The Non-Archimedean Polynomials and Merging of Stratified Knowledge Bases

Abstract. In this paper, a new algebraic representation by the non-Archimedean fields is proposed to model stratified/ranked knowledge bases. The non-Archimedean representation is in the form of the non-Archimedean polynomials. With the non-Archimedean representation, the most widely used ordering strategies are easily induced and compared. Moreover, a framework of prioritized merging operators using the non-Archimedean representation is presented. It is shown that these merging operators satisfy the prioritized merging properties proposed by Delgrande, Dubois and Lang. In addition, several prioritized merging operators in the literature are proved to be special cases of the framework. Furthermore, the egalitarist fusion of incommensurable ranked bases by Benferhat, Lagrue and Rossit is also derived from the non-Archimedean representation.