Aggregation of symbolic possibilistic knowledge bases from the postulate point of view

Abstract

Aggregation of knowledge bases in the propositional language was soon investigated and the requirements of aggregation processes of propositional knowledge bases basically are unified within the community of researchers and applicants. Aggregation of standard possibilistic knowledge bases where the weight of propositional formulas being numeric has also been investigated and applied in building the intelligent systems, in multi-criterion decision-making processes as well as in decisionmaking processes implemented by many people. Symbolic possibilistic logic (SPL for short) where the weight of the propositional formulas is symbols was proposed, and recently it was proven that SPL is soundness and completeness. In order to apply SPL in building intelligent systems as well as in decision-making processes, it is necessary to solve the problem of aggregation of symbolic possibilistic knowledge bases (SPK bases for short). This problem has not been researched so far. The purpose of this paper is to investigate aggregation processes of SPK bases from the postulate point of view in propositional language. These processes are implemented via impossibility distributions defined from SPK bases. Characteristics of merging operators, including hierarchical merging operators, of symbolic impossibility distributions (SIDs for short) from the postulate point of view will be shown in the paper.