A Phase-Sensitive Ranking Framework for Complex Pythagorean Neutrosophic Fuzzy Sets with a Application to Renewable Energy Resource Selection

Abstract

Identifying renewable energy resources is a big challenge nowadays, since it is characterized by incomplete data, conflicting expert opinions, economic challenges, limitations and sometimes vary with time and phase. Classical fuzzy and intuitionistic fuzzy models include membership and non-membership values but fails to address phase valued details. This paper introduces a ranking framework that combines Complex Pythagorean Neutrosophic Fuzzy Numbers (CPNFNs) with the TOPSIS method. This method characterizes truth, indeterminacy, and falsity using phase and amplitude elements. This work establishes formal condition for boundedness, monotonicity and discrimination and illustrates, illustrates these with six-alternatives renewable energy selection problem. In addition, a comparative analysis is carried out to access the robustness and stability . This framework is designed for decision-making contexts where both uncertainty and periodic information play a significant role.