Definition of general aggregation operators through similarity relations

Various extensions of the original max and min aggregation operators in fuz zy set theory are successfully used in practical applications, but lack a c lear conceptual model supporting them. Giving these operators a meaningful and simple interpretation is the topic of this paper. Aggregation operators are seen as different methods to measure distances to the essential refere nce points of the feature space, called Ideals. It has been proved that eve ry general aggregation operator can be associated with a corresponding metr ic, in which the result of its application is the distance to the Ideal. So me widely used operators correspond to familiar l - p norms, and new operat ors can be defined by specifying different metrics. Heterogeneous combinati ons of ANDs and ORs are treated in such a way that the distributivity and D e Morgan's laws hold. Applications to fuzzy constraint satisfaction problem and fuzzy control are discussed and interpreted geometrically. Classical o perators are particular cases of the proposed semantic model, and several o ther examples are given. (C) 2000 Elsevier Science B.V. All rights reserved .