### Journals Information

Mathematics and Statistics Vol. 9(4), pp. 608 - 616
DOI: 10.13189/ms.2021.090420
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## A Novel Concept of Uncertainty Optimization Based Multi-Granular Rough Set and Its Application

Pradeep Shende *, Arvind Kumar Sinha
Department of Mathematics, National Institute of Technology Raipur, Chhattisgarh, India

ABSTRACT

Data is generating at an exponential pace with the advancement in information technology. Such data highly contain uncertain and vague information. The rough set approximation is a way to find information in the data-set under uncertainty and to classify objects of the dataset. This work presents a mathematical approach to evaluate the data-sets uncertainties and their application to data reduction. In this work, we have extended the multi-granulation variable precision rough set in the context of uncertainty optimization. We develop an uncertainty optimization-based multi-granular rough set (UOMGRS) to minimize the uncertainties in the data set more effectively. Using UOMGRS, we find the most informative attribute in the feature space. It is desirable to minimize the rough set boundary region using the attribute having the highest approximation quality. Thus we group the attributes whose relative quality of approximation is the maximum to maximize the positive region and to minimize the uncertain region. We compare the UOMGRS with the single granulation rough set (SGRS) and the multi-granular rough set (MGRS). By our proposed method, we require only an average of 62% attributes for approximation whereas, SGRS and MGRS need an average of at least 72% of attributes in the data set for approximation of the concepts in the data-set. Our proposed method requires less amount of data for the classification of objects in the dataset. The method helps minimize the uncertainties in the dataset in a more efficient way.

KEYWORDS
Uncertainty Optimization, Multi-granulation, Rough Set, Optimization Algorithm, Data Reduction

Cite This Paper in IEEE or APA Citation Styles
(a). IEEE Format:
[1] Pradeep Shende , Arvind Kumar Sinha , "A Novel Concept of Uncertainty Optimization Based Multi-Granular Rough Set and Its Application," Mathematics and Statistics, Vol. 9, No. 4, pp. 608 - 616, 2021. DOI: 10.13189/ms.2021.090420.

(b). APA Format:
Pradeep Shende , Arvind Kumar Sinha (2021). A Novel Concept of Uncertainty Optimization Based Multi-Granular Rough Set and Its Application. Mathematics and Statistics, 9(4), 608 - 616. DOI: 10.13189/ms.2021.090420.