This paper investigates bipolar-valued hesitant fuzzy generalized semi-precontinuous mappings in bipolar-valued hesitant fuzzy topological spaces. It extends fuzzy topology theory to hesitant fuzzy information so that more flexible uncertainty treatment in decision-making, AI, and modeling can be achieved. The bipolar-valued hesitant fuzzy set can represent positive and negative membership grades without hesitation and thereby more capable of handling uncertainty and fuzzy data in realworld problems. We establish bipolar-valued hesitant fuzzy generalized semi-precontinuous mappings and their relation to other continuity forms such as semi-continuity and pre-continuity. New theorems shed light on these mappings, with the help of numerical examples. We also suggest applications in fuzzy decision analysis, computational intelligence, medical diagnosis, and engineering optimization. This research enhances fuzzy set theory by the incorporation of hesitant fuzzy logic and bipolar-valued topological structures. The findings are rigorous and provide the possibility of mappings in complicated topological spaces, further allowing the study of generalized fuzzy continuity and application in a variety of fields.
K. Kavitha (Thu,) studied this question.