The multigranular rough set (MGRS) models of Qian et al. were extended to put forth covering-based multigranular rough sets (CBMGRS) by Liu et al. in 2012. The equality of sets, which is restrictive and redundant, was extended first in Pawlak (Rough sets: theoretical aspects of reasoning about data. Kluwer, London, 1991) and subsequently in Tripathy (Int J Adv Sci Technol 31:23–36, 2011) to propose four types of rough set-based approximate equalities. These basic concepts of rough equalities have been extended to several generalized rough set models. In this paper, covering-based pessimistic multigranular (CBPMG) approximate rough equivalence is introduced and several of their properties are established. Real life examples are taken for constructing counter examples and also for illustration. We have also discussed how these equalities can be applied in approximate reasoning and our latest proposal is no exception. © Springer Nature Singapore Pte Ltd. 2018.

Balakrushna Tripathy

Department of Analytics

School of Computer Science and Engineering

Vellore Campus

Parida S.K.

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

Covering-Based Pessimistic Multigranular Approximate Rough Equivalences and Approximate Reasoning

Smart Computing and Informatics Smart Innovation, Systems and Technologies

Rough set model introduced by Pawlak in 1982 was dependent upon equivalence relations (equivalently on partitions), which had restricted its application due to its stringent requirements. The notion of covering is an extension of that of a partition and is generated by relations much less restricted than equivalence relations. Several covering based rough sets are found in literature. As the notion of rough sets, basic or otherwise are unigranular from the granular computing point of view, in order to handle more than one granular structures on a universe simultaneously, optimistic and pessimistic multigranular computing were introduced by Qian et al in 2006 and 2010 respectively. Combining the two concepts of covering and multigranulation, covering based multigranular models were introduced by Liu et al in 2012. The notion of mathematical equality of concepts is too stringent and less applicable in real life situations. In order to incorporate human knowledge into it, four types of approximate equalities basing upon rough sets were introduced by Novotny and Pawlak in 1985 and by Tripathy in 2011. In this paper, we study the covering based pessimistic multigranular approximate rough equalities and establish several of their properties and provide suitable examples for illustration and in constructing counter examples in the proofs. This is an attempt to generalize the notion of approximate equalities by one more level in order to extend their applicability.

International Journal of Rough Sets and Data Analysis

Covering Based Pessimistic Multigranular Approximate Rough Equalities and Their Properties

Since its inception rough set theory has proved itself to be one of the most important models to capture impreciseness in data. However, it was based upon the notion of equivalence relations, which are relatively rare as far as applicability is concerned. So, the basic rough set model has been extended in many directions. One of these extensions is the covering based rough set notion, where a cover is an extension of the concept of partition; a notion which is equivalent to equivalence relation. Fro m the granular computing point of view, all these rough sets are unigranular in character; i.e. they consider only a singular granular structure on the universe. So, there arose the necessity to define multigranular rough sets and as a consequence two types of multigranular rough sets, called the optimistic multigranular rough sets and pessimistic rough sets have been introduced. Four types of covering based optimistic multigranular rough sets have been introduced and their properties are studied. The notion of equality of sets, which is too stringent for real life applications, was extended by Novotny and Pawlak to define rough equalities. This notion was further extended by Tripathy to define three more types of approximate equalities. The covering based optimistic versions of two of these four approximate equalities have been studied by Nagaraju et al recently. In this article, we study the other two cases and provide a comparative analysis. © 2016 MECS.

International Journal of Intelligent Systems and Applications

Covering Based Optimistic Multigranular Approximate Rough Equalities and their Properties

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 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.

2013 Fourth International Conference on Computing, Communications and Networking Technologies (ICCCNT)

On the approximate equalities of multigranular rough sets and approximate reasoning

Covering based rough sets have been introduced as an extension of the basic rough sets introduced by Pawlak [5, 6]. There is only one way to define the lower approximation of a set using covering. However, as many as four definitions have been proposed for covering based upper approximation. Accordingly, we find four types of covering based rough sets in the literature. In [7], the concept of rough equivalences of sets, which extended the corresponding notions of approximate equalities of Novotny and Pawlak [2, 3, 4] were introduced and their properties were studied. In this article we further generalize these concepts to the setting of covering based rough sets and establish some of their properties. © 2009 IEEE.

Journal	Data powered by TypesetSmart Computing and Informatics Smart Innovation, Systems and Technologies
Publisher	Data powered by TypesetSpringer Singapore
ISSN	2190-3018
Open Access	0