Browsing by Author "Dalan Yildirim, Esra"

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Citation - WoS: 1
Citation - Scopus: 1
Different types of approximation operators on Gn-CAS via ideals
(University of Nis, 2024) Oya Bedre Özbakir; Esra Dalan Yildirim; Aysegül Çaksu Güler; Bedre Özbakir, Oya; Yildirim, Esra Dalan; Guler, Aysegul Caksu; Dalan Yildirim, Esra; Çaksu Güler, Aysegül; Ozbakir, Oya Bedre
A mathematical approach to dealing with the problems of ambiguity and indeterminacy in knowledge is called a rough set theory. It begins by using an equivalence relation to divide the universe into parts. Numerous generalized rough set models have been developed and investigated to increase their adaptability and extend their range of applications. In this context we introduce new generalized rough set models that are inspired by covering-based rough sets and ideals. In this paper lower and upper approximations of new types of covering rough sets based on j-neighborhoods complementary j-neighborhoods and j-adhesions are defined via ideals. The main features of these approximations are examined. The relationships among them are given by various examples and propositions. Some comparisons between our methods and others’ methods such as Abd El-Monsef et al.’s method [2] and Nawar et al.’s method [22] are given. A practical example is given to illustrate one of our methods is more precise. © 2024 Elsevier B.V. All rights reserved.
Citation - WoS: 2
Citation - Scopus: 1
MINIMAL INTUITIONISTIC OPEN AND MAXIMAL INTUITIONISTIC OPEN SETS
(YILDIZ TECHNICAL UNIV, 2020) Esra Dalan Yildirim; Aysegul Caksu Guler; Oya Bedre Ozbakir; Bedre Özbakir, Oya; Dalan Yildirim, Esra; Çaksu Güler, Ayşegül
In intuitionistic topological space we introduce the concepts of minimal intuitionistic open and maximal intuitionistic open sets. Also we give some of their basic properties. Regarding these sets we introduce and study some generalizations of intuitionistic continuous functions.
Citation - WoS: 13
Citation - Scopus: 12
New Topological Approaches to Rough Sets via Subset Neighborhoods
(WILEY, 2022) Esra Dalan Yildirim; Yildirim, Esra Dalan; Dalan Yildirim, Esra
This paper aims to obtain new types of approximations by using topological concepts. Firstly different kinds of topologies are generated by subset neighborhoods and relationships between them are studied. Then j-subset approximations based on these topologies are introduced and their basic properties are examined. In addition to this S-j-near open and theta beta(Sj)-open sets are defined and the connections among them are given. Later new approximations are presented with the help of the aforementioned sets and their main properties are investigated. Furthermore the proposed approximations are compared both with themselves and with the previous one. From this it is shown that the approximations based on theta beta(Sj)-open sets are more accurate than those based on S-j-open and S-j-near open sets under arbitrary binary relation and than those based on j-open sets under similarity relation. Finally a real-life problem related to COVID-19 is addressed to highlight the importance of applying the proposed approximations.