A New Q-Rung Picture Fuzzy Grey Relational Analysis Method and Investigation of Its Effectiveness

Abstract

Fuzzy logic plays an important role in decision making by modelling uncertain and imprecise situations. Recent studies in decision processes focus on extended versions of fuzzy sets designed to better represent uncertainty. One of these extensions is the q-Rung Picture Fuzzy Set (q-RPFS), which provides greater flexibility for decision makers when expressing their opinions under uncertainty. Other related extensions, such as q-Rung Orthopair Fuzzy Sets (q-ROFS) and Picture Fuzzy Sets (PFS), are also powerful tools for representing fuzziness and uncertainty. Combining the advantages of these approaches, q-RPFS offers an effective structure for handling uncertain and inconsistent data. In this study, a new q-Rung Picture Fuzzy Grey Relational Analysis (q-RPFGRA) method is proposed based on the q-RPFS framework. The proposed approach aims to improve the reliability and precision of decision-making results by reducing uncertainty and information loss. The effectiveness of the q-RPFGRA method is demonstrated through a project selection example taken from the literature. To verify the validity and applicability of the proposed method, a comparative analysis with existing operators is conducted and the results are integrated using the Borda method. This study represents the first application of the q-RPFGRA method in evaluation and decision making problems under a fuzzy environment.