Moore-Smith Convergence In Fuzzy Soft Topological Spaces And Its Applications

Since 2011,Tanay and Kandemir first proposed the definition of fuzzy soft topological spaces(Topological structure of fuzzy soft sets.Computer and Mathematics with Applications,2011,61:2952-2957),more and more scholars have studied the fuzzy soft topological space,and have achieved fruitful research results.Some important conclusions of general topology have been extended to fuzzy soft topological spaces,and some unique properties of fuzzy soft topological spaces have also been revealed.Moore-Smith convergence theory is an important part of general topology,and is also an important tool to study general topology.Therefore,it is of great significance to establish the Moore-Smith convergence theory in fuzzy soft topological spaces.The main purpose of this paper is to carry out a relatively systematic research on this,the main content includes:In the first part,the fuzzy soft point(Fuzzy Soft Filter Convergence.Filomat,2018,32(9):3325-3336)defined by Ibedou and Abbas is further studied.Some basic properties of"belonging"and"quasi-coincidence"between fuzzy soft points and fuzzy soft sets are given.On this basis,the properties of"neighborhood"and"Q-neighborhood"of fuzzy soft points are discussed.In the second part,the fuzzy soft net is constructed by using fuzzy soft points,and the concept of convergence and limit of fuzzy soft nets is defined.By using the convergence of fuzzy soft nets,the closure of fuzzy soft sets,the T₂ separation of fuzzy soft topological spaces and the compactness of fuzzy soft sets are described,and the continuity of fuzzy soft mapping is described.The corresponding conclusions from general topology are extended to fuzzy soft topological spaces.The concept of convergence of the fuzzy soft mapping net is put forward,and its characterization is given.In the third part,the convergence of the fuzzy soft filter is defined by using the method of Q-neighborhood.The relationship between fuzzy soft nets and fuzzy soft filters is studied.It is proved that fuzzy soft nets and fuzzy soft filters may be generated each other,and their convergence and limit are consistent.The open set,the closure of the fuzzy soft set,the T₂ separation of the fuzzy soft topological spaces and the continuity of the fuzzy soft mapping are described by the convergence of the fuzzy soft filter.In the fourth part,an applied mathematical model of the fuzzy soft set in medical diagnosis is established,which expands the application field of the fuzzy soft set theory.In this paper,the Moore-Smith convergence theory of fuzzy soft topological spaces is preliminarily constructed,which further enriches the theory of fuzzy soft topological spaces,and provides a powerful research tool for the further development of this field.