Identical foundation of probability theory and fuzzy set theory

摘要

Information fusion introduces special operators o in probability theory and fuzzy theory. Some serious data certify in each case these two quite distinct techniques. The article shows that four postulates are the unique aim of these two theories. Evidence theory and fuzzy set theory often replace probabilities in medicine, economy and control. Fuzzy theory is used for example in a Japanese photographic engine. We solved the challenge of unifying such different techniques. With the four postulates: noncontradiction, continuity, universality, context dependence, we obtain the same functional equation from which are deduced probability and fuzzy set theories. The same postulates apply 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.