Raghavan R

Department of Information Technology

School of Information Technology and Engineering

Vellore Campus

B.k.tripathy

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

International Journal of Intelligent Systems and Applications

Rough sets introduced by Pawlak as a model to capture impreciseness in data is unigranular from the granular computing point of view. In their attempts to introduce multigranulation using rough sets, two models called optimistic multigranular rough sets and pessimistic multigranular rough sets were introduce by Qian et al. in 2006 and 2010 respectively. It is well known that there are several extensions of the basic rough sets to make it more applicable and covering based rough set approach is one among them. Recently, the concept of multigranularity has been extended by Liu et al. to introduce four types of covering based optimistic multigranular rough sets (CBOMGRS). Later, Tripathy et al. introduced the notion of Covering Based Pessimistic Multigranular Rough Sets (CBPMGRS) and proved some of their properties. The important observation is that some of the properties of basic rough sets, which were not true for CBOMGRS, are true for CBPMGRS. So, CBPMGRS seems to be more natural extension of the basic concept than CBOMGRS. Recently Chai has shown that many of the results established by Liu et al. are incorrect, which they rectified. In our results in this paper, we analyse the same for CBPMGRS and incorporate the changes and establish some more properties of CBPMGRS. © Springer India 2015.

Advances in Intelligent Systems and Computing Information Systems Design and Intelligent Applications

Some More Properties of Covering Based Pessimistic Multigranular Rough Sets

As the notion of equality in mathematics is too stringent and less applicable in real life situations, Novotny and Pawlak introduced approximate equalities through rough sets. Three more types of such equalities were introduced by Tripathy et al. as further generalisations of these equalities. As rough set introduced by Pawlak is unigranular from the granular computing point of view, two types of multigranulations rough sets called the optimistic and the pessimistic multigranular rough sets have been introduced. Three of the above approximate equalities were extended to the multigranular context by Tripathy et al. recently. In this paper, we extend the last but the most general of these approximate equalities to the multigranular context. We establish several direct and replacement properties of this type of approximate equalities. Also, we illustrate the properties as well as provide counter examples by taking a real life example. © Springer India 2015.

Computational Intelligence in Data Mining - Volume 2 Smart Innovation, Systems and Technologies

On Multigranular Approximate Rough Equivalence of Sets and Approximate Reasoning

Rough sets were introduced by Pawlak as a model to capture impreciseness in data and several techniques in different directions have been developed to perform operations on such data through the model. But the basic model of rough set introduced is unigranular from the granular computing point of view. So, attempts have been made to introduce multigranulation using rough sets. Two models called optimistic multigranular rough sets and pessimistic multigranular rough sets were introduce by Qian et al in 2006 and 2010 respectively. However, like the basic case, the information granules generated were introduced by equivalence relations and as a result the granules are members of partitions induced on the universe. However, such concepts have limited applications due to the rarity of equivalence relations or equivalently partitions of universes the notion of cover is more general than partition and covers are available in abundance in real life situations. So, even in the case of basic rough sets the definition has been extended to develop covering based rough sets. Recently, the concept of multigranularity has been extended by Liu et al to introduce four types of covering based optimistic multigranular rough sets (CBOMGRS). In this paper we introduce the notion of Covering Based Pessimistic Multigranular Rough Sets (CBPMGRS) and proved some properties the important observation is that some of the properties of basic rough sets, which were not true for CBOMGRS, are true for CBPMGRS. So, CBPMGRS seems to be more natural extensions of the basic concepts than CBOMGRS. © 2014 IEEE.

2014 International Conference on Computational Intelligence and Communication Networks

On Covering Based Pessimistic Multigranular Rough Sets

Most of the researches in feature selection deal with homogeneous features that are with either numerical or categorical features. As discussed in [2] neighbourhood rough set model is one approach which deals with heterogeneous feature selection. The neighbourhood model is used to reduce numerical and categorical features by assigning different thresholds for different kinds of attributes. Recently Neighbourhood Based Multigranular Rough sets (NMGRS) was introduced and their properties were studied. We shall provide some critical appreciations of the results of this paper. One of the two characteristics used in real life applications of rough sets is their topological characterisations. In this article we study topological characteristics NMGRS. Some interesting algebraic properties of MGRSs were studied recently in [3]. We extend these studies to the NMGRS context. We shall also be illustrating the concepts a real life example. © 2014 IEEE.

2014 International Conference on Computer Communication and Informatics

On algebraic and topological properties of Neighbourhood Based Multigranular Rough Sets

Rough sets have been a successful model to capture impreciseness in data. The basic notion rough set introduced by Pawlak is a single granulation model from the granular computing point of view. Recently, this has been extended to multigranular rough set models. Pawlak and Novotny introduced the notions of rough set equalities which is called approximate equalities. These notions of equalities use the user knowledge to decide the equality of sets and hence generate approximate reasoning. In this article, we introduce the concepts of multigranular approximate equalities and establish their properties. Also, the replacement properties, which are obtained by interchanging the bottom equalities with the top equalities, have been established. We provide a real life example for both types of multigranulation and illustrate the interpretation of the approximate equalities through the example. © 2013 IEEE.

Journal	International Journal of Intelligent Systems and Applications
Publisher	MECS Publisher
ISSN	2074-904X
Open Access	0