Combination of paradoxical sources of information within the neutrosophic framework

The recent emergence of Smarandache's logic as foundations for a new general unifying theory for uncertain reasoning is becoming both anew philosophical and mathematical research field and could modify deeply our perception and understanding of our outer and inner worlds in coming years. The ability for neutrosophy to include all existing logics as special cases is undoubtedly appealing. Beside of all potential advantages of neutrosophy to handle antinomies and uncertainties, the current mathematical neutrosophic logic, does not deal directly with the important problem of combination of evidences provided by different bodies of evidence. This paper is the first attempt to develop new foundations for the combination of sources of information in a very general framework where information can be both uncertain and paradoxical. We develop a new rule of combination close to the ad-hoc Dempster-Shafer rule of combination where both conjunctions and disjunctions of assertions are explicitly taking into account in the fusion process. Through several simple examples, we show the efficiency of this new theory of plausible and paradoxical reasoning to solve problems where the Dempster-Shafer theory usually fails. Finally a theoretical bridge between the neutrosophic logic and our new theory is presented, in order to solve the delicate problem of the combination of neutrosophic evidences. The neutrosophic logic seems to be an appealing general framework (prerequesite)for dealing with uncertain and paradoxical sources of information through this new theory.