Pythagorean cubic fuzzy multiple attributes group decision method for sustainable supply chain management

A Pythagorean cubic fuzzy set (PCFS) is composed of Pythagorean fuzzy values and interval details. Unlike interval Pythagorean fuzzy sets, PCFS contains more data and can be valuable in complex multi-attribute group decision making (MAGDM). However, as a novel fuzzy set, certain essential principles of PCFS, such as the scoring function's implausibility and the absence of operations, require improvement. To address these concerns, we have refined the PCFS scoring function and introduced a new PCFS operation. Additionally, we have developed a PCFS reliability measure to account for uncertain expert opinions and attribute weights in MAGDM. Furthermore, overcoming the challenge of collecting PCFS evaluation data presents an obstacle. In the context of content distribution, the Heronian-mean (HM) operator tackles attribute association. While most existing Pythagorean-cubic fuzzy aggregation operators have an algebraic nature, we leverage the HM operator to establish a variety of Pythagorean cubic fuzzy aggregation operators. These operators showcase properties such as equivalence, monotonicity, boundedness, and commutative invariance. Finally, grounded in the Pythagorean cubic fuzzy HM aggregation operator, we introduce a MAGDM approach for sustainable supply chain management (SSCM). We conduct a practicality and superiority comparison with the existing Pythagorean cubic fuzzy aggregation operator. The primary contribution of this article is to enrich the research on aggregation operators of PCFS and expand their social applications in the realm of SSCM.