Yazar "Saldamli, Murat" seçeneğine göre listele

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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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    CONVERGENCE THEORY OF BIPOLAR FUZZY SOFT NETS AND ITS APPLICATIONS
    (Rocky Mt Math Consortium, 2024) Demir, Izzettin; Saldamli, Murat
    In a different way than in the literature, we define the concept of a quasicoincident using the bipolar fuzzy soft points we previously proposed (2021) and investigate its basic properties. We introduce the notion of a bipolar fuzzy soft net (for short BFS-net) and give convergence of the BFS-nets in a bipolar fuzzy soft topological space with useful results. We show how a BFS-net is derived from a BFS-filter and obtain a characterization about bipolar fuzzy soft Hausdorff spaces. Based on the idea of quasicoincident, we give a new kind of bipolar fuzzy soft continuity and analyze its relationship with the BFS-nets. We put forward the idea of compactness in the setting of bipolar fuzzy soft sets and characterize it through the contribution of the BFS-subnets. Finally, we present some examples to illustrate the defined concepts.
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    Proximity structures via the class of bipolar fuzzy soft sets
    (Univ Nis, Fac Sci Math, 2025) Saldamli, Murat; Demir, I. zzettin
    In this paper, we first define the concept of a proximity with the help of bipolar fuzzy soft sets and establish some of its properties. Then, we demonstrate the process of generating a bipolar fuzzy soft topology with the aid of a bipolar fuzzy soft proximity (for short BFS-proximity). Moreover, we give a new definition of bipolar fuzzy soft neighborhood based on BFS-proximity, enabling an alternative framework for analyzing the notion of BFS-proximity. Next, by using a family of BFS-proximities, we present the initial BFS-proximity structure. Finally, taking into account the proximity structure in the classical set theory, we derive a BFS-proximity structure and study on its related results.