Towards efficient algorithms for approximating a fuzzy relation by fuzzy rules: Case when “and”-and “or”-operation are distributive

A generic fuzzy relation often requires too many parameters to represent - especially when we have a relation between many different quantities X1,..., Xn,There is, however, a class of relations which require much fewer parameters to describe - namely, relations which come from fuzzy rules. It is therefore reasonable to approximate a given relation by fuzzy rules. In this paper, we explain how this can be done in an important case when “and”- and “or”-operation are distributive - and we also explain why this case is important.