Yazar "Aydin, Tugce" seçeneğine göre listele

Listeleniyor 1 - 3 / 3
  • [ X ]
    Öğe
    Interval-valued intuitionistic fuzzy parameterized interval-valued intuitionistic fuzzy soft matrices and their application to performance-based value assignment to noise-removal filters
    (Springer Heidelberg, 2022) Aydin, Tugce; Enginoglu, Serdar
    Recently, the concept of interval-valued intuitionistic fuzzy parameterized interval-valued intuitionistic fuzzy soft sets (d-sets) has successfully modelled decision-making problems, where the parameters and alternatives have interval-valued intuitionistic fuzzy values. In the present study, to be able to transfer a large number of data in such problems to a computer environment and to process them therein, we define the concept of interval-valued intuitionistic fuzzy parameterized interval-valued intuitionistic fuzzy soft matrices (d-matrices). Moreover, we introduce operations, such as union, intersection, and AND/OR/ANDNOT/ORNOT-products, on this concept and study some of their basic properties. We then configure the state-of-the-art soft decision-making (SDM) method constructed by d-sets to render it operable in d-matrices space. Furthermore, we apply it to a performance-based value assignment (PVA) to the seven noise removal filters to compare their ranking orders. Thereafter, we conduct a comparative analysis of the configured method with five state-of-the-art SDM methods. Finally, we discuss d-matrices for future research.
  • [ X ]
    Öğe
    Investigating Concepts in Soft Topological Structures through Subspaces
    (World Scientific Publ Co Pte Ltd, 2025) Arslan, Burak; Aydin, Tugce
    Following the study of Molodtsov on soft topological structures in 2015, this study discusses the concepts in soft topological structures through subspaces, investigates some of their crucial properties, and provides their characterizations. To ensure consistency with Molodtsov's framework, this paper defines the tau-neighborhood in a subspace S subset of X of any x is an element of S as tau(x) boolean AND S, noting that his definition of the tau-neighborhood in X of any x is an element of X is tau(x), which equals tau(x) boolean AND X. Moreover, this study researches some of the relations between concepts in a space and their correspondences in subspaces. Besides, it explores whether being tau-C-, tau-T-, tau-B-, and tau-I-soft discrete and indiscrete topologies is hereditary or not. Finally, this study handles if further research concerning these aspects is needed.
  • [ X ]
    Öğe
    Refining and extending the theoretical foundations of r-near topology
    (Amer Inst Mathematical Sciences-Aims, 2025) Aydin, Tugce
    The present paper aims to refine and extend the theoretical foundations of r-near topology. For this reason, it first redefines the concept of r-near neighborhoods to address inconsistencies in previous studies and clarifies the relationship between r-near open neighborhoods and r-near closure. This study then elaborates on the fundamental properties of r-near closed sets, r-near interior, rnear closure, and r-near neighborhoods. Subsequently, it introduces four novel concepts within rnear topology: r-near accumulation points, r-near isolated points, r-near exterior points, and rnear boundary points. Furthermore, this study explores some of their basic properties and provides illustrative examples regarding the aforesaid concepts. Additionally, it researches the relationships between r-near interior, r-near closure, and r-near exterior in the r-near topological spaces and their classical topological counterparts. Lastly, the study highlights the theoretical significance of r-near topology and suggests potential directions for further research.