Centroid-Induced Ranking of Triangular Picture Fuzzy Numbers and Applications in Decision-Making

This paper proposes the concept of a centroid for picture fuzzy numbers and particularly for triangular picture fuzzy numbers. The concept allows the implementation of a ranking function for the triangular picture fuzzy numbers, which has the advantage of reuniting the symmetry and asymmetry of the information. Then, empirical applications are considered for the picture fuzzy numbers. Specifically, multiple TPFNs are considered. The ranked, A comparison study is conducted for said ranked TPFNs relative to other methodologies in the specialized literature, illustrating that these methods exhibit limitations in specific scenarios. An additional compelling example is provided: before elections, opinion surveys are extensively utilised to assess voter intentions about candidates. The survey findings can be analysed through PFNs and the ranking mechanism proposed in this study. Another contribution of this paper is the development an algorithm meant to solve decision making problems in an uncertain environment. This is applied in the practical context of comparing the performance of several standards in two successive evaluations.