Automatic generation and reduction of the semi-fuzzy knowledge base in symbolic processing and numerical calculation

Typical fuzzy expert systems can only model human behavior on a rule-base level, but they cannot create the comprehensible rules which are difficult to acquire from experts. There is also a lack of logical dimension reduction method for the reduction of an existing rule base generated by experts or analytical modelling. We have proposed an inductive learning method with semantic intervals (SI) sufficiently approximated from normal convex fuzzy sets for generation (Zhao et al 1992) as well as reduction (Turksen and Zhao 1992) of the semi-fuzzy knowledge bases by using input-output data collected from objective processes. The validity of the approximation above is proved by the criterion of uncertainty compromise in approximation to adjacent fuzzy sets. The semi-fuzzy knowledge base consists of two main parts, i.e., a data base with the triangular semi-fuzzy sets (TSFSs) derived from the SI and a rule base containing the rule sets with the TSFSs.; The SI plays a key role in symbolic processing for inductive learning. To explore the validation, verification for this automatic knowledge acquisition scheme, an equivalence between the inductive learning with SI and a valid pseudo-Boolean logic simplification is proved. Based on the equivalence, the reliability, implementability and learnability are analyzed and acknowledged for the automatic generation and reduction of the rules with the TSFSs.; The TSFSs are functional numerical calculations of an inference engine. The interval valued compositional rule of inference (Turksen 1989) is extended as an adequate inference engine on the TSFSs to carry out the linguistic and numerical values.; The advantage of introducing the SI with the associated TSFS (the SI-TSFS pair) is to integrate symbolic processing and numerical calculations. The reduced semi-fuzzy knowledge base is generated through the SI-TSFS pair to overcome the difficulty of the fuzzy logic simplification. Originally this difficulty exists in the conventional fuzzy qualitative modelling technique. Furthermore, the derivation of the SI-TSFS is consistent with the separation theorem (Zadeh 1965).; In practical applications even when the condition for the equivalence is not satisfied, the proposed scheme can still provide the semi-fuzzy knowledge base with better testing results in both the classification and inference of a singleton numerical value. The proposed method has been shown to be successful in the modelling of continuous and discrete complex processes such as chemical vinylon synthesis, a repair parts service center, search and rescue satellite-aided tracking (SARSAT), human operation of a chemical plant and stock market activities.