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Using the OWA Operator in the Minkowski Distance
Authors: José M. Merigó, Anna M. Gil-Lafuente
Abstract:We study different types of aggregation operators such as the ordered weighted averaging (OWA) operator and the generalized OWA (GOWA) operator. We analyze the use of OWA operators in the Minkowski distance. We will call these new distance aggregation operator the Minkowski ordered weighted averaging distance (MOWAD) operator. We give a general overview of this type of generalization and study some of their main properties. We also analyze a wide range of particular cases found in this generalization such as the ordered weighted averaging distance (OWAD) operator, the Euclidean ordered weighted averaging distance (EOWAD) operator, the normalized Minkowski distance, etc. Finally, we give an illustrative example of the new approach where we can see the different results obtained by using different aggregation operators.
Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1084486Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1808
 R.R. Yager, "On Ordered Weighted Averaging Aggregation Operators in Multi-Criteria Decision Making", IEEE Trans. Systems, Man and Cybernetics, vol. 18, pp. 183-190, 1988.
 G. Beliakov, "Learning Weights in the Generalized OWA Operators", Fuzzy Opt. Decision Making, vol. 4, pp. 119-130, 2005.
 T. Calvo, G. Mayor, and R. Mesiar, Aggregation Operators: New Trends and applications, Physica-Verlag, New York, 2002.
 D.P. Filev, and R.R. Yager, "On the issue of obtaining OWA operator weights", Fuzzy Sets and Systems, vol. 94, pp. 157-169, 1998.
 R. Fullér, and P. Majlender, "On obtaining minimal variability OWA operator weights", Fuzzy Sets and Systems, vol. 136, pp. 203-215, 2003.
 P. Majlender, OWA operators with maximal Rényi entropy, Fuzzy Sets and Systems, vol. 155, pp. 340-360, 2005.
 J.M. Merig├│, New Extensions to the OWA Operators and its application in business decision making, Thesis (in Spanish), Dept. Business Administration, Univ. Barcelona, Barcelona, Spain, 2007.
 M. O-Hagan, "Fuzzy decision aids", in : Proc. 21st IEEE Asilomar Conf. on Signal, Systems and Computers, vol 2, Pacific Grove, CA, 1987, pp. 624-628.
 Y.M. Wang, and C. Parkan, "A minimax disparity approach for obtaining OWA operator weights", Information Sciences, vol. 175, pp. 20-29, 2005.
 Y.M. Wang, and C. Parkan, "A preemptive goal programming method for aggregating OWA operator weights in group decision making", Information Sciences, vol. 177, pp. 1867-1877, 2007.
 Z.S. Xu, "An Overview of Methods for Determining OWA Weights", Int. J. Intelligent Systems, vol. 20, pp. 843-865, 2005.
 R.R. Yager, "On generalized measures of realization in uncertain environments", Theory and Decision, vol. 33, pp. 41-69, 1992.
 R.R. Yager, Families of OWA operators, Fuzzy Sets and Systems, vol. 59, pp. 125-148, 1993.
 R.R. Yager, "On weighted median aggregation", Int. J. Uncertainty Fuzziness Knowledge-Based Syst., vol. 2, pp. 101-113, 1994.
 R.R. Yager, and D.P. Filev, "Parameterized "andlike" and "orlike" OWA operators", Int. J. General Systems, vol. 22, pp. 297-316, 1994.
 R.R. Yager, "Quantifier Guided Aggregation Using OWA operators", Int. J. Intelligent Systems, vol. 11, pp. 49-73, 1996.
 R.R. Yager, "Generalized OWA Aggregation Operators", Fuzzy Opt. Decision Making, vol. 3, pp.93-107, 2004.
 R.R. Yager, "An extension of the naïve Bayesian classifier", Information Sciences, vol. 176, pp. 577-588, 2006.
 R.R. Yager, "Centered OWA operators", Soft Computing, vol. 11, pp. 631-639, 2007.
 R.R. Yager, and J. Kacprzyck, The Ordered Weighted Averaging Operators: Theory and Applications, Kluwer Academic Publishers, Norwell, MA, 1997.
 N. Karayiannis, "Soft Learning Vector Quantization and Clustering Algorithms Based on Ordered Weighted Aggregation Operators", IEEE Trans. Neural Networks, vol. 11, 1093-1105, 2000.
 J.M. Merig├│, and A.M. Gil-Lafuente, "The Ordered Weighted Averaging Distance Operator", Lectures on Modelling and Simulation, vol. 2007 (1), to be published.
 J.M. Merig├│, and A.M. Gil-Lafuente, "On the Use of the OWA Operator in the Euclidean Distance", Int. J. Computer Science and Engineering, submitted for publication, 2008.
 J.M. Merig├│, and A.M. Gil-Lafuente, "Geometric Operators in the Selection of Human Resources", Int. J. Computer and Information Science and Engineering, submitted for publication, 2008.
 J.M. Merig├│, and M. Casanovas, "Ordered weighted geometric operators in decision making with Dempster-Shafer belief structure", in Proc. 13th Congress Int. Association for Fuzzy Set Management and Economy (SIGEF), Hammamet, Tunisia, 2006, pp 709-727.
 J. Dujmovic, "Weighted conjunctive and disjunctive means and their application in system evaluation", Publikacije Elektrotechnickog Faculteta Beograd, Serija Matematika i Fizika, No. 483, pp. 147-158, 1974.
 H. Dyckhoff, and W. Pedrycz, "Generalized means as model of compensative connectives", Fuzzy Sets and Systems, vol. 14, pp. 143- 154, 1984.
 F. Chiclana, F. Herrera, and E. Herrera-Viedma, "The ordered weighted geometric operator: Properties and application", in Proc. 8th Conf. Inform. Processing and Management of Uncertainty in Knowledgebased Systems (IPMU), Madrid, Spain, 2000, pp. 985-991.
 Z.S. Xu, and Q.L. Da, "The Ordered Weighted Geometric Averaging Operators", Int. J. Intelligent Systems, vol. 17, pp. 709-716, 2002.
 F. Herrera, E. Herrera-Viedma, and F. Chiclana, "A study of the origin and uses of the ordered weighted geometric operator in multicriteria decision making", Int. J. Intelligent Systems, vol. 18, pp. 689-707, 2003.
 A. Kaufmann, Introduction to the theory of fuzzy subsets, Academic Press, New York, 1975.
 A. Kaufmann, J. Gil-Aluja, and A. Terce├▒o, Mathematics for economic and business management, (in Spanish), Ed. Foro Cient├¡fico, Barcelona, Spain, 1994.
 E. Szmidt, and J. Kacprzyk, "Distances between intuitionistic fuzzy sets", Fuzzy Sets and Systems, vol. 114, pp. 505-518, 2000.
 J.M. Merig├│, and M. Casanovas, "Geometric operators in decision making with minimization of regret", Int. J. Computer Systems Science and Engineering, vol. 1, pp. 111-118, 2008.
 J. Gil Aluja, The interactive management of human resources in uncertainty, Kluwer Academic Publishers, Dordrecht, 1998.
 A.M. Gil-Lafuente, Fuzzy logic in financial analysis, Springer, Berlin, 2005.
 J.M. Merig├│, and A.M. Gil-Lafuente, "Unification point in methods for the selection of financial products", Fuzzy Economic Review, vol. 12, pp. 35-50, 2007.