**Commenced**in January 2007

**Frequency:**Monthly

**Edition:**International

**Paper Count:**31108

##### Using the OWA Operator in the Minkowski Distance

**Authors:**
José M. Merigó,
Anna M. Gil-Lafuente

**Abstract:**

**Keywords:**
Aggregation operators,
Minkowski distance,
OWA
operators,
Selection of strategies

**Digital Object Identifier (DOI):**
doi.org/10.5281/zenodo.1084486

**References:**

[1] 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.

[2] G. Beliakov, "Learning Weights in the Generalized OWA Operators", Fuzzy Opt. Decision Making, vol. 4, pp. 119-130, 2005.

[3] T. Calvo, G. Mayor, and R. Mesiar, Aggregation Operators: New Trends and applications, Physica-Verlag, New York, 2002.

[4] 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.

[5] R. Fullér, and P. Majlender, "On obtaining minimal variability OWA operator weights", Fuzzy Sets and Systems, vol. 136, pp. 203-215, 2003.

[6] P. Majlender, OWA operators with maximal Rényi entropy, Fuzzy Sets and Systems, vol. 155, pp. 340-360, 2005.

[7] 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.

[8] 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.

[9] Y.M. Wang, and C. Parkan, "A minimax disparity approach for obtaining OWA operator weights", Information Sciences, vol. 175, pp. 20-29, 2005.

[10] 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.

[11] Z.S. Xu, "An Overview of Methods for Determining OWA Weights", Int. J. Intelligent Systems, vol. 20, pp. 843-865, 2005.

[12] R.R. Yager, "On generalized measures of realization in uncertain environments", Theory and Decision, vol. 33, pp. 41-69, 1992.

[13] R.R. Yager, Families of OWA operators, Fuzzy Sets and Systems, vol. 59, pp. 125-148, 1993.

[14] R.R. Yager, "On weighted median aggregation", Int. J. Uncertainty Fuzziness Knowledge-Based Syst., vol. 2, pp. 101-113, 1994.

[15] R.R. Yager, and D.P. Filev, "Parameterized "andlike" and "orlike" OWA operators", Int. J. General Systems, vol. 22, pp. 297-316, 1994.

[16] R.R. Yager, "Quantifier Guided Aggregation Using OWA operators", Int. J. Intelligent Systems, vol. 11, pp. 49-73, 1996.

[17] R.R. Yager, "Generalized OWA Aggregation Operators", Fuzzy Opt. Decision Making, vol. 3, pp.93-107, 2004.

[18] R.R. Yager, "An extension of the naïve Bayesian classifier", Information Sciences, vol. 176, pp. 577-588, 2006.

[19] R.R. Yager, "Centered OWA operators", Soft Computing, vol. 11, pp. 631-639, 2007.

[20] R.R. Yager, and J. Kacprzyck, The Ordered Weighted Averaging Operators: Theory and Applications, Kluwer Academic Publishers, Norwell, MA, 1997.

[21] N. Karayiannis, "Soft Learning Vector Quantization and Clustering Algorithms Based on Ordered Weighted Aggregation Operators", IEEE Trans. Neural Networks, vol. 11, 1093-1105, 2000.

[22] 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.

[23] 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.

[24] 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.

[25] 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.

[26] 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.

[27] H. Dyckhoff, and W. Pedrycz, "Generalized means as model of compensative connectives", Fuzzy Sets and Systems, vol. 14, pp. 143- 154, 1984.

[28] 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.

[29] Z.S. Xu, and Q.L. Da, "The Ordered Weighted Geometric Averaging Operators", Int. J. Intelligent Systems, vol. 17, pp. 709-716, 2002.

[30] 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.

[31] A. Kaufmann, Introduction to the theory of fuzzy subsets, Academic Press, New York, 1975.

[32] A. Kaufmann, J. Gil-Aluja, and A. Terce├▒o, Mathematics for economic and business management, (in Spanish), Ed. Foro Cient├¡fico, Barcelona, Spain, 1994.

[33] E. Szmidt, and J. Kacprzyk, "Distances between intuitionistic fuzzy sets", Fuzzy Sets and Systems, vol. 114, pp. 505-518, 2000.

[34] 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.

[35] J. Gil Aluja, The interactive management of human resources in uncertainty, Kluwer Academic Publishers, Dordrecht, 1998.

[36] A.M. Gil-Lafuente, Fuzzy logic in financial analysis, Springer, Berlin, 2005.

[37] 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.