Extending multicriteria decision making by mixing t-norms and OWA operators

We consider the problem of multicriteria decision making. We indicate how the evaluation of an alternative involves a determination of the degree to which subsets of criteria are satisfied by the alternative. This calculation is based upon an anding of the satisfactions of the individual criteria in the subsets. We consider the possibility of using t-norms other than the Min for the and operation. Using this generalization we develop an extension of the OWA operators, called the TOWA, which involves a mixing of the t-norm with the OWA operator. We extend this generalization to other aggregation techniques, the Choquet and Sugeno integrals. We introduce the concept of the Power of a t-norm to provide an ordering over the t-norm operators. We look at Power of a number of families of t-norm. (c) 2005 Wiley Periodicals, Inc.