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A New Soft Set Operation: Complementary Soft Binary Piecewise Plus (+) Operation

Author

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  • Aslıhan SEZGÄ°N

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

  • Akın Osman ATAGÃœN

    (Department of Mathematics, Faculty of Arts and Science, Kırşehir Ahi Evran University, Kırşehir, Turkey)

Abstract

Soft set theory, introduced by Molodtsov, is as an important mathematical tool to deal with uncertainty and it has been applied to many fields both as theoretical and application aspects. Since 1999, different kinds of soft set operations has been defined and used in various types. In this paper, we define a new kind of soft set operation called, complementary soft binary piecewise plus operation and investigate its basic algebraic properties. Moreover, by examining the distribution rules, we contribute to the soft set literature by obtaining the relationships between this new soft set operation and some other types of soft set operations such as soft restrcited, extended, soft binary piecewise, and complementary soft binary piecewise operations. As proposing new soft set operations and obtaining their algebraic properties and implementations opens up new avenues for handling parametric data challenges in terms of decision-making methods and new cryptography approaches, and analyzing the algebraic structure of soft sets from the standpoint of new soft set operations offers a thorough understanding of the algebraic structure of soft sets, this paper can be regarded as both theoretical and application study.

Suggested Citation

  • Aslıhan SEZGÄ°N & Akın Osman ATAGÃœN, 2023. "A New Soft Set Operation: Complementary Soft Binary Piecewise Plus (+) Operation," Matrix Science Mathematic (MSMK), Zibeline International Publishing, vol. 7(2), pages 125-142, October.
    • Handle: RePEc:zib:zbmsmk:v:7:y:2023:i:2:p:125-142
    DOI: 10.26480/msmk.02.2023.125.142
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    References listed on IDEAS

    as
    1. Basit Ali & Naeem Saleem & Nozara Sundus & Sana Khaleeq & Muhammad Saeed & Reny George, 2022. "A Contribution to the Theory of Soft Sets via Generalized Relaxed Operations," Mathematics, MDPI, vol. 10(15), pages 1-14, July.
    2. 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.
    3. Aslıhan Sezgin & Naim Çağman & Akın Osman Atagün & Fitnat Nur Aybek, 2023. "Complemental Binary Operations Of Sets And Their Application To Group Theory," Matrix Science Mathematic (MSMK), Zibeline International Publishing, vol. 7(2), pages 114-121, October.
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