A New Soft Set Operation: Soft Binary Piecewise Symmetric Difference Operation

Year 2023, Volume: 5 Issue: 2, 189 - 208, 31.12.2023

Aslıhan Sezgin , Eda Yavuz

https://doi.org/10.47112/neufmbd.2023.18

Abstract

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, a new soft set operation, called soft binary piecewise symmetric difference operation, is defined, its properties are considered and examined comparatively with the basic algebraic properties of symmetric difference operation existing in classical set theory. Moreover, we prove that the set of all the soft sets with a fixed parameter set together with the soft binary piecewise symmetric difference operation and the restricted intersection operation is a commutative hemiring with identity and also Boolean ring.

Keywords

Soft Sets, Soft Sets Operations, Boolen Rings, Hemirings

Supporting Institution

YOK

Project Number

YOK

Thanks

POTENTIAL REVIEWERS ARE: 1) Faruk Karaaslan, [e-mail], Çankırı Karatekin Üniversitesi 2) Akın Osman Atagün, Yozgat Bozok University, [e-mail] 3)Muhammad Riaz, University of the Punjab , [e-mail] 4)Murat Lüzum, Van Yüzüncü Yıl Üniversitesi, [e-mail] 5) Şerif Özlü, Gaziantep üniversitesi, [e-mail]

Yeni Bir Esnek Küme İşlemi: Esnek İkili Parçalı Simetrik Fark İşlemi

Abstract

Molodtsov tarafından geliştirilen esnek küme teorisi hem teorik hem de pratik olarak birçok alanda uygulanmıştır. Belirsizliği ele almak için yararlı bir matematiksel araçtır. Ortaya atıldığından bu yana çok sayıda esnek küme işlemi varyasyonu tanımlanmış ve kullanılmıştır. Bu çalışmada, esnek ikili parçalı simetrik fark işlemi adı verilen yeni bir esnek küme işlemi tanımlanıp, özellikleri klasik küme teorisinde var olan simetrik fark işleminin temel cebirsel özellikleri ile karşılaştırmalı olarak ele alınmış ve incelenmiştir. Ayrıca, esnek ikili parçalı simetrik fark işlemi ve kısıtlanmıs kesisim işlemleri ile birlikte sabit parametreye sahip tüm esnek kümelerin oluşturduğu cebirsel yapının, birimli ve değişmeli bir hemiring ve ayrıca Boole halkası olduğu gösterilmiştir.

Keywords

Esnek Kümeler, Esnek Küme İşlemleri, Bool Halkası, Hemiring

Project Number

YOK

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