Membership Induced on Manifolds by Vector Fields and Flows

Kevin N. Otto and Andrew D. Lewis and Erik K. Antonsson

Fuzzy Sets and Systems
Volume 70, Number 1 (1995), Pages 15-29.


In many engineering and scientific applications, the need arises to perform differential calculations on manifolds. If such calculations involve imprecise data, methods for computing with such data must be determined. Definitions are given for memberships on manifolds induced by differentiation along vector fields, and by flows of vector fields with uncertain parameters. Examples are presented which illustrate the concepts.