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Applications of fuzzy \(\rho \)-ideals in \(\rho \)-algebras

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Abstract

Some new notions of fuzzy algebras like fuzzy \(\rho \)-subalgebra, fuzzy \(\rho \)-ideal, and fuzzy \({\overline{\rho }}\)-ideal are introduced in this work. Moreover, the relationships between our new notions and other types of fuzzy algebras like fuzzy d-subalgebra, fuzzy d-ideal, fuzzy BCK-subalgebra, and fuzzy BCK-ideal are investigated. Also, some basic characterizations of fuzzy \(\rho \)-ideal with their applications on images, Cartesian product, upper level, characteristic function, and strongest fuzzy relation are studied and discussed in this paper. Furthermore, several examples are presented to expound our notions in this work.

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Authors and Affiliations

  1. Department of Mathematics, University of Basrah, Basrah, 61004, Iraq

    Shuker Mahmood Khalil & Fatima Hameed

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  1. Shuker Mahmood Khalil
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  2. Fatima Hameed
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All authors read and approved the final manuscript.

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Correspondence to Shuker Mahmood Khalil.

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Communicated by V. Loia.

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Khalil, S.M., Hameed, F. Applications of fuzzy \(\rho \)-ideals in \(\rho \)-algebras. Soft Comput 24, 13997–14004 (2020). https://doi.org/10.1007/s00500-020-04773-3

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