Friedman, Y.; Sandler, U. Fuzzy dynamics as an alternative to statistical mechanics. (English) Zbl 0940.70015 Fuzzy Sets Syst. 106, No. 1, 61-74 (1999). Summary: 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 of “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 is 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 the corresponding differential equation of evolution for the possibility density covers most basic evolution equations in physics. Cited in 11 Documents MSC: 70H99 Hamiltonian and Lagrangian mechanics 82B31 Stochastic methods applied to problems in equilibrium statistical mechanics 03B52 Fuzzy logic; logic of vagueness Keywords:stochastic dynamics; min \(t\)-norm; product \(t\)-norm; Hamiltonian formulation; systems with uncertainty; fuzzy logic; extended state space; possibility density Software:DYNAMO PDFBibTeX XMLCite \textit{Y. Friedman} and \textit{U. Sandler}, Fuzzy Sets Syst. 106, No. 1, 61--74 (1999; Zbl 0940.70015) Full Text: DOI References: [1] Arnold, V. I., Mathematical Methods of Classical Mechanics, (Graduate Texts in Mathematics (1978), Springer: Springer New York) · Zbl 0386.70001 [2] Aubin, J.-P., Fuzzy differential inclusions, Prob. Control Inform. 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