Control the smog using strong picture fuzzy influence pair domination number

Smog is a thick haze of air pollution that harms human health and the environment. If we can control the factors of smog, then we can reduce it. A well-organized and valuable tool is a picture fuzzy influence graph \(\left( {PFIG} \right)\) for managing ambiguity in practical challenges, including uncertain data, figures, facts, and discoveries. A \(PFIG\) provides membership, non-membership, and neutral degree values of vertices, edges, and influence pairs. Using the picture fuzzy influence pairs, we can get information regarding the effect of one vertex on another vertex or edge of the same or another graph, which is a key feature as this can connect two disconnected graphs. This article represents some basic concepts such as strongest, strong, and weak picture fuzzy influence pairs, which help to propose the idea of domination in a \(PFIG\). Finally, we present a helpful, applicable, and practical application to control smog using the concept of domination in a \(PFIG\). The proposed work is cross-verified by some multi-criteria decision-making methods such as TOPSIS, VIKOR, and EDAS, as well as with some picture fuzzy entropies.