10.2190/18H8-9362-3363-3120 18H8936233633120 5 Andness-Directed Weighted Averaging Operators: Possibilities for Environmental Project Evaluation 333 348 20070221 20070221 20070221 20070221 18H8936233633120.pdf http://baywood.metapress.com/link.asp?target=contribution&id=18H8936233633120 4 P. N. Smith University of Queensland, Australia Some of the conventional methods of aggregating the performance of infrastructure projects with respect to multiple factors/impacts are considered. It is suggested that alternative forms of aggregation might be more useful; in particular, the ordered weighted averaging (OWA) operator introduced by Ronald Yager. Factor importance weights and fuzzy satisfaction of factors by projects may be aggregated prior to aggregation via an OWA operator. In this case OWA operator weights may be based on the "attitudinal character" of the decision-maker expressed in terms of the degree of "orness" and "andness" of the aggregation. One approach is maximum entropy aggregation where weights are derived to be as "even" (or as minimally dispersed) as possible subject to satisfying a given "orness" or "andness" constraint. Recently aggregation processes based on "andness" have been proposed by Henrik Larsen which have several desirable properties and may also be considered as alternative forms of aggregation. A simple example based on a hypothetical but realistic example by Horsak and Damico is given which involves the location of a hazardous waste disposal facility (PCB-contaminated transformer fluids) at one of three sites based on ten factors. R. Horsak and S. Damico, Selection and Evaluation of Hazardous Waste Disposal Sites Using Fuzzy Set Analysis, <i>Journal of the Air Pollution Control Association</i>, 35, pp. 1081-1085, 1985. G. Anandalingam and M. Westfall, Selection of Hazardous Waste Disposal Alternatives using Multiattribute Utility Theory and Fuzzy Set Theory, <i>Journal of Environmental Systems</i>, 18, pp. 69-85, 1988. M. M. Sobral, K. W. Hipel, and G. J. Farquhar, A Multi-Criteria Model of Solid Waste Management, <i>Journal of Environmental Management</i>, 12, pp. 97-110, 1981. P. N. Smith, Numeric Ordered Weighted Averaging Operators: Possibilities for Environmental Project Evaluation, <i>Journal of Environmental Systems</i>, 28, pp. 175-191, 2000-2001. P. N. Smith, Linguistic Ordered Weighted Averaging Operators: Possibilities for Environmental Project Evaluation, <i>Journal of Environmental Systems</i>, 28, pp. 257-269, 2000-2001. R. R. Yager, On Ordered Weighted Averaging Aggregation Operators in Multicriteria Decision Making, <i>IEEE Transactions on Systems, Man and Cybernetics</i>, 18, pp. 183-190, 1988. H. L. Larsen, Efficient Importance Weighted Aggregation Between Min and Max, <i>9th International Conference on Information Processing and Management of Uncertainty in Knowledge-Based Systems</i> (IPMU 2002), July 1-5, 2002. H. L. Larsen, Importance Weighted OWA Aggregation of Multicriteria Queries, <i>Proceeding of the North American Fuzzy Information Processing Society Conference (NAFIPS'99)</i>, New York, June 10-12, 1999, pp. 740-744, 1999. R. R. Yager, Criteria Importances in OWA Aggregation: An Application of Fuzzy Modelling, <i>Proceedings of the 6th IEEE International Conference on Fuzzy Systems, Barcelona</i>, 3, pp. 1677-1682, 1997. J.-S. R. Jang, C. T. Sun, and E. Mizutani, <i>Neuro-Fuzzy and Soft Computing: A Computational Approach to Learning and Machine Intelligence</i>, Prentice-Hall, 1997. R. R. Yager, On the Inclusion of Importances in OWA Aggregations, in <i>The Ordered Weighted Averaging Operators. Theory and Application</i>, R. R. Yager and J. Kacprzyk (eds.), Kluwer Academic, Boston, Massachusetts, pp. 41-59, 1997. R. R. Yager, Including Importances in OWA Aggregations Using Fuzzy Systems Modelling, <i>IEEE Transactions on Fuzzy Systems</i>, 6, pp. 286-294, 1998. R. R. Yager, On the Issue of Importance Qualification in Fuzzy Multi-Criteria Decision Making, <i>International Journal of Computational Intelligence and Organisations</i>, 1, pp. 35-48, 1996. D. P. Filev and R. R. Yager, Learning OWA Operator Weights from Data, <i>Proceedings of the 3rd IEEE Conference on Fuzzy Systems</i>, pp. 468-473, 1994. D. Filev and R. R. Yager, Analytical Properties of Maximum Entropy OWA Operators, <i>Information Science</i>, 85, pp. 11-27, 1995. R. Fullér and P. Majlender, On Obtaining Minimal Variability OWA Operator Weights, <i>Fuzzy Sets and Systems</i>, 136, pp. 203-215, 2003. Y.-M. Wang and C. Parkan, A Minimax Disparity Approach for Obtaining OWA Operator Weights, <i>Information Sciences</i>, 175, pp. 20-29, 2005. H. L. Larsen, Efficient Andness-Directed Importance Weighted Averaging Operators, <i>International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems</i>, 11, pp. 67-82, 2003. J. M. Fernández Salido and S. Murakami, Extending Yager's Orness Concept for the OWA Aggregators to Other Mean Operators, <i>Fuzzy Sets and Systems</i>, 139, pp. 515-542, 2003.