Abstract
In this paper, the concept of a fuzzy soft point is redefined, and the definition of a fuzzy soft net in a fuzzy soft topological space is given. On this basis, the convergence of a fuzzy soft net is defined by using the Q-neighborhood theory, and the continuity of fuzzy soft mappings is characterized by the net. The obtained results demonstrate that the concepts proposed in this paper are very suitable and will provide powerful research tools for further research in this field.
Highlights
In 1965, Zadeh introduced the concept of fuzzy sets in his classic work [1]
In 1999, Molodtsov [2] introduced the theory of soft sets, which have been applied in several fields, including the smoothness of functions, game theory, Riemann integration, and the theory of probability [3]
In 2009, Kharal and Ahmad [8] studied the properties of fuzzy soft images and fuzzy soft inverse images of fuzzy soft sets
Summary
In 1965, Zadeh introduced the concept of fuzzy sets in his classic work [1]. In 1999, Molodtsov [2] introduced the theory of soft sets, which have been applied in several fields, including the smoothness of functions, game theory, Riemann integration, and the theory of probability [3]. It is clear that eorem 1(1) does not hold for the union of infinite fuzzy soft sets For this reason, the concept of quasi-coincidence is subsequently introduced. In the work by Roy and Samanta [20], a fuzzy soft point Fe over (U, E) was said to be quasi-coincident with FA ∈ FS(U, E) if μFe(x) +μeFA (x) > 1 for some x ∈ U. A net {S(δ), δ ∈ Δ} in (U, E, τ) is said to be convergent to a point ξ if S is eventually quasi-coincident with each Q-neighborhood of ξ In this case, ξ is called the limit of S and is denoted by limS(δ)
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