified conceptual and computing platform. Rough set theory put forth by Pawlak is based upon single equivalence relation taken at a time. Therefore, from a granular computing point of view, it is single granular computing. In 2006, Qiang et al. introduced a multi-granular computing using rough set, which was called optimistic multigranular rough sets after the introduction of another type of multigranular computing using rough sets called pessimistic multigranular rough sets being introduced by them in 2010. Since then, several properties of multigranulations have been studied. In addition, these basic notions on multigranular rough sets have been introduced. Some of these, called the Neighborhood-Based Multigranular Rough Sets (NMGRS) and the Covering-Based Multigranular Rough Sets (CBMGRS), have been added recently. In this chapter, the authors discuss all these topics on multigranular computing and suggest some problems for further study.

Some Remarks on the Concept of Approximations from the View of Knowledge Engineering

2010 ◽  
Vol 4 (2) ◽  
pp. 1-11 ◽  
Author(s):  
Tsau Young Lin ◽  
Rushin Barot ◽  
Shusaku Tsumoto
Keyword(s):  
Set Theory ◽  
Rough Set ◽  
Granular Computing ◽  
Rough Set Theory ◽  
Knowledge Engineering ◽  
Topological Spaces

The concepts of approximations in granular computing (GrC) vs. rough set theory (RS) are examined. Examples are constructed to contrast their differences in the Global GrC Model (2nd GrC Model), which, in pre-GrC term, is called partial coverings. Mathematically speaking, RS-approximations are “sub-base” based, while GrC-approximations are “base” based, where “sub-base” and “base” are two concepts in topological spaces. From the view of knowledge engineering, its meaning in RS-approximations is rather obscure, while in GrC, it is the concept of knowledge approximations.

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.

A survey on granular computing and its uncertainty measure from the perspective of rough set theory

2019 ◽  
Vol 6 (1) ◽  
pp. 3-17 ◽  
Author(s):  
Yunlong Cheng ◽  
Fan Zhao ◽  
Qinghua Zhang ◽  
Guoyin Wang
Keyword(s):  
Set Theory ◽  
Rough Set ◽  
Granular Computing ◽  
Rough Set Theory ◽  
Uncertainty Measure

A New Weighting Approach Based on Rough Set Theory and Granular Computing for Road Safety Indicator Analysis

2015 ◽  
Vol 32 (4) ◽  
pp. 517-534 ◽  
Author(s):  
Tianrui Li ◽  
Da Ruan ◽  
Yongjun Shen ◽  
Elke Hermans ◽  
Geert Wets
Keyword(s):  
Set Theory ◽  
Rough Set ◽  
Road Safety ◽  
Granular Computing ◽  
Rough Set Theory ◽  
Safety Indicator ◽  
Indicator Analysis

scholarly journals Special Issue on Rough Sets and Granular Computing

2006 ◽  
Vol 10 (5) ◽  
pp. 605-605
Author(s):  
Hiroshi Sakai ◽  
◽  
Masahiro Inuiguchi ◽  
Keyword(s):  
Set Theory ◽  
Rough Set ◽  
Rough Sets ◽  
Web Site ◽  
Granular Computing ◽  
Rough Set Theory ◽  
Object Oriented ◽  
Relational Model ◽  
Formal Concept ◽  
Special Issue

Rough sets and granular computing, known as new methodologies for computing technology, are now attracting great interest of researchers. This special issue presents 12 articles, and most of them were presented at the second Japanese workshop on Rough Sets held at Kyushu Institute of Technology in Tobata, Kitakyushu, Japan, on August 17-18, 2005. The first article studies the relation between rough set theory and formal concept analysis. These two frameworks are analyzed and connected by using the method of morphism. The second article introduces object-oriented paradigm into rough set theory, and object-oriented rough set models are proposed. Theoretical aspects of these new models are also examined. The third article considers relations between generalized rough sets, topologies and modal logics, and some topological properties of rough sets induced by equivalence relations are presented. The fourth article focuses on a family of polymodal systems, and theoretical aspects of these systems, like the completeness, are investigated. By means of combining polymodal logic concept and rough set theory, a new framework named multi-rough sets is established. The fifth article focuses on the information incompleteness in fuzzy relational models, and a generalized possibility-based fuzzy relational model is proposed. The sixth article presents a developed software EVALPSN (Extended Vector Annotated Logic Program with Strong Negation) and the application of this software to pipeline valve control. The seventh article presents the properties of attribute reduction in variable precision rough set models. Ten kinds of meaningful reducts are newly proposed, and hierarchical relations in these reducts are examined. The eighth article proposes attribute-value reduction for Kansei analysis using information granulation, and illustrative results for some databases in UCI Machine Learning Repository are presented. The ninth article investigates cluster analysis for data with errors tolerance. Two new clustering algorithms, which are based on the entropy regularized fuzzy c-means, are proposed. The tenth article applies binary decision trees to handwritten Japanese Kanji recognition. The consideration to the experimental results of real Kanji data is also presented. The eleventh article applies a rough sets based method to analysing the character of the screen-design in every web site. The obtained character gives us good knowledge to generate a new web site. The last article focuses on rule generation in non-deterministic information systems. For generating minimal certain rules, discernibility functions are introduced. A new algorithm is also proposed for handling every discernibility function. Finally, we would like to acknowledge all the authors for their efforts and contributions. We are very grateful to reviewers for their thorough and on-time reviews, too. We are also grateful to Prof. Toshio Fukuda and Prof. Kaoru Hirota, Editors-in-Chief of JACIII, for inviting us to serve as Guest Editors of this Journal, and to Mr. Uchino and Mr. Ohmori of Fuji Technology Press for their kind assistance in publication of this special issue.

Sign in / Sign up

Export Citation Format

Share Document