Multidimensional Fuzzy Interpolative Reasoning Method Based on \lambda-Width Similarity

Fuzzy reasoning is the very important process in the intelligent systems. Very few papers address the research for interpolative reasoning under multidimensional sparse rules. Moreover, these methods sometimes can not guarantee the convexity of result. Nowadays, multidimensional sparse rules base focus on the premises composed of many fuzzy sets, but do not consider the consequences composed of multidimensional fuzzy sets. Thus the fuzzy production rule can not express the complicate problems in the real world. It needs to be extended. This paper proposes a similarity relation between fuzzy sets. Based on the similarity relation, then we propose an improved fuzzy interpolative reasoning method. Moreover, we extend the method to the case of complex multidimensional consequences.