The soft set theory developed by Molodtsov has been applied both theoretically and practically in many fields. It is a useful piece of mathematics for handling uncertainty. Numerous variations of soft set operations have been described and used since its introduction. In this paper, we define a new soft set operation, called complementary soft binary piecewise intersection operation, a unique soft set operation, and examine its basic algebraic properties. Additionally, we aim to contribute to the literature on soft sets by illuminating the relationships between this new soft set operation and other kinds of soft set operations by researching the distribution of this new soft set operation over other 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 intersection operation and the soft binary piecewise union operation is a zero-symmetric near-semiring and hemiring.
Soft sets Soft set operations Conditional complements Near-semiring
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The soft set theory developed by Molodtsov has been applied both theoretically and practically in many fields. It is a useful piece of mathematics for handling uncertainty. Numerous variations of soft set operations have been described and used since its introduction. In this paper, we define a new soft set operation, called complementary soft binary piecewise intersection operation, a unique soft set operation, and examine its basic algebraic properties. Additionally, we aim to contribute to the literature on soft sets by illuminating the relationships between this new soft set operation and other kinds of soft set operations by researching the distribution of this new soft set operation over other 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 intersection operation and the soft binary piecewise union operation is a zero-symmetric near-semiring and hemiring.
Soft sets Soft set operations Conditional complements Near-semiring
YOK
Birincil Dil | İngilizce |
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Konular | Cebir ve Sayı Teorisi |
Bölüm | Research Articles |
Yazarlar | |
Proje Numarası | YOK |
Erken Görünüm Tarihi | 2 Ekim 2023 |
Yayımlanma Tarihi | 15 Ekim 2023 |
Gönderilme Tarihi | 25 Haziran 2023 |
Kabul Tarihi | 28 Temmuz 2023 |
Yayımlandığı Sayı | Yıl 2023 Cilt: 6 Sayı: 4 |