Affiliations: [a] College of Mathematics and Information Science, Shaanxi Normal University, Xi’an, P.R. China
| [b] Department of Mathematics, Faculty of Science, Al-Azhar University, Assiut, Egypt
| [c] School of Mathematics and Statistics, Yulin University, Yulin, China
| [d] College of Information Science and Technology, Hainan Normal University, Haikou
Correspondence:
[*]
Corresponding author. Sheng-Quan Ma, College of Information Science and Technology, Hainan Normal University, Haikou 571158. E-mail: mashengquan@163.com.
Abstract: The aim of this paper is to introduce and study the concepts of fuzzifying semipre-θ-neighborhood system of a point, fuzzifying semipre-θ-closure of a set, fuzzifying semipre-θ-interior of a set, fuzzifying semipre-θ-open sets and fuzzifying semipre-θ-closed sets in fuzzifying topological spaces, and investigate some of their basic properties. Also, we present two types of functions in a fuzzifying topological spaces called fuzzifying strong β -irresolute and fuzzifying weak β -irresolute functions. The interrelations of these functions with the parallel existing allied concepts are established. Further, several characterizations of these functions along with different conditions for their existence are obtained.
Keywords: Łukasiewicz logic, fuzzifying topology, fuzzifying semipre-θ-closure of a set, fuzzifying semipre-θ-closed set, fuzzifying strong semipre-irresolute function
