A Circular Pythagorean Fuzzy Credibility Graph (CPyF-CG) Based TOPSIS Approach for MADM and its Application in Renewable Energy

Abstract

Multi-attribute decision-making (MADM) often requires combining judgments from multiple experts under uncertainty, hesitancy, and varying levels of credibility. Although classical TOPSIS and its fuzzy extensions provide useful rankings of alternatives, they generally treat alternatives as independent and overlook credibility-based interdependencies among them. To address this limitation, this study develops a TOPSIS framework based on the Circular Pythagorean Fuzzy Credibility Graph (CPyF-CG). Within the proposed framework, experts provide evaluations expressed as circular Pythagorean fuzzy credibility values, incorporating membership, non-membership, a radius representing uncertainty, and a credibility parameter. These assessments are aggregated using the CPyF weighted averaging operator while preserving admissibility within the fuzzy domain. A three-stage procedure comprising raw scoring, normalization, and credibility scaling transforms the aggregated values into a crisp decision matrix. The same procedure is applied to attribute weights. The main contribution of the CPyF-CG framework lies in its graph structure, in which credibility-weighted edges represent interdependencies among alternatives. The final closeness coefficients are adjusted using edge-based credibility factors, thereby incorporating both individual alternative performance and the reliability of their connections. The applicability of the proposed framework is illustrated through a case study of renewable energy planning in West Bengal, India. The results identify solar energy and small hydropower as the most suitable alternatives under the proposed evaluation framework.