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Algebraic Representation, Dualities and Beyond

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Algebraic Methods in General Rough Sets

Part of the book series: Trends in Mathematics ((TM))

Abstract

In this research chapter, dualities and representations of various kinds associated with the semantics of rough sets are explained, critically reviewed, new proofs have been proposed, open problems are specified and new directions are suggested. Some recent duality results in the literature are also adapted for use in rough contexts. New results are also proved on granular connections between generalized rough and L-fuzzy sets by the present author. Philosophical aspects of the concepts have also been considered by her in this research chapter.

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Acknowledgements

I would like to thank Ivo (Prof. Ivo Düntsch) for many discussions, remarks and for collaborating in the preparation of this research chapter. Initially, a joint chapter was planned, but it did not happen that way because of shortage of time. The first section of the chapter has in fact been partly written by Ivo. I would also like to thank the second readers of this chapter Sandor (Prof. Sándor Radeleczki) and Davide (Prof. Davide Ciucci) for their useful remarks.

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  1. Department of Pure Mathematics, University of Calcutta, Kolkata, India

    A. Mani

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  1. Department of Pure Mathematics, University of Calcutta, Kolkata, India

    A. Mani

  2. Department of Informatics, University of Milano-Bicocca, Milano, Italy

    Gianpiero Cattaneo

  3. Fujian Normal University, College of Mathematics and Informatics, Fuzhou, China

    Ivo DĂĽntsch

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Mani, A. (2018). Algebraic Representation, Dualities and Beyond. In: Mani, A., Cattaneo, G., Düntsch, I. (eds) Algebraic Methods in General Rough Sets. Trends in Mathematics. Birkhäuser, Cham. https://doi.org/10.1007/978-3-030-01162-8_6

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