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Fuzzy Ideals of Sheffer Stroke Hilbert Algebras

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Abstract

In this study, fuzzy subalgebras and ideals with t-conorms on Sheffer stroke Hilbert algebras are discussed. We state and prove relationships between the level-set of a fuzzy subalgebra with a t-conorm T (briefly, T-fuzzy subalgebra) and a subalgebra of a Sheffer stroke Hilbert algebra. Then the composition of T-fuzzy subalgebras and homomorphisms of Sheffer stroke Hilbert algebras are analyzed. By defining fuzzy subalgebras of Sheffer stroke Hilbert algebras, the relationships between fuzzy subalgebras and T-fuzzy subalgebras of this algebraic structure are investigated. Also, it is shown that every fuzzy ideal with t-conorm T (in short, T-fuzzy ideal) is a T-fuzzy subalgebra but the converse does not generally hold. As in T-fuzzy subalgebras of Sheffer stroke Hilbert algebras, some properties of the T-fuzzy ideals are proved.

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Acknowledgements

The authors are thankful to the referees for a careful reading of the paper and for valuable comments and suggestions.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Science, Ege University, 35100, Izmir, Turkey

    Tahsin Oner

  2. Department of Mathematics, Faculty of Arts and Sciences, İzmir University of Economics, Izmir, Turkey

    Tugce Katican

  3. Department of Pure Mathematics, Faculty of Mathematics and Computer, Shahid Bahonar University of Kerman, Kerman, Iran

    Arsham Borumand Saeid

Authors
  1. Tahsin Oner
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  2. Tugce Katican
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  3. Arsham Borumand Saeid
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Correspondence to Tahsin Oner.

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Oner, T., Katican, T. & Borumand Saeid, A. Fuzzy Ideals of Sheffer Stroke Hilbert Algebras. Proc. Natl. Acad. Sci., India, Sect. A Phys. Sci. 93, 85–94 (2023). https://doi.org/10.1007/s40010-022-00794-9

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  • DOI: https://doi.org/10.1007/s40010-022-00794-9

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