An investigation of filter, net, and proximity structures with a bipolar fuzzy soft approach

In this thesis, a novel definition of a bipolar fuzzy soft point is proposed, differing from the approach in the existing literature. Using this notion, the concepts of neighborhood and adherence point are introduced. A bipolar fuzzy soft filter structure is then defined, and its convergence properties are examined. Based on this structure, a multi-criteria group decision-making method is developed. Next, the idea of a bipolar fuzzy soft quasi coincidence is introduced, leading to the construction of a bipolar fuzzy soft net model. Also, the convergence of such nets is investigated, and their relationship with bipolar fuzzy soft filters is established. Furthermore, a bipolar fuzzy soft proximity structure is presented, and its connection with classical proximity is analyzed. Finally, the concept of a bipolar fuzzy soft cluster is given, and its relationships with both bipolar fuzzy soft filters and bipolar fuzzy soft proximity spaces are evaluated.