In an attempt to incorporate user knowledge in order to decide about the equality of sets, the concepts of approximate equalities using rough sets were introduced. These notions have been generalised in several ways and very recently [1] extended four types of approximate equalities using rough fuzzy sets instead of only rough sets. To be precise, a concept of leveled approximate equality was introduced and properties were studied. In this paper we extend this work with case studies to illustrate the applications of the concepts and compare them respectively. We also introduce and discuss the rough measures of basic sets, fuzzy sets and interpret four types of approximate equalities in terms of the accuracy measure as well as rough measures. The analysis had provided a clear distinguish notion in terms of the measures. © 2013 IEEE.

Balakrushna Tripathy

Department of Analytics

School of Computer Science and Engineering

Vellore Campus

Jhawar A

Vats E

Chan C.S.

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

Generalised approximate equalities based on rough fuzzy sets & rough measures of fuzzy sets

2013 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE)

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

Three types of rough equalities were introduced by Novotny and Pawlak ([7, 8,9]), which take care of approximate equalities of sets. These sets may not be equal in the usual sense. These notions were generalized by Tripathy, Mitra and Ojha ([12]), who introduced the concepts of rough equivalences of sets. These approximate equalities of sets capture equality of the concerned sets at a higher level than their corresponding rough equalities. Some more properties were proved in [13]. Two more approximate equalities were introduced by Tripathy [11] and comparative analysis of their efficiency was provided. In this paper, we generalise these approximate equalities by considering rough fuzzy sets instead of only rough sets. A concept of leveled approximate equality is introduced and properties are studied. We also provide suitable examples to illustrate the applications of the new notions and provide an analysis of their relative efficiency. © 2012 Springer India Pvt. Ltd.

Advances in Intelligent and Soft Computing Proceedings of the International Conference on Soft Computing for Problem Solving (SocProS 2011) December 20-22, 2011

An Analysis of Generalised Approximate Equalities Based on Rough Fuzzy Sets

In this chapter we mainly focus on the study of some topological aspects of rough sets and approximations of classifications. The topological classification of rough sets deals with their types. We find out types of intersection and union of rough sets, New concepts of rough equivalence (top, bottom and total) are defined, which capture approximate equality of sets at a higher level than rough equality (top, bottom and total) of sets introduced and studied by Novotny and Pawlak [23,24,25] and is also more realistic. Properties are established when top and bottom rough equalities are interchanged. Also, parallel properties for rough equivalences are established. We study approximation of classifications (introduced and studied by Busse [12]) and find the different types of classifications of an universe completely. We find out properties of rules generated from information systems and observations on the structure of such rules. The algebraic properties which hold for crisp sets and deal with equalities loose their meaning when crisp sets are replaced with rough sets. We analyze the validity of such properties with respect to rough equivalences. © 2009 Springer-Verlag Berlin Heidelberg.

Studies in Computational Intelligence Rough Set Theory: A True Landmark in Data Analysis

On Approximation of Classifications, Rough Equalities and Rough Equivalences

International Journal of Artificial Intelligence and Soft Computing

Rough equivalence and algebraic properties of rough sets

Rough Sets and Current Trends in Computing Lecture Notes in Computer Science

On Rough Equalities and Rough Equivalences of Sets

Generalised approximate equalities based on rough fuzzy sets &amp; rough measures of fuzzy sets

Journal	Data powered by Typeset2013 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE)
Publisher	Data powered by TypesetIEEE
ISSN	10987584
Open Access	0