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A New Soft Set Operation: Complementary Soft Binary Piecewise Union (∪) Operation

Author

Listed:
  • Aslıhan Sezgin

    (Department of Mathematics and Science Education, Faculty of Education, Amasya University, Amasya, Turkey)

  • Fitnat Nur Aybek

    (Department of Mathematics, Graduate School of Natural and Applied Sciences, Amasya University, Amasya, Turkey)

  • Nurcan Bilgili Güngör

    (Department of Mathematics, Faculty of Arts and Science, Amasya University, Amasya, Turkey)

Abstract

Molodtsov’s soft set theory has been used in various disciplines both theoretically and practically. It is an effective mathematical tool for dealing with uncertainty. Since its debut, numerous types of soft set operations have been presented and applied. In this study, we analyze the fundamental algebraic features of a novel soft set operation which we call complementary soft binary piecewise union operation. Additionally, by examining the distribution of complementary soft binary piecewise union operation over all other soft set operations’ type, it aims to contribute to the literature on soft sets by revealing relationships between this new soft set operation and other types of soft set operations. Moreover, we prove that the set of all the soft sets with a fixed parameter set together with the complementary soft binary piecewise union operation and the soft binary piecewise intersection operation is a zero-symmetric near-semiring.

Suggested Citation

  • Aslıhan Sezgin & Fitnat Nur Aybek & Nurcan Bilgili Güngör, 2023. "A New Soft Set Operation: Complementary Soft Binary Piecewise Union (∪) Operation," Acta Informatica Malaysia (AIM), Zibeline International Publishing, vol. 7(1), pages 38-53, February.
    • Handle: RePEc:zib:zbnaim:v:7:y:2023:i:1:p:38-53
    DOI: 10.26480/aim.01.2023.38.53
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