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Right Adjoint Algebras Versus Operator Left Residuated Posets

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Rough Sets (IJCRS 2021)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 12872))

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Abstract

Algebraic structures are essential in fuzzy frameworks such as fuzzy formal concept analysis and fuzzy rough set theory. This paper studies two general structures such as right adjoint algebras and operator left residuated posets, introducing several properties which relate them. Different extensions of the operators included in a given operator left residuated poset are presented and a reasoned analysis is shown to guarantee that the equivalence satisfied by the operators in this structure is not a generalization of the usual adjoint property, which is a basic property verified by right adjoint pairs. Operator left residuated posets are also studied in the framework of the Dedekind-MacNeille completion of a poset.

This work is partially supported by the 2014-2020 ERDF Operational Programme in collaboration with the State Research Agency (AEI) in projects TIN2016-76653-P and PID2019-108991GB-I00, and with the Department of Economy, Knowledge, Business and University of the Regional Government of Andalusia in project FEDER-UCA18-108612, and by the European Cooperation in Science & Technology (COST) Action CA17124.

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Authors and Affiliations

  1. Department of Mathematics, University of Cádiz, Cádiz, Spain

    M. Eugenia Cornejo & Jesús Medina

Authors
  1. M. Eugenia Cornejo
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  2. Jesús Medina
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Correspondence to M. Eugenia Cornejo .

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Editors and Affiliations

  1. University of Winnipeg, Winnipeg, MB, Canada

    Sheela Ramanna

  2. Ghent University, Gent, Belgium

    Chris Cornelis

  3. University of Milano-Bicocca, Milan, Italy

    Davide Ciucci

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Cornejo, M.E., Medina, J. (2021). Right Adjoint Algebras Versus Operator Left Residuated Posets. In: Ramanna, S., Cornelis, C., Ciucci, D. (eds) Rough Sets. IJCRS 2021. Lecture Notes in Computer Science(), vol 12872. Springer, Cham. https://doi.org/10.1007/978-3-030-87334-9_15

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  • DOI: https://doi.org/10.1007/978-3-030-87334-9_15

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-87333-2

  • Online ISBN: 978-3-030-87334-9

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