A Theoretical Formulation of Object-Oriented Rough Set Models

2006 ◽  
Vol 10 (5) ◽  
pp. 612-620 ◽  
Author(s):  
Yasuo Kudo ◽  
◽  
Tetsuya Murai ◽  
Keyword(s):  
Information Systems ◽  
Set Theory ◽  
Rough Set ◽  
Rough Set Theory ◽  
Object Oriented ◽  
Theoretical Formulation ◽  
Structural Hierarchy ◽  
Special Cases ◽  
Abstract Data ◽  
Lower And Upper Approximations

We introduce object-oriented paradigm into rough set theory. First, we provide concepts of class, object, and name, respectively. Class structures represent abstract data forms, and abstract structural hierarchy based on is-a relationship and has-a relationship. Object structures illustrate many kinds of objects and actual dependence among objects by is-a relationship and has-a relationship. Name structures provide concrete design of objects, and connect class structures and object structures consistently. Next, combining class, name and object structures, we propose object-oriented information systems, which include “traditional” information systems as special cases. Moreover, we introduce indiscernibility relations on the set of objects, lower and upper approximations, and object-oriented rough sets in the object-oriented information systems.

scholarly journals Multiset concepts in two-universe approximation spaces

2020 ◽  
Vol 28 (1) ◽  
Author(s):  
O. A. Embaby ◽  
Nadya A. Toumi
Keyword(s):  
Decision Making ◽  
Information Systems ◽  
Set Theory ◽  
Rough Set ◽  
Rough Set Theory ◽  
Approximation Space ◽  
Approximation Spaces ◽  
Lower And Upper Approximations ◽  
Two Universes ◽  
Basic Sets

Abstract Rough set theory over two universes is a generalization of rough set model to find accurate approximations for uncertain concepts in information systems in which uncertainty arises from existence of interrelations between the three basic sets: objects, attributes, and decisions. In this work, multisets are approximated in a crisp two-universe approximation space using binary ordinary relation and multi relation. The concept of two universe approximation is applied for defining lower and upper approximations of multisets. Properties of these approximations are investigated, and the deviations between them and corresponding notions are obtained; some counter examples are given. The suggested notions can help in the modification of the decision-making for events in which objects have repetitions such as patients visiting a doctor more than one time; an example for this case is given.

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.

Rough set theory for the interval-valued fuzzy information systems

2008 ◽  
Vol 178 (8) ◽  
pp. 1968-1985 ◽  
Author(s):  
Zengtai Gong ◽  
Bingzhen Sun ◽  
Degang Chen
Keyword(s):  
Information Systems ◽  
Set Theory ◽  
Rough Set ◽  
Rough Set Theory ◽  
Fuzzy Information ◽  
Interval Valued

On Quasi Discrete Topological Spaces in Information Systems

2012 ◽  
Vol 3 (2) ◽  
pp. 38-52 ◽  
Author(s):  
Tutut Herawan
Keyword(s):  
Information System ◽  
Information Systems ◽  
Topological Space ◽  
Set Theory ◽  
Rough Set ◽  
Rough Set Theory ◽  
Topological Spaces ◽  
Discrete Topology

This paper presents an alternative way for constructing a topological space in an information system. Rough set theory for reasoning about data in information systems is used to construct the topology. Using the concept of an indiscernibility relation in rough set theory, it is shown that the topology constructed is a quasi-discrete topology. Furthermore, the dependency of attributes is applied for defining finer topology and further characterizing the roughness property of a set. Meanwhile, the notions of base and sub-base of the topology are applied to find attributes reduction and degree of rough membership, respectively.

Rough Sets for Discovering Concurrent System Models from Data Tables

2011 ◽  
pp. 239-268 ◽  
Author(s):  
Krzysztof Pancerz ◽  
Zbigniew Suraj
Keyword(s):  
Information Systems ◽  
Set Theory ◽  
Rough Set ◽  
Petri Net ◽  
Rough Set Theory ◽  
Research Trend ◽  
Concurrent System ◽  
System Models ◽  
Data Tables ◽  
New Research

This chapter constitutes the continuation of a new research trend binding rough set theory with concurrency theory. In general, this trend concerns the following problems: discovering concurrent system models from experimental data represented by information systems, dynamic information systems or specialized matrices, a use of rough set methods for extracting knowledge from data, a use of rules for describing system behaviors, and modeling and analyzing of concurrent systems by means of Petri nets on the basis of extracted rules. Some automatized methods of discovering concurrent system models from data tables are presented. Data tables are created on the basis of observations or specifications of process behaviors in the modeled systems. Proposed methods are based on rough set theory and colored Petri net theory.

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 Reduction of Neighborhood-Based Generalized Rough Sets

2011 ◽  
Vol 2011 ◽  
pp. 1-22 ◽  
Author(s):  
Zhaohao Wang ◽  
Lan Shu ◽  
Xiuyong Ding
Keyword(s):  
Information Systems ◽  
Set Theory ◽  
Rough Set ◽  
Rough Sets ◽  
Rough Set Theory ◽  
Open Problems ◽  
The Third ◽  
Generalized Rough Sets

Rough set theory is a powerful tool for dealing with uncertainty, granularity, and incompleteness of knowledge in information systems. This paper discusses five types of existing neighborhood-based generalized rough sets. The concepts of minimal neighborhood description and maximal neighborhood description of an element are defined, and by means of the two concepts, the properties and structures of the third and the fourth types of neighborhood-based rough sets are deeply explored. Furthermore, we systematically study the covering reduction of the third and the fourth types of neighborhood-based rough sets in terms of the two concepts. Finally, two open problems proposed by Yun et al. (2011) are solved.

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