The basic rough sets as introduced by Pawlak have been extended in many directions. Two such extensions are the rough sets on fuzzy approximation spaces and the rough sets by De et al. in 1999 and rough sets on intuitionistic fuzzy approximation spaces by Tripathy in 2006. There are several properties of these two types of rough sets established so far. However, in this paper we show that some of the properties established are erroneous through counter examples, establish their correct versions and illustrate their application in real life situations through an example in computer vision. © Springer Nature Singapore Pte Ltd. 2017.

Balakrushna Tripathy

Department of Analytics

School of Computer Science and Engineering

Vellore Campus

Mohanty R.R.

Vellore Institute of Technology (VIT) is a private university located in&nbsp;Tamil Nadu, India. Founded in 1984, as Vellore Engineering College, the institution offers 20 undergraduate, 34 postgraduate, four integrated and four research programs. It has campuses in Vellore, Amravati, Bhopal and Chennai.

VIT is one of the top ranked private universities in India according to NIRF, THE and QS Rankings.&nbsp;Govt. of India has recognized&nbsp;VIT, Vellore as an&nbsp;Institution of Eminence. This has allowed VIT to take independent quality initiatives and move up in world ranking.

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VIT University

Advances in Intelligent Systems and Computing Proceedings of Sixth International Conference on Soft Computing for Problem Solving

In the past few years the original concept of rough sets, as introduced by Pawlak [26] has been extended in many different directions. Some of these extensions are obtained by relaxing the requirement of the basic relations to be equivalence relations [14,15,31,32,34,35,37,38].That is by dropping the requirement of transitivity or symmetry. One such approach is to replace the equivalence relations by fuzzy proximity relations. The notions of rough sets thus generated are called rough sets defined upon fuzzy approximation spaces [14,15]. A generalization of this is obtained by taking intuitionistic fuzzy proximity relations instead of equivalence relations, called rough sets on intuitionistic fuzzy approximation spaces [37,38]. In this chapter we shall be concentrating on the study of these two notions of rough sets. It is our objective to define these types of rough sets along with related concepts and establish their properties which are parallel to those of basic rough sets. Several real life applications shall be considered in the sequel to illustrate the power and necessity of these generalized models of rough sets in the representation and study of imperfect knowledge. © 2009 Springer-Verlag Berlin Heidelberg.

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Some Properties of Rough Sets on Intuitionistic Fuzzy Approximation Spaces and Their Application in Computer Vision

Journal	Data powered by TypesetAdvances in Intelligent Systems and Computing Proceedings of Sixth International Conference on Soft Computing for Problem Solving
Publisher	Data powered by TypesetSpringer Singapore
ISSN	2194-5357
Open Access	0