Intuitionistic Fuzzy Sets with Fuzzy Choquet Integrals over Fuzzy Differential Equations

The dual nature of uncertainty, which encompasses both vagueness and hesitation, is frequently not captured by conventional fuzzy systems. In the context of fuzzy differential equations (FDEs), this paper presents a sophisticated mathematical framework that combines intuitionistic fuzzy sets (IFSs) and fuzzy choquet integrals. By adding degrees of membership, non-membership, and hes- itation, IFSs expand on the traditional fuzzy paradigm. Meanwhile, the Fuzzy Choquet Integral al- lows for the aggregation of interdependent data, going beyond the constraints of additive measures. We show that our method can be applied to dynamic systems, develop a generalized solution the- ory for fuzzy differential equations under intuitionistic uncertainty, and provide simulation-based validations. The framework creates new opportunities in domains like finance, health systems, and environmental modelling where complicated, ambiguous, and hesitant information predominates.