A Theory of Relative Information

Abstract

Basically, this chapter proposes a new model of linear observation in ℝ² and a new theory of relative information in the sense that the informational content of a given message explicitly depends upon the state of the observer. After a short analysis of the phenomena of observation and of aggregation, we introduce the particular case of linear observations with informational invariance and we arrive at the existence of two models: one with Euclidean invariance, and the other one with Minkowskian invariance. Then we consider messages defined by natural languages, and, by using very simple and general arguments, we describe them by a syntactic space and a semantic space, that is to say an entropy of symbol H(α) and an entropy of meaning H(a). The main assumption is that the observer receives the syntax and the semantics of the message via a linear transformation with informational invariance, and one can show that this observation is necessarily Minkowskian. One then has two models: the first one in which it is the entropies H(α) and H(a) that are observed by this process, and the second which involves the observation of the Shannonian transinformations I(β/α) and I(b/a). The theory is described and comparisons with standard results are made. One of the consequences of the observation modelling is a new approach to fuzziness.