On vague logics and approximate reasoning based on vague linear transformation

Abstract

As a generalisation of the Fuzzy Sets theory, vague set has been proven to be a new tool in dealing with vague information. In this article, we attempt to generalise the techniques of fuzzy inference in a vague environment. In the rule-based inference system, an ‘if … then …’ rule can be considered a transformer that implements information conversion between input–output ends. Thus, according to the logical operations of vague linguistic variables, we introduce an approach to approximation inference based on linear transformation, and then discuss the representations for several inference structures regarding single rule, multi-rules and compound rules. By defining the inclusion function of vague sets, we provide vague rough approximation based on measure of inclusion, and then present a method on rule creation from a decision system. A case study on the prediction for welding deformation is used to illustrate the effectiveness of the proposed approaches.