Yeni Bir Esnek Küme İşlemi: Tümleyenli Genişletilmiş Fark İşlemi

Öz

Esnek küme teorisinin birçok teorik ve pratik uygulaması vardır. İlk kez 1999 yılında Molodtsov tarafından belirsizlik durumlarını temsil etmenin bir yolu olarak tanıtıldı. Esnek küme teorisinin temel yapı taşları esnek küme işlemleridir. İlk çıkışından bu yana, çeşitli bağlamlarda esnek küme işlemlerinin çeşitli türleri tanımlanmış ve kullanılmıştır. Teoriyi ilerletmek amacıyla bu çalışmada tümleyenli genişletilmiş fark işlemi olarak isimlendirilen yeni bir esnek küme işlemi tanımlanmıştır. Özellikleri, klasik kümelerdeki fark işlemi ile kıyaslanarak kapsamlı bir şekilde tartışılmıştır. Ayrıca, bu işlemin diğer esnek küme işlemleri ile nasıl bir ilişkisi olduğunu belirlemek amacıyla bu işlemin diğer esnek küme işlemlerine dağılımı da incelenmiştir.

Anahtar Kelimeler

• Esnek küme
• Koşullu tümleyenler
• Tümleyenli genişletilmiş işlemler

A New Type of Extended Soft Set Operations: Complementary Extended Difference Operation

Öz

Soft set theory has many theoretical and practical applications. It was first introduced by Molodtsov in 1999 as a way to represent specific situations including uncertainty. The fundamental building blocks of soft set theory are soft set operations. Since its debut, several types of soft set operations have been defined and utilized in diverse contexts. In order to further the theory, a new soft set operation known as the complementary extended difference operation is defined in this paper. Its properties are thoroughly discussed, with particular attention to how it differs from the difference operation in classical sets. Additionally, the distribution of this operation over other types of soft set operations is examined in order to determine how this operation relates to other soft set operations.

Anahtar Kelimeler

• Soft set
• Conditional complements
• Complementary extended soft set operations

Kaynakça

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