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Algebraic Semantics of Proto-Transitive Rough Sets

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Transactions on Rough Sets XX

Part of the book series: Lecture Notes in Computer Science ((TRS,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.

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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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  1. Department of Pure Mathematics, University of Calcutta, 9/1B, Jatin Bagchi Road, Kolkata, 700029, India

    A. Mani

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  1. A. Mani
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Correspondence to A. Mani .

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  1. University of Manitoba , Winnipeg, Manitoba, Canada

    James F. Peters

  2. University of Warsaw , Warsaw, Poland

    Andrzej Skowron

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Mani, A. (2016). Algebraic Semantics of Proto-Transitive Rough Sets. In: Peters, J., Skowron, A. (eds) Transactions on Rough Sets XX. Lecture Notes in Computer Science(), vol 10020. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-53611-7_3

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  • DOI: https://doi.org/10.1007/978-3-662-53611-7_3

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