The design and evaluation of a picture fuzzy mining safety system with picture fuzzy differential equations

The mining industry continues to play a significant role in developing the economy in developing countries. The need for minerals influences the magnitude of the mining industry, and safety concerns have taken on considerable importance in this sector. Equipment failure and breakdown will severely disrupt production and cause accidents for the mining workers. Most safety studies in the mining industry consider deterministic models with crisp parameters. This study addresses safety in the mining industry under uncertainty and fuzziness. We present a picture fuzzy mining safety system with picture fuzzy differential equations. We examine and discuss the solutions to a mining safety model using triangular picture fuzzy numbers. We further study the shutdown probability at the mining system in safe and unsafe modes.