Complex Pythagorean parameterized fuzzy sets and their applications to countering digital crime and digital terrorism and supply chain management problem

The existing concepts of complex fuzzy sets (CFS), complex intuitionistic fuzzy sets (CIFS), complex Pythagorean fuzzy sets (CPFS), complex q-rung orthopair fuzzy sets, and complex linear Diophantine fuzzy sets (CLDFS) have numerous applications in diverse fields. However, these concepts have certain limitations, which make it difficult for decision-makers to deal with complicated real-life problems. To ease these restrictions, we introduce the concept of complex Pythagorean parameterized fuzzy sets (CPPFS) with the addition of reference parameters. The parameterizations of the CPPFS are efficient in modeling incomplete data in decision-making problems, providing valuable information to classify a physical system. Score functions and accuracy functions are defined over CPPFS. Several aggregation operators such as complex Pythagorean parameterized fuzzy weighted averaging (CPPFWA) operator, complex Pythagorean parameterized fuzzy weighted Geometric (CPPFWG) operator, complex Pythagorean parameterized fuzzy ordered weighted averaging (CPPFOWA) operator, complex Pythagorean parameterized fuzzy ordered weighted geometric (CPPFOWG) operator, complex Pythagorean parameterized fuzzy hybrid averaging (CPPFHA) operator, and complex Pythagorean parameterized fuzzy hybrid geometric (CPPFHG) operator are constructed with the properties such as idempotency, monotonicity, and boundedness. Real-life applications of the proposed concept are illustrated through the selection of sustainable housing designs and renewable energy systems. Moreover, the proposed methods are applied to the problem of supply chain management, digital crime and digital terrorism problem, and the selection of research grant projects. Comparative and sensitive analyses are performed to demonstrate the superiority, feasibility, and easiness of the proposed methods to the existing methods. The proposed methods provide accurate and effective results in decision-making problems.