Representation of Uncertainty for Limit Processes

Title: Representation of Uncertainty for Limit Processes

Research Question: How can we mathematically represent and handle uncertainty that arises in limit processes during computation and measurement?

Methodology: The authors propose a fuzzy limit approach. They introduce two types of fuzzy derivatives: weak and strong. Weak fuzzy derivatives generate a new concept of a weak derivative, even in the case of exact limits.

Results: The authors show that classical results for limits and derivatives can be directly derived from the corresponding results for fuzzy limits and derivatives. This suggests that the new technique can be used to better utilize numerical computations, particularly in cases where uncertainty is multiplied by the uncertainty of input information.

Implications: This research has implications for various fields that use limit processes, such as continuous functions, calculus, differential equations, and topology. It provides a mathematical technique to take into account the intrinsic uncertainty of a model, which can lead to more accurate and reliable results. Additionally, it has potential applications in artificial intelligence and other areas that rely on numerical computations.

Link to Article: https://arxiv.org/abs/0112008v1 Authors: arXiv ID: 0112008v1