Identical Foundation of Probability theory and Fuzzy Set Theory

Information fusion introduces special operators ◦ in probability theory and fuzzy theory. Some serious data certify in each cases these two quite distinct techniques. This communication will show that four postulates are the unique aim of these two theories. Evidence theory and fuzzy set theory replace often probabilities in medicine, economy and control. Fuzzy theory is used for example in Japanese photographic engine. We have solve the challenge of unifying such different techniques. With the four postulates : non-contradiction, continuity, universality, context dependence we obtain the same functional equation from which are deduced probability and fuzzy set theories. The same postulates applies to confidences either in the dependence or independence situation. The foundation for the various modern theories of information fusion has been unified in the framework of uncertainty by deductions. The independence between elementary confidences do not need to be understood in the sense of probabilistic meaning.