Complex interval-valued Fermatean fuzzy sets in E-waste recycling partners for human health and environment

This study introduces the concept of Complex Interval-Valued Fermatean Fuzzy Sets and presents a comprehensive investigation of their theoretical properties. The proposed framework extends the traditional Fermatean fuzzy set by incorporating complex-valued and interval-valued information, thereby enhancing its capability to represent uncertainty, ambiguity, and indeterminacy in complex decision-making environments. To strengthen the theoretical foundation, fundamental concepts and comparative measures are developed. In addition, essential set-theoretic operations such as union, intersection, complement, conjunction (“and”), and disjunction (“or”) are formally defined, along with illustrative examples and rigorous proofs of their properties. Furthermore, a Complex Interval-Valued Fermatean Fuzzy Weighted Averaging operator is proposed to aggregate decision information. The operator is shown to satisfy important properties, including idempotency, boundedness, and monotonicity, ensuring its reliability and consistency. To demonstrate the applicability and effectiveness of the proposed model, a multi-criteria decision-making problem is considered. The results illustrate that the proposed approach can effectively evaluate alternatives and determine their ranking under complex uncertain conditions, highlighting its potential for practical applications in decision-making problems.