The complexity of decision environments poses challenges for individuals engaged in decision-making proceedings. Picture fuzzy linguistic sets (PFLSs) are an effective tool for depicting the inherent subjective nature of human cognition. Aiming for the promotion of a general theory on PFLSs, we conduct a critical research to identify some limitations of a recent publication in Cognitive Computation [2018, 10(2), 242–259]. This published article is a meaningful and interesting study that initiates the PFLS as well as introduces the corresponding operations and the Archimedean picture fuzzy linguistic weighted arithmetic averaging operator. Unfortunately, we have carefully analyzed these operations and found that they may not be appropriate to all situations within picture fuzzy linguistic environment, which would result in the violation of human cognition. To eliminate this limitation, we explore and suggest novel operational laws and an aggregation operator for PFLSs from a modified version, so as to support further study on picture fuzzy linguistic group decision-making. Furthermore, a comparative and illustrative example is presented to validate the advantages of our modified operations. Towardly, the research outcome will be of significant benefit to promoting the development of picture fuzzy linguistic decision-making theory. Accordingly, our contribution to improving the current research on PFLSs makes their application in solving realistic problems feasible and practical.