Riemann Integral Based Cross-Entropy for Continuous Function Valued Intuitionistic Fuzzy Sets and an Extended CODAS

Continuous function valued intuitionistic fuzzy sets (CFIFSs) offer a notable advancement, departing from rigid numerical representations. Our contribution includes a novel cross-entropy measure based on the Riemann integral for CFIFSs, gauging differentiation between two sets. Recognizing fuzzy set and entropy diversity, we propose a criteria weighting process in multi-criteria decision making (MCDM) applicable across various types of fuzzy sets. This innovative approach integrates into the extended Combinative Distance-Based Assessment (CODAS) method, a MCDM method, designed for continuous function valued intuitionistic fuzzy environments for the first time. Grounding these theoretical advancements practically, we apply the extended CODAS method to a new real-world investment strategies assessment problem. A comprehensive sensitivity analysis addresses financial market complexities, providing insights into our approach’s robustness.