The nearest point problems in fuzzy quasi-normed spaces

Motivated by the fact that the fuzzy quasi-normed space provides a suitable framework for complexity analysis and has important roles in discussing some questions in theoretical computer science, this paper aims to study the nearest point problems in fuzzy quasi-normed spaces. First, by using the theory of dual space and the separation theorem of convex sets, the properties of the fuzzy distance from a point to a set in a fuzzy quasi-normed space are studied comprehensively. Second, more properties of the nearest point are given, and the existence, uniqueness, characterizations, and qualitative properties of the nearest points are obtained. The results obtained in this paper are of great significance for expanding the application fields of optimization theory.