1 Four Versions of the Proportional Conflict Redistribution Rules of Combination in Information Fusion Florentin Smarandache Department of Mathematics and Science University of New Mexico 200 College Road Gallup, NM 87301, USA smarand@unm.edu Jean Dezert ONERA/DTIM/IED 29 Avenue de la Division Leclerc 92320 Châtillon, France Jean.Dezert@onera.fr Abstract: In this paper we propose four versions of a Proportional Conflict Redistribution rule (PCR) for information fusion together with many examples. Going from the first rule (PCR1a and PCR1b) to the second rule (PCR2) and the third rule (PCR3) the process of implementation becomes more complex, but the correctitude of redistribution increases. The PCR rules redistribute the conflicting mass, after the conjunctive rule has been applied, proportionally with some functions depending on the masses assigned to their corresponding columns in the mass matrix. There are infinitely many ways these functions (weighting factors) can be chosen, and the problem is to see which ones are the best. Any fusion combination rule is at some degree ad-hoc. Keywords: Conjunctive rule, partial and total conflicts, Dempster’s rule, Yager’s rule, TBM, Dubois-Prade’s rule, Dezert-Smarandache classic and hybrid rules, PCR rules ACM Classification: I.2.4. 1. Introduction. This paper is an extension of the previous paper [Smarandache-Dezert, 2004b] on Proportional Conflict Redistribution Rule.. We first present the formulas for the conjunctive rule and total and partial conflicts, then try to unify some theories using an adequate notation. The big picture in applying the PCR rules of fusion combination is as follows: first one uses the conjunctive rule, second one computes the conflicting mass, and third one redistributes the conflicting mass to non-empty sets. The way the redistribution is done makes the distinction between other rules and the PCR rules, and also the distinction among PCR versions themselves.