Topological Structure of Pawlak Approximation Spaces and Generalized Rough Sets

Year 2018, Volume: 9 Issue: Ek (Suppl.) 1, 305 - 315, 14.12.2018

Sadık Bayhan , Mehmet Şen

https://doi.org/10.29048/makufebed.444556

Cited By: 1

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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