Dynamical system modelling for picture fuzzy multi-criteria public opinion on transportation infrastructure

This work presents a novel approach for modelling dynamic fuzzy multi-criteria decision-making problems. We consider a problem where members of a population evaluate alternatives under a given criterion by taking either of three options: agree, neutral, or disagree. The physical partitioning of the population gives rise to the notion of describing the performance of alternatives under multiple criteria as Picture fuzzy sets, with operations that can aggregate multi-criteria performance into real numbers. Then, the dynamic performance of the alternatives is described by considering the interactions of the partitions of the populations, modelled as a system of differential equations constructed for each criterion. We provided proof of the basic properties of each system, including nonnegativity and boundedness of solutions, and presented the points of convergence. Parameter values were estimated by performing time-series clustering. The proposed approach was applied numerically in modelling multi-criteria public opinion of a bus rapid transit project—a single alternative, where nine criteria were evaluated. Initial performance values under multiple criteria were obtained using a survey, and four scenarios representing possible government interventions were evaluated. The time-dependent performance profiles of the public about the project were obtained, with insights indicating the efficacy of the proposed model.