A Fuzzy Unified Framework for Imprecise Knowledge

When building Knowledge-Based Systems, we are often faced with vague data. The formers are generally modeled and treated using fuzzy logic, which is based on fuzzy set theory, or using symbolic multi-valued logic, which is based on multi-set theory. To provide a unified framework to handle simultaneously both types of information, we propose in this paper a new approach to translate multi-valued knowledge into fuzzy knowledge. For that purpose, we put forward a symbolic-to-fuzzy conversion method to automatically generate fuzzy sets from an initial multi-set. Once unified, handling heterogeneous knowledge become feasible. We apply our proposal in Rule-Based Systems where an approximate reasoning is required in their inference engine. Once new facts are deduced and in order to make the translation completely transparent for the user, we also provide a fuzzy-to-symbolic conversion method. Its purpose is to restore the original knowledge type if they were multi-valued. Our proposal offer a high flexibility to the user to reason regardless to the knowledge type. In addition, it is an alternative to overcome the modeling shortcoming of abstract data by taking advantage of a rigorous mathematical framework of fuzzy logic. A numerical study is finally provided to illustrate the potential application of the proposed methodology.