Sustainable decision support system in Industry 4.0 under uncertainties with m-polar picture fuzzy information aggregation

This article introduces the concept of m-polar picture fuzzy sets to address the inherent ambiguity in sustainability-related decision-making in Industry 4.0. We present a set of novel aggregation operators specifically developed for m-PPFSs, including the m-polar picture fuzzy weighted averaging operator, which assigns different weights to each element, and the ordered weighted averaging operator, which aggregates elements based on their ranked values and assigned weights. Additionally, the weighted geometric operator applies a geometric mean approach with weighted inputs, and the ordered weighted geometric operator combines the properties of ordered values and geometric aggregation. These operators provide versatile tools for handling m-PPFS data in various decision-making and computational contexts, playing a critical role in enhancing the multi-criteria decision-making process. Our framework further enables the application of blockchain technology for tracking raw material provenance, optimizing resource utilization, automating waste recycling through smart contracts, and supporting circular supply chain practices. In addition, Industry 4.0 technologies such as the Internet of Things and advanced analytics enable real-time monitoring and predictive maintenance, strengthening sustainability efforts. To evaluate the performance of the proposed aggregation operators, we compare them with existing methods in fuzzy set theory. The results demonstrate that our approach offers superior precision, robustness, and adaptability, outperforming traditional methods in addressing sustainability challenges within the manufacturing sector. In this study, we proposed novel aggregation operators that significantly improve efficiency, accuracy, and flexibility over existing methods, offering robust solutions to sustainability-related decision-making challenges.