Special fuzzy measures on infinite countable sets and related aggregation functions
While both additive and symmetric fuzzy measures on a finite universe are completely described by a probability distribution vector, this is no more the case of a countably infinite universe. After a brief discussion of additive fuzzy measures on positive integers, we characterize all symmetric fuzzy measures on integers by means of three constants and of two probability distribution vectors. OWA operators for n arguments were introduced by Yager in 1988. Grabisch in 1995 has shown representation of OWA operators by means of Choquet integral with respect to symmetric normed capacities. Based on symmetric capacities on positive integers, we extend the concept of OWA operators to infinitary sequences and thus we develop the concept of infinitary OWA operators. (C) 2010 Elsevier B.V. All rights reserved.
symmetric fuzzy measure additive fuzzy measure owa operator choquet integral k-order additivity p-symmetry