Rough Küme Teorisinde Tanımlı İki Değişkenli ϖ Dereceden Lacunary İstatistiksel Yakınsama

Öz

Belirsizlik içeren dizilerde yakınsama yaklaşımı, ilk olarak Pawlak tarafından belirsiz ve muğlak bilgileri ele almak amacıyla formüle edilen rough küme teorisinin gelişimiyle birlikte giderek daha fazla ilgi görmüştür. Bu temele dayanarak, Liu’nun rough dizilerin yakınsamasına ilişkin tanımı da dahil olmak üzere çeşitli genellemeler ortaya konmuştur. Bu çalışmada, rough yakınsama kavramı iki değişkenli dizilere genişletilerek, rough değişkenler için ϖ dereceden lacunary istatistiksel yakınsama adı verilen yeni bir yaklaşım sunulmaktadır. Bu yaklaşım, lacunary dizilerin düzensiz indeks yapısını rough iki değişkenli verilerin yapısıyla birleştirerek daha kapsamlı ve uyarlanabilir bir yakınsama çerçevesi sağlamaktadır. Önerilen yöntem ayrıca klasik toplamlanabilme (summability) teknikleriyle karşılaştırılmış ve karmaşık belirsiz veri yapılarıyla başa çıkmadaki potansiyel uygulamalarını ortaya koyan teorik sonuçlar aracılığıyla analiz edilmiştir.

Anahtar Kelimeler

• Lacunary istatistiksel yakınsama
• ϖ dereceden iki değişkenli istatistiksel yakınsama
• rough değişkenler

On the Bivariate Lacunary Statistical Convergence of Order ϖ in Rough Set Theory

Öz

The approach to convergence for sequences involving uncertainty has gained increasing attention with the development of rough set theory, originally formulated by Pawlak to address imprecise and vague information. Using this foundation as a basis, various generalizations have been introduced, including Liu's definition of the convergence of rough sequences. In this article we extend the notion of rough convergence to the concept of bivariate sequences, introducing a new concept of lacunary statistical convergence of order ϖ for rough variables. This approach integrates the irregular indexing of lacunary sequences with the structure of rough bivariate data, offering a more comprehensive and adaptable convergence framework. The proposed method is also compared with classical summability techniques, and its behavior is analyzed through theoretical results that demonstrate its potential applications in dealing with complex uncertain data structures.

Anahtar Kelimeler

• lacunary statistical convergence
• bivariate statistical convergence of order ϖ
• rough variables

Kaynakça

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