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.

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.

Rough Sets

2011 ◽  
pp. 129-151
Author(s):  
Theresa Beaubouef ◽  
Frederick E Petry
Keyword(s):  
Set Theory ◽  
Rough Set ◽  
Fuzzy Set ◽  
Rough Sets ◽  
Rough Set Theory ◽  
Object Oriented ◽  
Uncertainty Management ◽  
Database Model ◽  
Management Of Uncertainty ◽  
Object Oriented Database

This chapter discusses ways in which rough set theory can enhance databases by allowing for the management of uncertainty. Rough sets can be integrated into an underlying database model, relational or object oriented, and also used in design and querying of databases. Because rough sets are a versatile theory, they can also be combined with other theories. The authors discuss the rough relational database model, the rough object oriented database model, and fuzzy set and intuitionistic set extensions to each of these models. Comparisons and benefits of the various approaches are discussed, illustrating the usefulness and versatility of rough sets for uncertainty management in databases.

Rough Sets

2009 ◽  
pp. 1127-1150
Author(s):  
Theresa Beaubouef ◽  
Frederick E. Petry
Keyword(s):  
Set Theory ◽  
Rough Set ◽  
Rough Sets ◽  
Relational Databases ◽  
Rough Set Theory ◽  
Object Oriented ◽  
Uncertainty Management ◽  
Database Model ◽  
Management Of Uncertainty ◽  
Object Oriented Database

This chapter discusses ways in which rough-set theory can enhance databases by allowing for the management of uncertainty. Rough sets can be integrated into an underlying database model, relational or object oriented, and also used in the design and uerying of databases, because roughsets are a versatile theory, theories. The authors discuss the rough relational databases model, the rough object-oriented database model, and fuzzy set and intuitionistic set extensions to each of these models. Comparisons and benefits of the various approaches are discussed, illustrating the usefulness and versatility of rough sets for uncertainty management in databases.

scholarly journals Rough Set Approximation as Formal Concept

2006 ◽  
Vol 10 (5) ◽  
pp. 606-611 ◽  
Author(s):  
Nozomi Ytow ◽  
◽  
David R. Morse ◽  
David McL. Roberts ◽  
◽  
...  
Keyword(s):  
Set Theory ◽  
Rough Set ◽  
Rough Sets ◽  
Formal Concept Analysis ◽  
Rough Set Theory ◽  
The Other ◽  
Formal Concept ◽  
Object Based ◽  
Formal Concepts ◽  
Set Approximation

Formal Concept Analysis (FCA) defines a formal concept as a pair of sets: objects and attributes, called extent and intent respectively. A rough set, on the other hand, approximates a concept using sets of objects only (in terms of FCA). We show that 1) a formal concept can be composed using a set of objects and its complement, 2) such object-based formal concepts are isomorphic to formal concepts based on objects and attributes, 3) upper and lower approximations of rough sets give generalization of formal concept, and 4) the pair of positive and negative sets (sensu rough set theory) are isomorphic to complemental formal concepts when the equivalence of the rough set gives positive and negative sets unique to each of the formal concepts. Implications of this are discussed.

Approximations in Rough Sets vs Granular Computing for Coverings

2010 ◽  
Vol 4 (2) ◽  
pp. 63-76 ◽  
Author(s):  
Guilong Liu ◽  
William Zhu
Keyword(s):  
Binary Relation ◽  
Set Theory ◽  
Rough Set ◽  
Rough Sets ◽  
Granular Computing ◽  
Rough Set Theory ◽  
Knowledge Discovery In Databases ◽  
Equivalence Relations ◽  
Binary Relations ◽  
Covering Rough Set

Rough set theory is an important technique in knowledge discovery in databases. Classical rough set theory proposed by Pawlak is based on equivalence relations, but many interesting and meaningful extensions have been made based on binary relations and coverings, respectively. This paper makes a comparison between covering rough sets and rough sets based on binary relations. This paper also focuses on the authors’ study of the condition under which the covering rough set can be generated by a binary relation and the binary relation based rough set can be generated by a covering.

scholarly journals A Variable Precision Covering-Based Rough Set Model Based on Functions

2014 ◽  
Vol 2014 ◽  
pp. 1-5 ◽  
Author(s):  
Yanqing Zhu ◽  
William Zhu
Keyword(s):  
Set Theory ◽  
Rough Set ◽  
Rough Sets ◽  
Granular Computing ◽  
Rough Set Theory ◽  
Misclassification Rate ◽  
Extended Model ◽  
Variable Precision ◽  
Rate Functions ◽  
Variable Precision Rough Set

Classical rough set theory is a technique of granular computing for handling the uncertainty, vagueness, and granularity in information systems. Covering-based rough sets are proposed to generalize this theory for dealing with covering data. By introducing a concept of misclassification rate functions, an extended variable precision covering-based rough set model is proposed in this paper. In addition, we define thef-lower andf-upper approximations in terms of neighborhoods in the extended model and study their properties. Particularly, two coverings with the same reductions are proved to generate the samef-lower andf-upper approximations. Finally, we discuss the relationships between the new model and some other variable precision rough set models.

Rough Sets and Granular Computing in Geospatial Information

2010 ◽  
pp. 154-159
Author(s):  
Iftikhar U. Sikder
Keyword(s):  
Knowledge Discovery ◽  
Set Theory ◽  
Rough Set ◽  
Rough Sets ◽  
Granular Computing ◽  
Spatial Reasoning ◽  
Rough Set Theory ◽  
Geospatial Information

The representation of geographic entities is characterized by inherent granularity due to scale and resolution specific observations. This article discusses the various aspects of rough set-based approximation modeling of spatial and conceptual granularity. It outlines the context and applications of rough set theory in representing objects with intermediate boundaries, spatial reasoning and knowledge discovery.

Analysing diabetes using rough sets

2020 ◽  
pp. 533-538
Author(s):  
S. Arjun Raj ◽  
M. Vigneshwaran
Keyword(s):  
Set Theory ◽  
Rough Set ◽  
Rough Sets ◽  
Rough Set Theory ◽  
International Diabetes Federation ◽  
Published Data ◽  
Lower And Upper Approximations

In this article we use the rough set theory to generate the set of decision concepts in order to solve a medical problem.Based on officially published data by International Diabetes Federation (IDF), rough sets have been used to diagnose Diabetes.The lower and upper approximations of decision concepts and their boundary regions have been formulated here.

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.

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