A Conversion Framework from Complex Numbers to Complex q-Rung Orthopair Fuzzy Sets for Multi-Criteria Decision Making
Abstract: This paper introduces a novel conversion framework that systematically transforms complex numbers into Complex q-Rung Orthopair Fuzzy Sets (Cq-ROFS), thereby bridging classical complex analysis with modern fuzzy decision theory. By exploiting the polar representation z = r e^(iθ), we derive membership and non-membership amplitude functions that satisfy the q-rung orthopair constraint µ^q + ?^q ≤ 1 for any q ≥ 1. We establish key algebraic properties- closure, idempotency, commutativity, and associativity- and prove a Phase-Amplitude Consistency Theorem that guarantees information fidelity during conversion. A Complex q-Rung Orthopair Weighted Averaging (Cq-ROWA) operator is developed for aggregation, and a score-function-based ranking scheme is proposed. The framework is validated on a supplier-selection case study involving five alternatives and four criteria, demonstrating superior discrimination power compared with existing Cq-ROFS and Pythagorean fuzzy approaches. Sensitivity and comparative analyses confirm robustness across varying values of q.
Keywords: Complex q-Rung Orthopair Fuzzy Sets, Complex Numbers, Conversion Framework, Multi-Criteria Decision Making, Aggregation Operators, Supplier Selection
How to Cite?: Dr. Guddu Kumar, "A Conversion Framework from Complex Numbers to Complex q-Rung Orthopair Fuzzy Sets for Multi-Criteria Decision Making", Volume 15 Issue 10, October 2026, International Journal of Science and Research (IJSR), Pages: 148-150, https://www.ijsr.net/getabstract.php?paperid=SR26927215255, DOI: https://dx.doi.org/10.21275/SR26927215255