A new interpretation on fuzzy differential equations: Linguistic concepts evolving over time

Fuzzy differential equations have been explored in many different ways, including theoretical aspects and in applications. The interpretation that is given to the fuzziness is a uncertainty due to fluctuations accumulated in the measurement process or due to partial information. This has much to do with a probabilistic interpretation. We propose to interpret the fuzziness as Zadeh first stated: membership to a non-sharp concept. As example we solve a fuzzy initial value problem whose independent variable is the time and the unknown variable is regarded as a single concept (the word “tall”) whose compatibility (membership) function varies over time. In summary, the main novelty is that the fuzzy differential equation models a concept evolving over time.