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Authors: Sutapa Mahato 1 and S. Tiwari 2

Affiliations: 1 Centre for Data Science, ITER, Siksha ’O’ Anusandhan (Deemed to be University), Bhubaneswar-751030, India ; 2 Department of Mathematics and Computing, Indian Institute of Technology(ISM), Dhanbad-826004, India

Keyword(s): L-Fuzzy Approximation Space, Category Theory, Functor, Coalgebra, Dialgebra, Powerset Theory.

Abstract: This paper is to establish a relationship between powerset theories and the category of dialgebras over the category of L-fuzzy approximation space, where L is a residuated lattice. Also, we show that the category FAS of L-fuzzy approximation spaces is a category of F-coalgebras. Interestingly, we introduce a functor having both the left/right adjoint from the category FAS to the category UAS of upper approximation sets. Further, the category J-Coal of J-coalgebras and the category (J,K)-Dial of (J;K)-dialgebras are introduced over the category FAS and it is shown that they are topological categories.

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Paper citation in several formats:
Mahato, S. and Tiwari, S. (2023). On the Categories of Coalgebras, Dialgebras and Powerset Theory over L-Fuzzy Approximation Spaces. In Proceedings of the 15th International Joint Conference on Computational Intelligence - FCTA; ISBN 978-989-758-674-3; ISSN 2184-3236, SciTePress, pages 348-358. DOI: 10.5220/0012182100003595

@conference{fcta23,
author={Sutapa Mahato and S. Tiwari},
title={On the Categories of Coalgebras, Dialgebras and Powerset Theory over L-Fuzzy Approximation Spaces},
booktitle={Proceedings of the 15th International Joint Conference on Computational Intelligence - FCTA},
year={2023},
pages={348-358},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0012182100003595},
isbn={978-989-758-674-3},
issn={2184-3236},
}

TY - CONF

JO - Proceedings of the 15th International Joint Conference on Computational Intelligence - FCTA
TI - On the Categories of Coalgebras, Dialgebras and Powerset Theory over L-Fuzzy Approximation Spaces
SN - 978-989-758-674-3
IS - 2184-3236
AU - Mahato, S.
AU - Tiwari, S.
PY - 2023
SP - 348
EP - 358
DO - 10.5220/0012182100003595
PB - SciTePress

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