Time-varying multi-period emergency decision-making based on dissimilarity measure and definite integral in the picture fuzzy context

With increasingly frequent and serious emergency problems, timely and optimal emergency decision-making (EDM) becomes the key to reducing casualties and losses. EDM is characterized by urgency, volatility, and un-certainty, thus it is crucial to deal with considerably ambiguous information. This paper mainly investigates the continuous dynamic EDM problem with picture fuzzy (PF) information. First, we construct a dissimilarity measure between picture fuzzy numbers (PFNs) to discriminate PF information. Next, we deduce the differential and integral of the PF function (PFF) based on the basic operations of PFNs and then apply the theory to time-varying (TV) PF circumstance such that the TV-PF weighted averaging operator can be defined according to the derived linear operation of time-varying PF integral. In order to reduce the computational difficulty of PF in-tegral on each period, we adopt the way of numerical integration for approximation and divide the integration intervals into smaller and more ones to improve the accuracy. Based on these, we propose the aggregation method of the dynamic decision information represented by TV-PFNs and combine the TODIM method to establish a methodology of EDM with TVPF information. Finally, we apply the proposed methodology to an emergency case and illustrate the feasibility and validity through sensitivity analysis and comparison analysis.