The fuzzy inference system based on axiomatic fuzzy sets using overlap functions as aggregation operators and its approximation properties

As significant vehicles for applying fuzzy set theories, fuzzy inference systems (FISs) have been widely utilized in artificial intelligence. However, challenges such as computational complexity and subjective design persist in FIS implementation. To address these issues, this paper introduces the fuzzy inference system based on axiomatic fuzzy sets (FIS-AFSs), which includes a fuzzy rule base and a fuzzy inference engine. This system eliminates the need for subjective decisions in the selection of fuzzification and defuzzification methods. The theoretical foundation of the approach involves defining the multi-dimensional vague partition (VP) of the multi-dimensional universe using an overlap function to aggregate one-dimensional VPs. Additionally, an axiomatic fuzzy set (AFS) on the multi-dimensional universe is defined. Building on this foundation, algorithms for single-input single-output (SISO) and multi-input single-output (MISO) fuzzy inference are developed using AFSs, eliminating the need for subjective fuzzy implication operators. The FIS-AFSs, with its universal approximation property and theoretical approximation precision, are then analyzed. Experimental tests are conducted to evaluate the approximation capabilities of the FIS-AFSs. Results from both theoretical analysis and experimental testing demonstrate that FIS-AFSs can achieve high approximation precision.