Extended fuzzy relations: Application to fuzzy expert systems

Abstract This paper introduces the concept of an extended fuzzy relation, which is a relation whose values are vectors of fuzzy relations, some of which may also be extended fuzzy relations. Our motivation is to use extended fuzzy relations to replace blocks of rules in a fuzzy expert system with one rule. The extended fuzzy relation method is shown to contain the generalized modus ponens as a special case. The construction of extended fuzzy relations is illustrated in two examples taken from diagnosing mental disorders and image processing. We argue that the existence of an extended fuzzy relation for a block of rules may be a criterion for parallel execution of this block instead of sequential firing of the rules.