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  • Küçük Resim Yok
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    Bipolar fuzzy soft filter and its application to multi-criteria group decision-making
    (Univ Nis, Fac Sci Math, 2025) Demir, Izzettin; Saldamli, Murat; Okurer, Merve
    The convergence theory is not only a basic theory of topology but also has wide applications in other fields including information technology, economics and computer science. The convergence of filters is also one of the most important tools used in topology to characterize certain concepts such as the closure of a set, continuous mapping, Hausdorff space and so on. Besides, multi-criteria group decision making (for short MCGDM) aims to make unanimous decision based on different criterions to find the most accurate solution of real world problems and so that the MCGDM plays a very important role in our daily life problems. In this paper, taking into account all of these, we firstly introduce the notion of a bipolar fuzzy soft filter (for short BFS-filter) by using bipolar fuzzy soft sets (for short BFS-sets). Also, we define the idea of an ultra BFS-filter and establish some of its properties. Moreover, we investigate the convergence of BFS-filters in a bipolar fuzzy soft topological space (BFS-topological space) with related results. After introducing the concepts of a bipolar fuzzy soft continuity (BFS-continuity) and a bipolar fuzzy soft Hausdorfness (BFS-Hausdorffness), with the aid of the convergence of BFS-filters, we discuss the characterizations of these concepts. Next, we develop a multi-criteria group decision-making method based on the BFS-filters to deal with uncertainties in our daily life. Finally, we present a numerical example to make a decision for selection of best alternative.
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    N-esnek topolojik uzayların bazı özellikleri
    (Düzce Üniversitesi, 2023) Okurer, Merve; Demir, İzzettin
    Bu tez çalışmasında, Riaz ve diğ. [1] tarafından verilen N-esnek kümelerin topolojik yapısı çalışılmaya devam edilmiştir. İlk olarak, Demir [2] tarafından önerilen N-esnek kümelerin tümleyen işlemi kullanılarak N-esnek kapalı kümeler yeniden tanımlanmış ve bu kümelerin temel özellikleri incelenmiştir. Daha sonra, bir N-esnek sürekli dönüşüm kavramı verilerek bu dönüşüm ve bir N-esnek kapalı küme arasındaki ilişkiler araştırılmıştır. Ayrıca, N-esnek dönüşümler ailesi yardımıyla bir başlangıç N-esnek topolojisi elde edilmiştir. Bunun yanı sıra, yeni bir N-esnek topolojik alt uzay kavramı tanımlanmış ve bu kavramın önemli özellikleri çalışılmıştır. Son olarak, elde edilen sonuçların daha iyi anlaşılabilmesi için bazı örnekler gösterilmiştir.
  • Küçük Resim Yok
    Öğe
    A new approach to n-soft topological structures
    (Rocky Mt Math Consortium, 2023) Demir, Izzettin; Okurer, Merve
    We study the topological structure of N-soft sets given by Riaz et al. (J. Intell. Fuzzy Syst. 36:6 (2019), 6521-6536). Firstly, we redefine N-soft closed sets using the complement operation of N-soft sets proposed in (Math. Methods Appl. Sci. 44:8 (2021), 7343-7358) and investigate their basic properties. Then, we introduce the concept of an N-soft continuous mapping and also obtain the initial N-soft topology determined by a family of N-soft mappings. Furthermore, we establish a new concept of N-soft topological subspace and analyze some related properties of this concept. Finally, we present some examples to better understand the defined concepts.