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The Induced Generalized Hybrid Averaging Operator and its Application in Financial Decision Making
Authors: José M. Merigó, Montserrat Casanovas
Abstract:We present the induced generalized hybrid averaging (IGHA) operator. It is a new aggregation operator that generalizes the hybrid averaging (HA) by using generalized means and order inducing variables. With this formulation, we get a wide range of mean operators such as the induced HA (IHA), the induced hybrid quadratic averaging (IHQA), the HA, etc. The ordered weighted averaging (OWA) operator and the weighted average (WA) are included as special cases of the HA operator. Therefore, with this generalization we can obtain a wide range of aggregation operators such as the induced generalized OWA (IGOWA), the generalized OWA (GOWA), etc. We further generalize the IGHA operator by using quasi-arithmetic means. Then, we get the Quasi-IHA operator. Finally, we also develop an illustrative example of the new approach in a financial decision making problem. The main advantage of the IGHA is that it gives a more complete view of the decision problem to the decision maker because it considers a wide range of situations depending on the operator used.
Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1085245Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1135
 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, A. Pradera, and T. Calvo, Aggregation Functions: A guide for practitioners, Springer-Verlag, Berlin, 2007.
 T. Calvo, G. Mayor, and R. Mesiar, Aggregation Operators: New Trends and applications, Physica-Verlag, New York, 2002.
 J.M. Merig├│, New Extensions to the OWA Operators and its application in decision making, PhD Thesis (in Spanish), Dept. Business Administration, Univ. Barcelona, Barcelona, Spain, 2008
 J.M. Merig├│, and M. Casanovas, "Induced aggregation operators in decision making with Dempster-Shafer belief structure", Int. J. Intelligent Systems (to be published).
 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, 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.
 R.R. Yager, "Generalized OWA Aggregation Operators", Fuzzy Opt. Decision Making, vol. 3, pp.93-107, 2004.
 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.
 G. Beliakov, "Learning Weights in the Generalized OWA Operators", Fuzzy Opt. Decision Making, vol. 4, pp. 119-130, 2005.
 G.H. Hardy, J.E. Littlewood, and G. P├│lya, Inequalities, Cambridge University Press, Cambridge, 1934.
 A.N. Kolmogoroff, "Sur la notion de la moyenne", Atti Della Accademia Nazionale Dei Lincei, vol. 12, pp. 388-391, 1930.
 M. Nagumo, "Uber eine klasse der mittelwerte", Japanese J. of Mathematics, vol. 6, pp. 71-79, 1930.
 J. Fodor, J.L. Marichal, and M. Roubens, "Characterization of the ordered weighted averaging operators", IEEE Trans. Fuzzy Systems, vol. 3, pp. 236-240, 1995.
 J.M. Merig├│, and A.M. Gil-Lafuente, "The induced generalized OWA operator", Information Sciences, vol. 179, pp. 729-741, 2009.
 R.R. Yager, "Induced aggregation operators", Fuzzy Sets and Systems, vol. 137, pp. 59-69, 2003.
 R.R. Yager, and D.P. Filev, "Induced ordered weighted averaging operators", IEEE Trans. Syst. Man Cybern., vol. 29, pp. 141-150, 1999.
 J.M. Merig├│, and M. Casanovas, "The fuzzy generalized OWA operator", In Proceedings of the Conference SIGEF 2007, pp. 504-517, Poiana-Brasov, Romania, 2007.
 J.M. Merig├│, M. Casanovas, "The uncertain generalized OWA operator and its application in the selection of financial strategies", In Proceedings of the International Conference AEDEM 2007, pp. 547- 556, Krakow, Poland, 2007.
 J.H. Wang, and J. Hao, "A new version of 2-tuple fuzzy linguistic representation model for computing with words", IEEE Trans. Fuzzy Systems, vol. 14, pp. 435-445, 2006.
 P.A. Schaefer, and H.B. Mitchell, "A generalized OWA operator", Int. J. Intelligent Systems, vol. 14, pp. 123-143, 1999.
 Z.S. Xu, and Q.L. Da, "An Overview of Operators for Aggregating Information", Int. J. Intelligent Systems, vol. 18, pp. 953-969, 2003.
 Z.S. Xu, "A method based on linguistic aggregation operators for group decision making with linguistic preference relations", Information Sciences, vol. 166, pp. 19-30, 2004.
 Z.S. Xu, "A Note on Linguistic Hybrid Arithmetic Averaging Operator in Multiple Attribute Group Decision Making with Linguistic Information", Group Decision and Negotiation, vol. 15, pp. 593-604, 2006.
 R.R. Yager, "On weighted median aggregation", Int. J. Uncertainty Fuzziness and Knowledge-Based Systems, vol. 2, pp. 101-113, 1994.
 R.R. Yager, "Quantifier Guided Aggregation Using OWA operators", Int. J. Intelligent Systems, vol. 11, pp. 49-73, 1996.
 R.R. Yager, E-Z OWA weights, In Proceedings of the 10th International Fuzzy Systems Association (IFSA) World Congress, Istanbul, Turkey, pp. 39-42, 2003.
 R.R. Yager, "Centered OWA operators", Soft Computing, vol. 11, pp. 631-639, 2007.
 R.R. Yager, and D.P. Filev, "Parameterized "andlike" and "orlike" OWA operators", Int. J. General Systems, vol. 22, pp. 297-316, 1994.