Z-Continuous maps in Fermatean fuzzy topological spaces and its application

Abstract

In this paper, we undertake a detailed study of various types of functions in Fermatean fuzzy topological spaces, namely Fermatean fuzzy Z-continuous, Fermatean fuzzy Z-irresolute, strongly Fermatean fuzzy Z-continuous, and perfectly Fermatean fuzzy Z-continuous functions. We present rigorous definitions and characterizations of these functions, explore their interrelationships, and establish several fundamental properties supported by illustrative examples. Furthermore, we demonstrate the practical significance of the proposed concepts by developing a real-life decision-making application based on entropy measures defined over Fermatean fuzzy sets, thereby showcasing their potential in handling uncertainty and imprecision in complex problem-solving scenarios.