Bipolar fuzzy soft filter and its application to multi-criteria group decision-making

Abstract

The convergence theory not only is 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 bestalternative.