A Split-Combination Method for Merging Inconsistent Possibilistic Knowledge Bases

In this paper, a new method for merging multiple inconsistent knowledge bases in the framework of possibilistic logic is presented. We divide the fusion process into two steps: one is called the splitting step and the other is called the combination step. Given several inconsistent possibilistic knowledge bases (i.e. the union of these possibilistic bases is inconsistent), we split each of them into two subbases according to the upper free degree of their union, such that one subbase contains formulas whose necessity degrees are less than the upper free degree and the other contains formulas whose necessity degrees are greater than the upper free degree. In the second step, we combine the former using the maximum (or more generally, T-conorm) combination mode, while combining the latter using the minimum (or more generally, T-norm) combination mode. The union of the possibilistic bases obtained by the second step is taken as the final result of the combination of the possibilistic bases that we want to merge. We prove that when the possibilistic bases are consistent with each other, the result of our new combination method is equivalent to that of the minimum (T-norm) based combination mode. However, when the sources are inconsistent with each other, the result of our combination mode is better than that obtained by using the maximum (T-conorm) based mode. An alternative approach to splitting the possibilistic bases is introduced in the last section. The combination mode obtained by this splitting method can be applied to combine knowledge bases which are flat, i.e., without any priority between their elements.