A MATHEMATICAL EXTENSION OF ROUGH SET-BASED ISSUES TOWARD UNCERTAIN INFORMATION ANALYSIS

Rough set theory was originally proposed for analyzing data gathered in data tables, often referred to as information systems. The lower and upper approximations introduced within this theory are known as the very useful concepts. The theory as a whole now becomes a recognized foundation for granular computing. This paper investigates the rough set-based issues for analyzing table data with uncertainty. In reality, tables with non-deterministic information are focused on instead of tables with deterministic information, and several mathematical properties are examined. Especially, decision rule generation from tables with non-deterministic information is highlighted. This investigation is also applied to tables with uncertain numerical data. As a result, a new mathematical framework for analyzing tables with uncertain information is formalized.

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Analysing diabetes using rough sets

Advances in Mathematics: Scientific Journal ◽

10.37418/amsj.9.2.1 ◽

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.

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Certain models of granular computing based on rough fuzzy approximations

Journal of Intelligent & Fuzzy Systems ◽

10.3233/jifs-191165 ◽

2020 ◽

Vol 39 (3) ◽

pp. 2797-2816

Author(s):

Muhammad Akram ◽

Anam Luqman ◽

Ahmad N. Al-Kenani

Keyword(s):

Social Networks ◽

Social Network ◽

Problem Solving ◽

Granular Computing ◽

Research Study ◽

Network Models ◽

Mathematical Framework ◽

Human Reasoning ◽

Accuracy Measures ◽

Lower And Upper Approximations

An extraction of granular structures using graphs is a powerful mathematical framework in human reasoning and problem solving. The visual representation of a graph and the merits of multilevel or multiview of granular structures suggest the more effective and advantageous techniques of problem solving. In this research study, we apply the combinative theories of rough fuzzy sets and rough fuzzy digraphs to extract granular structures. We discuss the accuracy measures of rough fuzzy approximations and measure the distance between lower and upper approximations. Moreover, we consider the adjacency matrix of a rough fuzzy digraph as an information table and determine certain indiscernible relations. We also discuss some general geometric properties of these indiscernible relations. Further, we discuss the granulation of certain social network models using rough fuzzy digraphs. Finally, we develop and implement some algorithms of our proposed models to granulate these social networks.

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

International Journal of Uncertainty Fuzziness and Knowledge-Based Systems ◽

10.1142/s0218488504002631 ◽

2004 ◽

Vol 12 (01) ◽

pp. 37-46 ◽

Cited By ~ 220

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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Rough Set Theory, Granular Computing on Partition

Encyclopedia of Database Systems ◽

10.1007/978-0-387-39940-9_3495 ◽

2009 ◽

pp. 2453-2453

Keyword(s):

Set Theory ◽

Rough Set ◽

Granular Computing ◽

Rough Set Theory

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Multi-Granular Computing through Rough Sets

Advances in Secure Computing, Internet Services, and Applications - Advances in Information Security, Privacy, and Ethics ◽

10.4018/978-1-4666-4940-8.ch001 ◽

2014 ◽

pp. 1-34 ◽

Cited By ~ 1

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.

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

International Journal of Cognitive Informatics and Natural Intelligence ◽

10.4018/jcini.2010040101 ◽

2010 ◽

Vol 4 (2) ◽

pp. 1-11 ◽

Cited By ~ 5

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.

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Rough Sets for Discovering Concurrent System Models from Data Tables

Rough Computing ◽

10.4018/978-1-59904-552-8.ch012 ◽

2011 ◽

pp. 239-268 ◽

Cited By ~ 7

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.

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Multidimensional Model-Based Decision Rules Mining

Post-Mining of Association Rules ◽

10.4018/978-1-60566-404-0.ch016 ◽

2009 ◽

pp. 311-334 ◽

Cited By ~ 1

Author(s):

Qinrong Feng ◽

Duoqian Miao ◽

Ruizhi Wang

Keyword(s):

Rough Set ◽

Rough Set Theory ◽

Decision Rules ◽

Data Sets ◽

Multidimensional Model ◽

Massive Data Sets ◽

The Hierarchical Structure ◽

Abstract Level ◽

Data Tables ◽

The Universe

Decision rules mining is an important technique in machine learning and data mining, it has been studied intensively during the past few years. However, most existing algorithms are based on flat data tables, from which sets of decision rules mined may be very large for massive data sets. Such sets of rules are not easily understandable and really useful for users. Moreover, too many rules may lead to over-fitting. Thus, a method of decision rules mining from different abstract levels was provided in this chapter, which aims to improve the efficiency of decision rules mining by combining the hierarchical structure of multidimensional model and the techniques of rough set theory. Our algorithm for decision rules mining follows the so called separate-and-conquer strategy. Namely, certain rules were mined beginning from the most abstract level, and supporting sets of those certain rules were removed from the universe, then drill down to the next level to recursively mine other certain rules which supporting sets are included in the remaining objects until no objects remain in the universe or getting to the primitive level. So this algorithm can output some generalized rules with different degree of generalization.

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The Incremental Knowledge Acquisition Based on Hash Algorithm

International Journal of Uncertainty Fuzziness and Knowledge-Based Systems ◽

10.1142/s0218488516500173 ◽

2016 ◽

Vol 24 (03) ◽

pp. 347-366 ◽

Cited By ~ 3

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.

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