Rule reduction for efficient inferencing in similarity based reasoning

The two most important models of inferencing in approximate reasoning with fuzzy sets are Zadeh’s Compositional Rule of Inference (CRI) and Similarity Based Reasoning (SBR). It is known that inferencing in the above models is resource consuming (both memory and time), since these schemes often consist of discretisation of the input and output spaces followed by computations in each point. Also an increase in the number of rules only exacerbates the problem. As the number of input variables and / or input / output fuzzy sets increases, there is a combinatorial explosion of rules in multiple fuzzy rule based systems. In this paper, given a fuzzy if-then rule base that is used in an SBR inference mechanism, we propose to reduce the number of rules by combining the antecedents of the rules that have the same consequent. We also present some sufficient conditions on the operators employed in SBR inference schemes such that the inferences obtained using the original rule base and the reduced rule base obtained as above are identical. Subsequently, these conditions are investigated and many solutions are presented for some specific SBR inference schemes.