A Study of the Origin and Uses of the Ordered Weighted Geometric Operator in Multicriteria Decision Making F. Herrera, * E. Herrera-Viedma, † Department of Computer Science and Artificial Intelligence, University of Granada, 18071—Granada, Spain F. Chiclana ‡ Centre for Computational Intelligence, Department of Computing Science, De Montfort University, The Gateway LE1 9BH Leicester—United Kingdom The ordered weighted geometric (OWG) operator is an aggregation operator that is based on the ordered weighted averaging (OWA) operator and the geometric mean. Its application in multi- criteria decision making (MCDM) under multiplicative preference relations has been presented. Some families of OWG operators have been defined. In this article, we present the origin of the OWG operator and we review its relationship to the OWA operator in MCDM models. We show a study of its use in multiplicative decision-making models by providing the conditions under which reciprocity and consistency properties are maintained in the aggregation of multiplicative preference relations performed in the selection process. © 2003 Wiley Periodicals, Inc. 1. INTRODUCTION In any multicriteria decision-making (MCDM) problem the final solution must be obtained from the synthesis of performance degrees of criteria. 1,2 To this end, the aggregation of information is fundamental. The ordered weighted geometric (OWG) operator is an aggregation operator that we define and characterize in Ref. 3, to design multiplicative decision-making models, 4,5 i.e., MCDM processes using multiplicative preference relations 6 to express the preferences about alternatives. It is based on the ordered weighted averaging (OWA) operator 7 and on the geometric mean. Recently, some families of OWG operators were presented in Ref. 8. * Author to whom all correspondence should be addressed: e-mail: herrera@decsai.ugr.es. † e-mail: viedma@decsai.ugr.es. ‡ e-mail: fchiclana@teleline.es. INTERNATIONAL JOURNAL OF INTELLIGENT SYSTEMS, VOL. 18, 689 –707 (2003) © 2003 Wiley Periodicals, Inc. Published online in Wiley InterScience (www.interscience.wiley.com). • DOI 10.1002/int.10106