Intuitionistic fuzzy topological operators via controlled sets

Topological concepts are widely used in the mathematical modeling of spatial objects with uncertain boundaries. Determining suitable operators for the interior, closure, and boundary is one of the main problems that researchers are interested in. Therefore, fuzzy topological and intuitionistic fuzzy topological operators have been examined in such problems. Different methods are used to fuzzify the elements of a region under study. However, determining the non-membership degrees of a region based on its membership degrees remains a separate problem. In this study, this problem is addressed by applying controlled set theory. The resulting intuitionistic fuzzy representations are then processed using intuitionistic fuzzy pre-interior and pre-closure operators to examine the interior, closure, and boundary characteristics of the spatial regions affected by Mikania micrantha. The results show how the proposed method changes these values for different parameter settings and offers a new way to model uncertainty in spatial regions.