A COMPREHENSIVE STUDY ON SOFT BINARY PIECEWISE DIFFERENCE OPERATION

Year 2024, Volume: 12 Issue: 1, 32 - 54, 27.02.2024

Aslıhan Sezgin Hamza Çalışıcı

https://doi.org/10.20290/estubtdb.1356881

Abstract

Soft set theory, developed by Molodtsov, has been applied both theoretically and practically in many fields. It is a useful mathematical tool for handling uncertainty. Numerous variations of soft set operations, which is a crucial concept for the theory, have been described and used since its introduction. In this paper, we explore more about soft binary piecewise difference operation (defined first as “difference of soft sets”) and its whole properties are examined especially in comparison with the basic properties of difference operation in classical set theory. Several striking properties of soft binary piecewise operations are obtained as analogous to the characteristic of difference operation in classical set theory. Also, we show that the collection of all soft sets with a fixed parameter set together with the soft binary piecewise difference operation is a bounded BCK-algebra.

Keywords

soft sets, soft set operations, soft binary piecewise difference operation

Project Number

YOK

ESNEK İKİLİ PARÇALI FARK İŞLEMİNE KAPSAMLI BİR BAKIŞ

Abstract

Molodtsov tarafından geliştirilen esnek küme teorisi hem teorik hem de pratik olarak birçok alanda uygulanmıştır. Bu teori, belirsizliği ele almak için yararlı bir matematiksel araçtır. Teori için çok önemli bir kavram olan esnek küme işlemlerinin çok sayıda varyasyonu, teorinin ortaya atılmasından bu yana tanımlanmış ve kullanılmıştır. Bu çalışmada, esnek ikili parçalı fark işlemi (ilk olarak "esnek kümelerin farkı" olarak tanımlanan) hakkında daha fazla bilgi elde edip, bu işlemin tüm özellikleri, özellikle klasik küme teorisindeki fark işleminin temel özellikleriyle karşılaştırmalı olarak incelenecektir. Esnek ikili parçalı işlemlerin birçok çarpıcı özelliği, klasik küme teorisindeki fark işleminin karakteristiğine benzer şekilde elde edilmiştir. Ayrıca, esnek ikili parçalı fark işleminin sabit parametreye sahip esnek kümeler kümesi üzerinde sınırlı bir BCK-cebiri olduğu gösterilmiştir.

Keywords

ESNEK KÜMELER, ESNEK KÜME İŞLEMLERİ, ESNEK İKİLİ PARÇALI FARK İŞLEMİ

Supporting Institution

YOK

Project Number

YOK

Thanks

YOK

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