A relativistic approach to modelling dynamic systems involving human factors†

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Abstract
The mathematical framework of special relativity and of general relativity, which involve explicitly the relativistic reference to the observers, should hold also to depict dynamic systems involving human factors. The present paper is focused mainly on the use of special relativity. After a brief resume of the physical features of this theory, we use it to define a general model for general systems, and the Lorentz equations are introduced, which are the nub of the following matter. Applying the model to the concept of class leads directly to the new concept of relativistic fuzzy sets. It is different from that of usual fuzzy sets in the sense that the fuzziness on a set explicitly depends upon the observers, and we have composition laws, with respect to the observers, for the fuzziness functions. The framework of an algebra for relativistic fuzzy sets is given. Applying the relativistic model to random processes gives a new look to the classical prior and posterior probabilities and the illustrative example of a Bayesian pattern recognition system exhibits the genuine meaning of the relativistic probability concept so introduced. Then dynamic systems are described in two stages, the Lorentz stage, and the differential one ; and we so obtain a new model which may take into account some uncertainties which are truly deterministic in nature, like the effect of technology on economic systems for instance. The conclusion outlines the future of the approach.

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