Soft Covering Based Rough Sets and Their Application

Soft rough sets which are a hybrid model combining rough sets with soft sets are defined by using soft rough approximation operators. Soft rough sets can be seen as a generalized rough set model based on soft sets. The present paper aims to combine the covering soft set with rough set, which gives rise to the new kind of soft rough sets. Based on the covering soft sets, we establish soft covering approximation space and soft covering rough approximation operators and present their basic properties. We show that a new type of the soft covering upper approximation operator is smaller than soft upper approximation operator. Also we present an example in medicine which aims to find the patients with high prostate cancer risk. Our data are 78 patients from Selçuk University Meram Medicine Faculty

Root Canal Morphology of Mandibular Primary Molars: A Micro-CT Study

Objectives: Frequency of typical and non-typical root and canal morphology of primary teeth, which in clinical practice cannot be detected using 2D radiographic images, should be known by clinicians to decrease failures arising from complexity of root canal morphologies. The aim of this in vitro study was to evaluate morphologic variations in mandibular primary molars’ root canal systems. Materials and Methods: Primary mandibular 1st (n=17) and 2nd (n=33) molars were scanned using micro-CT. 3D root models were obtained and root canal morphologies were evaluated according to a modified Vertucci classification. Type 1 and Type 4 canal morphologies were evaluated as ‘normal’ and all other types and ‘non-typical’ canal morphology were evaluated as ‘abnormal’ root canal morphology. Results: Most common root canal morphology among mandibular primary 1st molars were Vertucci Type 4 morphology for both mesial and distal roots (47% and 41.2% respectively), and non-typical morphology for both the mesial and distal roots (45.7% and 21.2% respectively) of mandibular primary 2nd molars. Conclusions: Wide range of morphologic variations and frequency of non-typical morphology could be seen especially among mandibular primary 2nd molars and use of disinfectant irrigants and root canal fillings with high antibacterial efficacies are important in order to decrease failures arising from these inaccessible areas

Decompositions of some forms of continuity

In this paper, αCN3 -sets [3] and αCN5 -sets [3] are introduced and characterizations of α-I -open [6], semi -I -open [6], αCN3 -and αCN5-sets are investigated. Also, new decompositions of α -I -continuity and semi -I -continuity are obtained using these sets.Bu çalışmada, αIN3 -[3] and αIN5 -[3] kümeleri verilecek, α - I - açık, semi - I - açık, αIN3 -ve αIN5 - kümelerinin karakterizasyonları incelenecektir. Bu kümelerden yararlanarak α -I - sürekli ve semi - I - sürekliliğin yeni ayrışımları da elde edilecektir

Decompositions of new classes of functions

In this paper, ?IN5-sets, SIN5 -sets, PIN5-sets, ßIN5-sets are introduced via idealization. Using these sets, new classes of generalizations of non-continuous functions are obtained and some of their properties are given. Also, decompositions of strongly ? - I-continuity, strongly ?-pre-I-irresoluteness, I-irresoluteness and strongly semi-ß - I-irresoluteness are established. © 2007 Elsevier Ltd. All rights reserved

Some new sets and decompositions of A I-R-continuity, α-I-continuity, continuity via idealization

Açıkgöz, Ahu ( Aksaray, Yazar )The concepts of I-R closed set, A I-R-set, α I M 1-set, α I M 2-set, α I N 1-set, α I N 2-set, α I N 3-set, α I N 4-set and α I N 5-set are introduced via idealization. New decompositions of some weaker forms of continuity are obtained by using these sets...

BULANIK b-I-SÜREKLİ FONKSİYONLAR ÜZERİNE

Bulanık ideal topolojik uzaylarda bulanık b-I-süreklilik ve b-I-açık küme kavramları araştırıldı ve bunların bazı özellikleri elde edildi. Ayrıca, kümeler ve fonksiyonların bazı diğer tiplerle ilişkisi çalışıldı

On Fuzzy δ-I-Open Sets and Decomposition of Fuzzy α-I-continuity

Abstract: We introduce the notions of fuzzy δ-I-open sets and fuzzy semi δ-I-continuos functions in fuzzy ideal topological space and investigate some of their properties. Additionaly, we obtain decompositions of fuzzy semi-I-continuous functions and fuzzy α-I-continuous functions by using fuzzy δ-I-open sets. Key words: Fuzzy δ-I-open sets, fuzzy semi δ-I-continuity, fuzzy α-I-continuity Bulanık Delta-I-Açık Kümeler ve Bulanık Alfa-I-Sürekliliğin Dağılımı Üzerine Özet: Bulanık ideal topolojik uzaylarda bulanık delta-I-açık küme ve bulanık yarı delta-I-sürekli fonksiyon kavramlarını tanımladık ve bunların bazı özelliklerini araştırdık. Ayrıca, bulanık delta-I-açık kümeleri kullanarak bulanık alfa-I-sürekli ve bulanık yarı-I-sürekli fonksiyonların ayrışımını elde ettik. Anahtar kelimeler: Bulanık delta-I-açık kümeler, bulanık yarı delta-I-süreklilik, bulanık alfa-I- süreklili

On fuzzy α-I-continuous and fuzzy α-I-open functions

WOS: 000268060100017Recently, El-Naschie has shown that the notion of fuzzy topology may be relevant to quantum particle physics in connection with string theory and E-infinity space time theory. In this paper, we Study the concepts of fuzzy alpha-I-continuity and fuzzy alpha-I-openness in fuzzy ideal topological spaces, and obtain several characterizations and some properties of these functions. Also, we investigate their relationship with other types of functions

On some strongly functions defined by α-open

WOS: 000265471400041In this paper is to introduce and investigate new classes of generalizations of non-continuous functions, obtain some of their properties and to hold decompositions of strong alpha-irresolute in topological spaces