A linguistic picture fuzzy number ranking method based on score function and double exact function

A new ranking method based on an improved score function and a double exact function is proposed to address the deficiency that existing ranking methods cannot effectively identify equal linguistic picture fuzzy numbers (LPFNs). Firstly, property analysis and numerical simulation experiments reveal that existing ranking methods are only sufficient conditions and fail to judge equality. Then, the proposed method is theoretically proved to be a necessary and sufficient condition for equality. Furthermore, its effectiveness is verified by voting results, computational complexity and the results of numerical examples. Finally, a fuzzy multi-attribute decision-making (MADM) method for linguistic pictures is proposed by combining the linguistic picture fuzzy weighted average operator, which is applied to the decision-making problem of the cooperator selection scheme. Example analysis verifies that the new ranking method is reasonable and feasible, and it provides a new solution idea for the linguistic picture fuzzy MADM problem with known attribute weight information.