Fuzzy dynamics as an alternative to statistical mechanics

✍ Scribed by Y. Friedman; U. Sandler

• Publisher: Elsevier Science
• Year: 1999
• Tongue: English
• Weight: 833 KB
• Volume: 106
• Category: Article
• ISSN: 0165-0114
• DOI: 10.1016/s0165-0114(98)00357-1

✦ Synopsis

We propose a description of continuous evolution of systems with uncertainty based on min or product t-norms of fuzzy logic. We show that the dynamics has a Hamiltonian form in the extended state space composed from "physical" and "information" components if the min t-norm is used. This description is useful when available information on a system behavior is mainly ordinal and not numerical. It was shown, also, that if the product t-norm is used, the dynamics on a continuous universe is similar to the stochastic processes dynamics, but a probability distribution is replaced by a possibility density. We show, that such replacement leads to a principal extension of the stochastic process theory and correspondence differential equation of evolution for the possibility density cover most basic evolution equations in physics. (~) 1999 Elsevier Science B.V. All rights reserved.