Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 31093
Using Fuzzy Numbers in Heavy Aggregation Operators

Authors: José M. Merigó, Montserrat Casanovas


We consider different types of aggregation operators such as the heavy ordered weighted averaging (HOWA) operator and the fuzzy ordered weighted averaging (FOWA) operator. We introduce a new extension of the OWA operator called the fuzzy heavy ordered weighted averaging (FHOWA) operator. The main characteristic of this aggregation operator is that it deals with uncertain information represented in the form of fuzzy numbers (FN) in the HOWA operator. We develop the basic concepts of this operator and study some of its properties. We also develop a wide range of families of FHOWA operators such as the fuzzy push up allocation, the fuzzy push down allocation, the fuzzy median allocation and the fuzzy uniform allocation.

Keywords: fuzzy numbers, Aggregation operators, Fuzzy OWAoperator, Heavy OWA operator

Digital Object Identifier (DOI):

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1248


[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] T. Calvo, G. Mayor, and R. Mesiar, Aggregation Operators: New Trends and applications, Physica-Verlag, New York, 2002.
[3] G. Canfora, and L. Troiano, "An Extensive Comparison between OWA and OFNWA Aggregation", in: Proc. of the 8th SIGEF Congress, Napoli, Italy, 2001.
[4] S.J. Chen, and S.M. Chen, "A new method for handling multi-criteria fuzzy decision making problems using FN-IOWA operators", Cybernetics and Systems, vol. 34, pp. 109-137, 2003.
[5] 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.
[6] 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, 2007.
[7] J.M. Merig├│, and M. Casanovas, "Induced and uncertain heavy ordered weighted averaging operators", Fuzzy Sets and Systems, to be published.
[8] H.B. Mitchell, and D.D. Estrakh, "An OWA operator with fuzzy ranks", Int. J. Intelligent Systems, vol. 13, pp. 69-81, 1998.
[9] V. Torra, Information Fusion in Data Mining, Springer, New York, 2002.
[10] Z.S. Xu, "A fuzzy ordered weighted geometric operator and its application in fuzzy AHP", Systems, Engineering and Electronics, vol. 24, pp. 31-33, 2002.
[11] Z.S. Xu, "An Overview of Methods for Determining OWA Weights", Int. J. Intelligent Systems, vol. 20, pp. 843-865, 2005.
[12] Z.S. Xu, and Q.L. Da, "An Overview of Operators for Aggregating Information", Int. J. Intelligent Systems, vol. 18, pp. 953-969, 2003.
[13] R.R. Yager, "On generalized measures of realization in uncertain environments", Theory and Decision, vol. 33, pp. 41-69, 1992.
[14] R.R. Yager, "Families of OWA operators", Fuzzy Sets and Systems, vol. 59, pp. 125-148, 1993.
[15] R.R. Yager, "On weighted median aggregation", Int. J. Uncertainty Fuzziness Knowledge-Based Systems, vol. 2, pp. 101-113, 1994.
[16] R.R. Yager, "Constrained OWA Aggregation", Fuzzy Sets and Systems, vol. 81, pp. 89-101, 1996.
[17] R.R. Yager, "Quantifier Guided Aggregation Using OWA operators", Int. J. Intelligent Systems, vol. 11, pp. 49-73, 1996.
[18] R.R. Yager, "Heavy OWA Operators", Fuzzy Optim. Decision Making, vol. 1, pp. 379-397, 2002.
[19] R.R. Yager, "Monitored heavy fuzzy measures and their role in decision making under uncertainty", Fuzzy Sets and Systems, vol. 139, pp. 491- 513, 2003.
[20] R.R. Yager, and J. Kacprzyck, The Ordered Weighted Averaging Operators: Theory and Applications, Kluwer Academic Publishers, Norwell, MA, 1997.
[21] S.S.L. Chang, and L.A. Zadeh, "On fuzzy mapping and control", IEEE Trans. Systems, Man and Cybernetics, vol. 2, pp. 30-34, 1972.
[22] L.A. Zadeh, "The Concept of a Linguistic Variable and its application to Approximate Reasoning. Part 1", Information Sciences, vol. 8, pp. 199- 249, "Part 2", Information Sciences, vol. 8, pp. 301-357, "Part 3", Information Sciences, vol. 9, pp. 43-80, 1975.
[23] D. Dubois, and H. Prade, "Operations on fuzzy numbers", Int. J. Systems Science, vol. 9, pp. 613-626, 1978.
[24] D. Dubois, and H. Prade, Fuzzy Sets and Systems: Theory and Applications, Academic Press, New York, 1980.
[25] A. Kaufmann, and M.M. Gupta, Introduction to fuzzy arithmetic, Publications Van Nostrand, Rheinhold, 1985.
[26] A. Kaufmann, and J. Gil Aluja, Management techniques for the treatment of uncertainty, (in Spanish), Ed. Hispano-europea, Spain, 1987.
[27] A. Kaufmann, J. Gil-Aluja, and A. Terceño, Mathematics for economic and business management, (in Spanish), Ed. Foro Científico, Barcelona, Spain, 1994.
[28] M. Mizumoto, and K. Tanaka, "The four operations of arithmetic on fuzzy numbers", Systems, Computing and Control, vol. 7, pp. 73-81, 1976.
[29] S. Nahmias, "Fuzzy variables", Fuzzy Sets and Systems, vol. 1, pp. 97- 110, 1978.
[30] K.J. Arrow, L. Hurwicz, "An optimality criterion for decision making under ignorance", in: C.F. Carter, J.L. Ford (Eds.), Uncertainty and Expectations in Economics, Kelley, New Jersey, 1972.