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.

Balakrushna Tripathy

Department of Analytics

School of Computer Science and Engineering

Vellore Campus

Mitra A.

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

On algebraic and topological properties of Neighbourhood Based Multigranular Rough Sets

2014 International Conference on Computer Communication and Informatics

The notion of rough sets [4] was used by Novotny and Pawlak [1, 2, 3] to introduce the concept of rough equality, in order to incorporate user knowledge in determining the equality of sets, which is a natural phenomenon in day to day life. Even this notion was shown to be deficient and was extended by Tripathy et al [6, 9] to define the notion of rough equivalence of sets, which is more suitable in real life situations. Tripathy [7] added two more approximate equalities to this list in order to complete the kinds of approximate equalities. Algebraic properties of sets with mathematical equality have very little meaning when sets are replaced with rough sets. As a consequence, replacing equality by rough equivalence the algebraic properties were studied by Tripathy et al [10]. In our present work, we have made an analysis of the validity of the algebraic properties with respect to the four kinds of approximate equalities and provide a comparative study to establish that rough equivalence is the best and rough equality is the worst among these approximate equalities with respect to the algebraic properties involving rough sets. The topological characterisations of rough sets leading to four types of rough sets and operations on them [8] are being used in the sequel. We support our descriptions with a running real life example of shares. © 2013 IEEE.

2013 IEEE International Conference on Computational Intelligence and Computing Research

Algebric properties of rough sets using topological characterisations and approximate equalities

The definition of basic rough sets depends upon a single equivalence relation defined on the universe or several equivalence relations taken one each taken at a time. In the view of granular computing, classical rough set theory is based upon single granulation. The basic rough set model was extended to rough set model based on multi-granulations (MGRS) in [6], where the set approximations are defined by using multi-equivalences on the universe and their properties were investigated. Using the hybridized rough fuzzy set model introduced by Dubois and Prade [2], rough fuzzy set model based on multi-granulation is introduced and studied by Wu and Kou [15]. Topological properties of rough sets introduced by Pawlak in terms of their types were recently studied by Tripathy and Mitra [11]. These were extended to the context of incomplete multi granulation by Tripathy and Raghavan [12]. Recently, the concept of multi-granulations based on rough fuzzy sets by Tripathy and Nagaraju [13]. In a recent paper, Tripathy et al [14] introduced the concept of incomplete multigranulation on rough intuitionistic fuzzy sets (MGRIFS) and studied some of its topological properties. In this paper we continue further by introducing the concept of accuracy measures on MGRIFS and prove some of their properties. Our findings are true for both complete and incomplete intuitionistic fuzzy rough set models based upon multi granulation. The concepts and results established in [13] and [14] open a new direction in the study of multigranulation for further study. © 2012 Springer-Verlag GmbH.

Advances in Intelligent and Soft Computing Advances in Computer Science, Engineering & Applications

Some Concepts of Incomplete Multigranulation Based on Rough Intuitionistic Fuzzy Sets

The definition of basic rough sets [3] depends upon either a single equivalence relation defined on a universe or several equivalence relations defined over the universe, taken one each taken at a time. In the view of granular computing, classical rough set theory is based upon single granulation. Extending this notion, a rough set model based on multi-granulations (MGRS) was introduced in [5]. In this approach, approximations of sets were defined through multiple equivalence relations on the universe and their properties were investigated. Using hybridization of fuzzy set [13] with rough set the concept of rough fuzzy set was introduced by Dubois and Prade [1]. Recently, a Rough Fuzzy Set Model was introduced and studied by Wu and Kou [12], which is based on Multiple Granulation. Topological properties of rough sets introduced by Pawlak in terms of their types were recently studied by Tripathy and Mitra [10]. These were extended to the context of incomplete multi granulation by Tripathy and Raghavan [11]. In this paper we introduce incomplete multigranulation on rough fuzzy sets, study their basic properties and extend the topological properties in [11] to this context. Our findings are true for both complete and incomplete fuzzy rough set models based upon multi granulation. © 2012 Springer-Verlag.

Communications in Computer and Information Science Global Trends in Information Systems and Software Applications

Topological Properties of Incomplete Multigranulation Based on Rough Fuzzy Sets

International Journal of Information Technology and Computer Science

Some Algebraic Properties of Multigranulations and an Analysis of Multigranular Approximations of Classifications

International Journal of Intelligent Systems and Applications

On Some Comparison Properties of Rough Sets Based on Multigranulations and Types of Multigranular Approximations of Classifications

A Comparative Analysis of Multigranular Approaches and on Topoligical Properties of Incomplete Pessimistic Multigranular Rough Fuzzy Sets

On Some Topological Properties of Pessimistic Multigranular Rough Sets

International Journal of Granular Computing, Rough Sets and Intelligent Systems

Some topological properties of rough sets and their applications

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