Soft ditopolojik-fuzzy soft topolojik uzaylar ve tıpta uygulamalar
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Dosyalar
Tarih
2014-05-16
Yazarlar
Dergi Başlığı
Dergi ISSN
Cilt Başlığı
Yayıncı
Selçuk Üniversitesi Fen Bilimleri Enstitüsü
Erişim Hakkı
info:eu-repo/semantics/openAccess
Özet
Bu tezde belirsizliğe farklı bir yaklaşım olarak Molodtsov tarafından geliştirilmiş soft kümeler ile topolojik yapılar ve soft ile fuzzy kümelerin bir araya getirilmesiyle oluşturulmuş melez bir model olan fuzzy soft kümeler ile fuzzy topolojik kavramlar arasındaki ilişkiler incelenmiştir. Ayrıca soft kümeleri kullanarak prostat kanserini teşhis etmek için bir uzman sistem tasarlanmıştır. Tezin ikinci bölümünde verilen soft ditopolojik uzaylar birbirinden bağımsız olarak tanımladığımız soft açıklarla ilgili özelliklerin bulunduğu soft topolojik uzaylar ve soft kapalılarla ilgili özelliklerin bulunduğu soft kotopolojik uzaylardan elde edilmiştir. Soft topoloji ve soft kotopolojilerde sırasıyla τ-soft süreklilik, τ-soft ayırma aksiyomları, κ-soft süreklilik ve κ-soft ayırma aksiyomları verilmiştir. Bu kavramlar soft ditopolojik uzaylarda da incelenmiştir. Tezin üçüncü bölümünde fuzzy soft topolojik uzaylar incelenmiş, bu uzaylarda komşuluk, Q-komşuluk, alt uzay, fuzzy soft iç ve kapanış noktaları gibi kavramlar verilmiş ve quasi ayırma aksiyomları çalışılmıştır. Tezin dördüncü bölümünde son yıllarda erkeklerde sıkça görülen prostat kanserinin teşhisi için soft kümelerden faydalanarak elde ettiğimiz ve soft uzman sistemler olarak adlandırdığımız bir tahmin sistemi tasarlanmıştır. Tasarladığımız bu sistem, hastanın prostat spesifik antijen (PSA), yaş ve prostat hacmi (PV) verilerini kullanarak prostat kanseri olma riski yüzdesini hesaplayan bir programdır. Hesaplanan bu yüzde ile uzman doktora hasta hakkında bir fikir vermek amaçlanmıştır. Bu yolla maliyeti yüksek olan ve hastada bazı fiziksel zararlara neden olabilen biyopsi işlemini gereksiz yere uygulamak engellenebilir. Tasarladığımız sistemin prostat kanseri teşhisi için kullanılması önerilir.
In this thesis, both the relation between soft set, defined by Molodtsov as a new method for vagueness, and its corresponding topological structures and the relation between fuzzy soft sets, a combination of fuzzy and soft sets, and its correponding fuzzy topological structures are investigated. Moreover by using soft sets an expert system to diagnose the prostate cancer is devised. In the second section, soft ditopology is defined as a synthesis of soft topology which is used to describe soft openness-type properties of a space and the soft cotopology which deals with its soft closedness-type properties. τ-soft continuity, τ-soft seperation axioms and κ-soft continuity, κ-soft seperation axioms are investigated in soft topological and soft cotopological spaces, respectively. These concepts are also studied in soft ditopological spaces. In the third section fuzzy soft topological spaces are given and the concepts as neihgborhood, Q-neighborhood, relative fuzzy soft topology, fuzzy soft interior and closure points are defined and the quasi seperation axioms are investigated. In the fourth section a prediction system, called soft expert system, is designed to diagnose the prostate cancer which is the second most common cause of cancer death among men. In our system the percantage of prostate cancer risk is obtained by using the data of prostate specific antigen, age and prostate volume. We aim to help to the doctor to decide whether the biopsy is necessary for a patient. It is known that biopsy has high cost and sometimes can lead some complications for patients. For this reason it is important to reduce the number of biopsy operations. Since our system prevents unnecessary biopsy operations, it is suggested to use soft expert system to diagnose the prostate cancer.
In this thesis, both the relation between soft set, defined by Molodtsov as a new method for vagueness, and its corresponding topological structures and the relation between fuzzy soft sets, a combination of fuzzy and soft sets, and its correponding fuzzy topological structures are investigated. Moreover by using soft sets an expert system to diagnose the prostate cancer is devised. In the second section, soft ditopology is defined as a synthesis of soft topology which is used to describe soft openness-type properties of a space and the soft cotopology which deals with its soft closedness-type properties. τ-soft continuity, τ-soft seperation axioms and κ-soft continuity, κ-soft seperation axioms are investigated in soft topological and soft cotopological spaces, respectively. These concepts are also studied in soft ditopological spaces. In the third section fuzzy soft topological spaces are given and the concepts as neihgborhood, Q-neighborhood, relative fuzzy soft topology, fuzzy soft interior and closure points are defined and the quasi seperation axioms are investigated. In the fourth section a prediction system, called soft expert system, is designed to diagnose the prostate cancer which is the second most common cause of cancer death among men. In our system the percantage of prostate cancer risk is obtained by using the data of prostate specific antigen, age and prostate volume. We aim to help to the doctor to decide whether the biopsy is necessary for a patient. It is known that biopsy has high cost and sometimes can lead some complications for patients. For this reason it is important to reduce the number of biopsy operations. Since our system prevents unnecessary biopsy operations, it is suggested to use soft expert system to diagnose the prostate cancer.
Açıklama
Anahtar Kelimeler
Fuzzy soft quasi ayırma aksiyomları, Fuzzy soft quasi seperation axioms, Fuzzy soft topolojik uzaylar, Fuzzy soft topological spaces, Prostat kanseri, Prostate cancer, Soft ayırma aksiyomları, Soft ditopological spaces, Soft ditopolojik uzaylar, Soft expert system, Soft remote komşuluk, Soft remote neighborhood, Soft uzman sistem, Soft seperation axioms
Kaynak
WoS Q Değeri
Scopus Q Değeri
Cilt
Sayı
Künye
Dizman, T. H. (2014). Soft ditopolojik-fuzzy soft topolojik uzaylar ve tıpta uygulamalar. Selçuk Üniversitesi, Yayımlanmış doktora tezi, Konya.
