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    A fixed point theorem on soft G-metric spaces
    (Int Scientific Research Publications, 2016) Guler, Aysegul Caksu; Yildirim, Esra Dalan; Ozbakir, Oya Bedre
    We introduce soft G-metric spaces via soft element. Then, we obtain soft convergence and soft continuity by using soft G-metric. Also, we prove a fixed point theorem for mappings satisfying sufficient conditions in soft G-metric spaces. (C)2016 All rights reserved.
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    Novel Graph Neighborhoods Emerging from Ideals
    (MDPI, 2023) Guler, Aysegul Caksu; Balci, Mehmet Ali; Batrancea, Larissa M.; Akguller, Omer; Gaban, Lucian
    Rough set theory is a mathematical approach that deals with the problems of uncertainty and ambiguity in knowledge. Neighborhood systems are the most effective instruments for researching rough set theory in general. Investigations on boundary regions and accuracy measures primarily rely on two approximations, namely lower and upper approximations, by using these systems. The concept of the ideal, which is one of the most successful and effective mathematical tools, is used to obtain a better accuracy measure and to decrease the boundary region. Recently, a generalization of Pawlak's rough set concept has been represented by neighborhood systems of graphs based on rough sets. In this research article, we propose a new method by using the concepts of the ideal and different neighborhoods from graph vertices. We examine important aspects of these techniques and produce accuracy measures that exceed those previously = reported in the literature. Finally, we show that our method yields better results than previous techniques utilized in chemistry.
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    ON MENGER SPACES VIA IDEALS
    (Central Missouri State Univ, Dept Mathematics & Computer Science, 2021) Yildirim, Esra Dalan; Guler, Aysegul Caksu; Ozbakir, Oya Bedre
    In this paper, we define J-Menger, J-star Menger, and J-strongly star Menger spaces using ideals, and give their relations to related spaces. We also investigate some properties of them. Finally, we show that the concepts of J-Menger, J-star Menger, and J-strongly star Menger are equivalent in the class of paracompact spaces.
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    Rough approximations based on different topologies via ideals
    (Scientific And Technological Research Council Turkey, 2022) Guler, Aysegul Caksu; Yildirim, Esra Dalan; Ozbakir, Oya Bedre
    In this paper, we generalize the notations of rough sets based on the topological space. Firstly, we produce various topologies by using the concept of ideal, Cj -neighbourhoods and Pj -neighbourhoods. When we compare these topologies with previous topologies, we see that these topologies are more general. Then we introduce new methods to find the approximations by using these generated topologies. When we compare these methods with the previous methods, we see that these methods are more accurate.