Soft topolojik uzaylar üzerine ve soft örtü tabanlı rough kümelerin tıp alanında uygulaması
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Dosyalar
Tarih
2015-07-14
Yazarlar
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Yayıncı
Selçuk Üniversitesi Fen Bilimleri Enstitüsü
Erişim Hakkı
info:eu-repo/semantics/openAccess
Özet
Bu tezin amacı; bazı regüler genelleştirilmiş kapalı küme çeşitlerini soft topolojik uzaylarda, supra soft topolojik uzaylarda ve soft topolojik uzaylarda bir soft ideal kavramına dayanarak incelemektir. Ayrıca soft rough kümelerin genelleştirilmesi olan soft örtü tabanlı rough kümeleri tanımlamak ve bu kümelerin, tıp alanında hastalık teşhisinde kullanılan bir uygulamasını vermektir. Bu tez beş bölümden oluşmaktadır. Birinci bölümde; tezde kullanılan kavramların literatür bilgileri kısaca verilmiştir. İkinci bölümde; belirsizlik için iki farklı matematiksel yaklaşım olarak önerilen rough küme ve soft küme teorileri ile ilgili bilinen temel kavramlar ve bazı özellikler verilmiştir. Üçüncü bölümde; klasik topolojik uzaylardan daha genel olan soft topolojik uzaylar ve özellikleri hatırlatılmıştır. Soft topolojik uzaylarda daha önce tanımlanmış olan soft genelleştirilmiş kapalı kümeler ve soft regüler genelleştirilmiş kapalı kümelerden daha zayıf olan soft genelleştirilmiş pre-regüler kapalı kümeler ve özellikleri incelenmiştir. Ayrıca soft regüler genelleştirilmiş kapalı kümeler, soft ideal kavramına dayanılarak yeniden tanımlanmış ve özellikleri araştırılmıştır. Dördüncü bölümde; soft topolojik uzaylardan daha genel olan supra soft topolojik uzay kavramı verilmiş ve bu uzaylarda supra soft regüler genelleştirilmiş kapalı kümeler ve özellikleri araştırılmıştır. Ayrıca karşıt örnekler verilerek soft regüler genelleştirilmiş kapalı kümelerin bazı özelliklerinin supra soft topolojik uzaylarda sağlanmadığı gösterilmiştir. Son bölümde; rough kümeler ve soft örtü kümeler kullanılarak soft örtü yaklaşım uzayı elde edilmiştir. Soft rough kümelerin genelleştirilmesi olan soft örtü tabanlı rough kümeler ve çeşitleri incelenmiş, bu kümelerin temel özellikleri ve topolojik özellikleri de araştırılmıştır. Ayrıca soft örtü tabanlı rough kümeler; biyopsi gerekliliğini belirleyen ve doktorlara kanser riskinin sıralamasını veren bir metod ile birlikte kullanılmış ve sonuç olarak biyopsi yapılan hasta sayısı azaltılmıştır.
The aim of this thesis is to examine some kinds of regular generalized closed sets in soft topological spaces, supra soft topological spaces and soft topological spaces depending on a concept of soft ideal. The thesis also to define soft covering based rough sets, which is an extension of the concept of soft rough sets, and to give an application which used in medicine for disease diagnosis. This thesis consists of five sections. In the first chapter, the literature of notions that are used in this thesis is briefly given. In the second chapter, some basic concepts and properties related to rough set and soft set theories, which proposed as two different mathematical approaches for vagueness, are given. In the third chapter, soft topological spaces, which are more general than the classical topological spaces and their properties, are recalled. Soft generalized pre-regular closed sets, which are weaker than the soft generalized closed sets and soft regular generalized closed sets that are defined in soft topological spaces before, and their properties are examined. Moreover, soft generalized regular closed sets are redefined depending on a concept of soft ideal and their properties are investigated. In the fourth chapter, supra soft topological spaces, which are more general than the soft topological spaces, are given and properties of supra soft regular generalized closed sets are investigated in these spaces. Also, by giving counterexamples it is shown that some properties of soft regular generalized closed sets are not provided in supra soft topological spaces. In the last chapter, soft covering approximation space is obtained by using the rough sets and soft covering sets. Some types of soft covering based rough sets, which is an extension of the concept of soft rough sets and basic and topological properties of these sets are investigated. Besides, soft covering based rough sets are used together with a method which determines the necessity of biopsy and gives to doctors a range of the risk of cancer. Consequently, the number of patients that are biopsied is reduced.
The aim of this thesis is to examine some kinds of regular generalized closed sets in soft topological spaces, supra soft topological spaces and soft topological spaces depending on a concept of soft ideal. The thesis also to define soft covering based rough sets, which is an extension of the concept of soft rough sets, and to give an application which used in medicine for disease diagnosis. This thesis consists of five sections. In the first chapter, the literature of notions that are used in this thesis is briefly given. In the second chapter, some basic concepts and properties related to rough set and soft set theories, which proposed as two different mathematical approaches for vagueness, are given. In the third chapter, soft topological spaces, which are more general than the classical topological spaces and their properties, are recalled. Soft generalized pre-regular closed sets, which are weaker than the soft generalized closed sets and soft regular generalized closed sets that are defined in soft topological spaces before, and their properties are examined. Moreover, soft generalized regular closed sets are redefined depending on a concept of soft ideal and their properties are investigated. In the fourth chapter, supra soft topological spaces, which are more general than the soft topological spaces, are given and properties of supra soft regular generalized closed sets are investigated in these spaces. Also, by giving counterexamples it is shown that some properties of soft regular generalized closed sets are not provided in supra soft topological spaces. In the last chapter, soft covering approximation space is obtained by using the rough sets and soft covering sets. Some types of soft covering based rough sets, which is an extension of the concept of soft rough sets and basic and topological properties of these sets are investigated. Besides, soft covering based rough sets are used together with a method which determines the necessity of biopsy and gives to doctors a range of the risk of cancer. Consequently, the number of patients that are biopsied is reduced.
Açıklama
Anahtar Kelimeler
Soft topolojik uzay, Soft genelleştirilmiş pre-regüler kapalı kümeler, Soft ideale bağlı soft regüler genelleştirilmiş kapalı kümeler, Supra soft regüler genelleştirilmiş kapalı kümeler, Soft rough kümeler, Soft örtü tabanlı rough kümeler, Soft topological space, Soft generalized pre-regular closed sets, Soft regular generalized closed sets with respect to a soft ideal, Supra soft regular generalized closed sets, Soft rough sets, Soft covering based rough sets
Kaynak
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Künye
Ergül, Z. G. (2015). Soft topolojik uzaylar üzerine ve soft örtü tabanlı rough kümelerin tıp alanında uygulaması. Selçuk Üniversitesi, Yayımlanmış doktora tezi, Konya.
