Topological Structure of Pawlak Approximation Spaces and Generalized Rough Sets

Abstract

The rough set theory is based on the foundation information systems. The structure of information systems is closely related to the equivalence relation, which is a special type of relation in mathematical sense. Rough set approximation is concerned with imperfect or vague information and taking the fundamental science center, which uses mathematics effectively. Approximation operators play an important role in constructing uncertainty. Beginning at this point, there is a connection between the approximation operators and the topology, which is an important branch of mathematics.  In this study, the similarities of basic topological concepts and concepts in rough set theory will be given comparatively. The generalization of the lower and upper approximation operators forming the dual pair in Pawlak approximation spaces and the relations between them will be examined.

Keywords

• Rough set,Approximation space,Lower approximation,Upper approximation,Generalized approxima-tion space

Pawlak Yaklaşım Uzaylarının Topolojik Yapısı ve Genelleştirilmiş Kaba Kümeler

Abstract

Kaba küme teorisinin temeli bilgi sistemlerine dayanır. Bilgi sistemlerinin yapısı matematiksel anlamda özel bir bağıntı türü olan denklik bağıntısı ile yakından ilişkilidir. Kaba küme yaklaşımı eksik ya da belirsiz bilgiyle ilgilenir ve temel bir bilim dalı olan matematiği merkezine alarak etkin bir şekilde kullanır. Belirsizliğin yapılandırılmasında yaklaşım operatörleri önemli rol üstlenirler. Tam bu noktadan başlayarak, yaklaşım operatörleri ve matematiğin önemli bir dalı olan topoloji arasında bağlantı kurulmaktadır. Bu çalışmada temel topolojik kavramlar ile kaba küme teorisinde yer alan kavramların benzerlikleri karşılaştırmalı olarak verilecektir. Pawlak yaklaşım uzaylarında dual çift oluşturan alt ve üst yaklaşım operatörlerinin genelleştirilmesi ve aralarındaki ilişkiler incelenecektir.

Keywords

• Kaba küme,Yaklaşım uzayı,Alt yaklaşım,Üst yaklaşım,Genelleştirilmiş yaklaşım uzayı

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