A Minkowskian theory of observation: Application to uncertainty and fuzziness

Abstract

This paper examines various ways to introduce subjectivity in the measures of uncertainty. In the first part, by using a simple physical remark concerning discrete entropy in Shannon sense, we derive a so-called ‘complete discrete entropy’ which provides a unified approach to discrete and continuous entropy, and applies directly to variables which involves both probability and possibility. In the second part, by using three elementary axioms, we derive a Minkowskian theory of observation which holds when the observable is a pair (syntax, semantics) and which involves a parameter which is directly related to the subjectivity of the observer. This model is then applied to the observation of uncertainty, transinformation and membership, in which case it provides a new approach to fuzzy number.