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Linear Diophantine fuzzy substructures of ordered semigroups

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Abstract

As an extension of the fuzzy set, linear Diophantine fuzzy set (LDFS) was recently introduced. In this paper, we apply the concept of LDFS in ordered semigroups by introducing some new related concepts. More precisely, we study LDF-ideals and LDF-interior ideals of ordered semigroups, illustrate non-trivial examples on each, and present some of their properties. Finally, and using LDFS, we discuss the simplicity of an ordered semigroup.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, Abu Dhabi University, Zayed City, United Arab Emirates

    M. Al Tahan

  2. Department of Mathematics, Tafila Technical University, Tafila, Jordan

    S. Al-Kaseasbeh

  3. Department of Mathematical Sciences, Yazd University, Yazd, Iran

    B. Davvaz

  4. Department of Mathematics, Manipal Institute of Technology, Manipal Academy of Higher Education, Manipal, India

    P. Harikrishnan

Authors
  1. M. Al Tahan
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  2. S. Al-Kaseasbeh
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  3. B. Davvaz
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  4. P. Harikrishnan
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Correspondence to S. Al-Kaseasbeh.

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Tahan, M.A., Al-Kaseasbeh, S., Davvaz, B. et al. Linear Diophantine fuzzy substructures of ordered semigroups. Afr. Mat. 35, 35 (2024). https://doi.org/10.1007/s13370-024-01175-8

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