Proceedings of the First International Conference on Neutrosophy, Neutrosophic Logic, Neutrosophic Set, Neutrosophic Probability and Statistics

Neutrosophy is a new branch of philosophy, introduced by Florentin Smarandache in 1980, which studies the origin, nature, and scope of neutralities, as well as their interactions with different ideational spectra. Neutrosophic Logic is a general framework for unification of all existing logics. The main idea of NL is to characterize each logical statement in a 3D Neutrosophic Space, where each dimension of the space represents respectively the truth (T), the falsehood (F), and the indeterminacy (I) of the statement under consideration, where T, I, F are standard or non-standard real subsets of ]-0, 1+[. Moreover, in NL each statement is allowed to be over or under true, over or under false, and over or under indeterminate by using hyper real numbers developed in the non-standard analysis theory. It is the foundation for a new theory of paradoxical and plausible reasoning [i.e. Dezert-Smarandache Theory (ref. n.)] has been developed, that takes into account in the combination process itself the possibility for uncertain and paradoxical information. The basis for the development of this theory is to work with the hyper-power set of the frame of discernment relative to the problem under consideration rather than its classical power set since, in general, the frame of discernment cannot be fully described in terms of an exhaustive and exclusive list of disjoint elementary hypotheses. In such general case, no refinement is possible to apply directly the Dempster-Shafer Theory (DST) of evidence. In our new theory [i.e. DSmT (ref. n.)], the rule of combination is justified from the maximum entropy principle and there is no mathematical impossibility to combine sources of evidence even if they appear at first glance in contradiction (in Shafer's sense) since the paradox between sources of evidence yields unavoidable paradoxes. This theory has shown, through many illustrated examples, that conclusion drawn from it provides results which agrees perfectly with the human reasoning and is useful to take a decision on complex problems where DST usually fails. This book has been devoted to the development of a theoretical bridge between neutrosophic logic and this new theory, in order to solve the delicate problem of combination of neutrosophic evidences. The neutrosophic logic serves as the most general framework (prerequisite) for dealing with uncertain and paradoxical sources of information through this new theory (DSmT)