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Analysis of \(\Gamma \)-semigroups based on bipolar complex fuzzy sets

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Abstract

Keeping in view the importance of fuzzy algebraic structures, in this manuscript, we develop the concept of bipolar complex fuzzy (BCF) \(\Gamma \)-subsemigroup (BCF-\(\Gamma \)SSG), bipolar complex fuzzy left \(\Gamma \)-ideal (BCF-L\(\Gamma \)I), bipolar complex fuzzy right \(\Gamma \)-ideal (BCF-R\(\Gamma \)I), bipolar complex fuzzy \(\Gamma \)-ideal (BCF-\(\Gamma \)I), bipolar complex fuzzy \(\Gamma \)-bi-ideal (BCF-\(\Gamma \)BI), bipolar complex fuzzy \(\Gamma \)-(1, 2) ideal (BCF- \(\Gamma \)(1, 2)I), bipolar complex fuzzy left \(\Gamma \)-duo, bipolar complex fuzzy right \(\Gamma \)-duo, and their related outcomes in the environment of \(\Gamma \)-semigroup. We also develop the notions of bipolar complex fuzzy left \(\Gamma \)-simple, bipolar complex fuzzy right \(\Gamma \)-simple, bipolar complex fuzzy \(\Gamma \)-simple, and their linked results in the framework of \(\Gamma \)-semigroup.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, International Islamic University Islamabad, Islamabad, Pakistan

    Tahir Mahmood & Ubaid ur Rehman

  2. Department of Mathematics, Faculty of Science, King Abdulaziz University, P. O. Box 80348, Jeddah, 22254, Saudi Arabia

    Majed Albaity

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  1. Tahir Mahmood
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  2. Ubaid ur Rehman
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  3. Majed Albaity
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Correspondence to Tahir Mahmood or Majed Albaity.

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Communicated by Graçaliz Pereira Dimuro.

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Mahmood, T., ur Rehman, U. & Albaity, M. Analysis of \(\Gamma \)-semigroups based on bipolar complex fuzzy sets. Comp. Appl. Math. 42, 262 (2023). https://doi.org/10.1007/s40314-023-02376-w

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  • DOI: https://doi.org/10.1007/s40314-023-02376-w

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