Foundations for a New Theory of Plausible and Paradoxical Reasoning

The processing of uncertain information has always been a hot topic of research since mainly the 18th century. Up to the middle of the 20th century, most theoretical advances have been devoted to the theory of probabilities through the works of eminent mathematicians like J. Bernoulli (1713), A. De Moivre (1718), T. Bayes (1763), P. Laplace (1774), K. Gauss (1823), S. Poisson (1837), E. Borel (1909), R. Fisher (1930), A. Kolmogorov (1933), B. De Finetti (1958), L. Savage (1967), T. Fine (1973), E. Jaynes (1995) to name just few of them. With the development of computer science, the second half of the 20th century has became very prolific for the development of new original theories dealing with uncertainty and imprecise information. Mainly, three major theories are available now as alternative to the theory of probabilities for the automatic plausible reasoning in expert systems: the fuzzy set theory developed by L. Zadeh in sixties (1965), the Shafer’s theory of evidence in the seventies (1976) and the theory of possibilities by D. Dubois and H. Prade in eighties (1985) and, very recently, the unifying avant-gardiste neutrosophy theory proposed by F. Smarandache (2000). This paper is focused on the development of a new theory of plausible and paradoxical reasoning which can be interpreted as a generalization of the theory of evidence. After a brief presentation of the Dempster-Shafer theory in section 2, we set up the foundations of our new theory in section 3 and discuss the justification of the new rule of combination of uncertain and paradoxical sources of evidences. Several illustrative examples of the power and the usefulness of our new theory are also presented and compared with results drawn from the classical Dempster-Shafer theory.