Representation of Uncertainty for Limit Processes
Abstract
Many mathematical models utilize limit processes. Continuous functions and the calculus, differential equations and topology, all are based on limits and continuity. However, when we perform measurements and computations, we can achieve only approximate results. In some cases, this discrepancy between theoretical schemes and practical actions changes drastically outcomes of a research and decisionmaking resulting in uncertainty of knowledge. In the paper, a mathematical approach to such kind of uncertainty, which emerges in computation and measurement, is suggested on the base of the concept of a fuzzy limit. A mathematical technique is developed for differential models with uncertainty. To take into account the intrinsic uncertainty of a model, it is suggested to use fuzzy derivatives instead of conventional derivatives of functions in this model.
 Publication:

arXiv eprints
 Pub Date:
 December 2001
 arXiv:
 arXiv:cs/0112008
 Bibcode:
 2001cs.......12008B
 Keywords:

 Artificial Intelligence;
 Numerical Analysis;
 G.1;
 E.1