Atanassov’s intuitionistic fuzzy sets (AIFSs), characterized by a membership function, a nonmembership function, and a hesitancy function, is a generalization of a fuzzy set. Various aggregation operators are defined for AIFSs to deal with multicriteria decision-making problems in which there exists a prioritization of criteria. However, these existing intuitionistic fuzzy prioritized aggregation operators are not monotone with respect to the total order on Atanassov’s intuitionistic fuzzy values (AIFVs), which is undesirable. We propose an intuitionistic fuzzy prioritized arithmetic mean based on the Łukasiewicz triangular norm, which is monotone with respect to the total order on AIFVs, and therefore is a true generalization of such operations. We give an example that a consumer selects a car to illustrate the validity and applicability of the proposed method aggregation operator.

A type-2 fuzzy logic system (FLS) can handle numerical and linguistic uncertainties, but, like a type-1 FLS, rule explosion is one of its major disadvantages. In this paper, we present a design method which can tremendously reduce rule number for interval type-2 fuzzy logic systems using an SVD-QR method. The SVD-QR method is performed after extracting two fuzzy basis function expansions from the interval type-2 FLS. We evaluate this method by applying it to a time-series forecasting problem in conjunction with back-propagation training, and demonstrate that tremendous rule number reduction ratio is achieved with very little performance degradation. © 2000 John Wiley & Sons, Inc.