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Algebraic Semantics of Proto-Transitive Rough Sets

Chapter
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10020)

Abstract

Rough Sets over generalized transitive relations like proto-transitive ones have been initiated recently by the present author. In a recent paper, approximation of proto-transitive relations by other relations was investigated and the relation with rough approximations was developed towards constructing semantics that can handle fragments of structure. It was also proved that difference of approximations induced by some approximate relations need not induce rough structures. In this research, the structure of rough objects is characterized and a theory of dependence for general rough sets is developed and used to internalize the Nelson-algebra based approximate semantics developed earlier by the present author. This is part of the different semantics of PRAX developed in this paper by her. The theory of rough dependence initiated in earlier papers is extended in the process. This paper is reasonably self-contained and includes proofs and extensions of representation of objects that have not been published earlier.

Keywords

Proto-transitive relations Generalized transitivity Rough dependence Rough objects Granulation Algebraic semantics Approximate relations Approximate semantics Nelson algebras Axiomatic theory of granules Contamination problem Knowledge 

Notes

Acknowledgment

The present author would like to thank Prof Mihir Chakraborty for discussions on PRAX and the referee for drawing attention to [8] and related references in particular.

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Copyright information

© Springer-Verlag GmbH Germany 2016

Authors and Affiliations

  1. 1.Department of Pure MathematicsUniversity of CalcuttaKolkataIndia

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