# THE GENERALIZED HYBRID AVERAGING OPERATOR AND ITS APPLICATION IN FINANCIAL DECISION MAKING

### José M. Merigó, Montserrat Casanovas

#### 2008

#### Abstract

We present the generalized hybrid averaging (GHA) operator. It is a new aggregation operator that generalizes the hybrid averaging (HA) operator by using the generalized mean. Then, we are able to generalize a wide range of mean operators such as the HA, the hybrid quadratic averaging (HQA), etc. The HA is an aggregation operator that includes the ordered weighted averaging (OWA) operator and the weighted average (WA). Then, with the GHA, we are able to get all the particular cases obtained by using generalized means in the OWA and in the WA such as the weighted geometric mean, the ordered weighted geometric (OWG) operator, the weighted quadratic mean (WQM), etc. We further generalize the GHA by using quasi-arithmetic means. Then, we obtain the quasi-arithmetic hybrid averaging (Quasi-HA) operator. Finally, we apply the new approach in a financial decision making problem.

#### References

- Beliakov, G., 2005. Learning Weights in the Generalized OWA Operators. Fuzzy Optimization and Decision Making, 4, pp. 119-130.
- Calvo, T., Mayor, G., Mesiar, R., 2002. Aggregation Operators: New Trends and Applications. PhysicaVerlag, New York.
- Fodor, J., Marichal, J.L., Roubens, M., 1995. Characterization of the ordered weighted averaging operators. IEEE Transactions on Fuzzy Systems, 3, pp. 236-240.
- Karayiannis, N., 2000. Soft Learning Vector Quantization and Clustering Algorithms Based on Ordered Weighted Aggregation Operators. IEEE Transactions on Neural Networks, 11, pp. 1093-1105.
- Merigó, J.M., 2007. New extensions to the OWA operator and its application in business decision making. Unpublished thesis (in Spanish), Department of Business Administration, University of Barcelona.
- Merigó, J.M. Casanovas, M., 2007. The fuzzy generalized OWA operator. In Proceedings of the XIVth Congress of International Association for fuzzy-set management and economy (SIGEF). Poiana-Brasov, Romania, pp. 504-517.
- Merigó, J.M., Gil-Lafuente, A.M., 2007. The induced generalized OWA operator. In Proceedings of the 5th EUSFLAT Conference. Ostrava, Czech Republic, vol. 2, pp. 463-470.
- Xu, Z.S., 2004. A method based on linguistic aggregation operators for group decision making with linguistic preference relations. Information Sciences, 166, pp. 19-30.
- Xu, Z.S., 2006. A Note on Linguistic Hybrid Arithmetic Averaging Operator in Multiple Attribute Group Decision Making with Linguistic Information. Group Decision and Negotiation, 15, pp. 593-604.
- Xu, Z.S., Da, Q.L., 2003. An overview of operators for aggregating the information. International Journal of Intelligent Systems, 18, pp. 953-969.
- Yager, R.R., 1988. On Ordered Weighted Averaging Aggregation Operators in Multi-Criteria Decision Making. IEEE Transactions on Systems, Man and Cybernetics, B 18, pp. 183-190.
- Yager, R.R., 1993. Families of OWA operators. Fuzzy Sets and Systems, 59, pp. 125-148.
- Yager, R.R., 1996. Quantifier guided aggregation using OWA operators. International Journal of Intelligent Systems, 11, pp. 49-73.
- Yager, R.R., 2004. Generalized OWA Aggregation Operators. Fuzzy Optimization and Decision Making, 3, pp. 93-107.
- Yager, R.R., Filev, D.P., 1994. Parameterized andlike and orlike OWA Operators. International Journal of General Systems, 22, pp. 297-316.
- Yager, R.R., Kacprzyk, J., 1997. The Ordered Weighted Averaging Operators: Theory and Applications. Kluwer Academic Publishers, Norwell, MA.

#### Paper Citation

#### in Harvard Style

M. Merigó J. and Casanovas M. (2008). **THE GENERALIZED HYBRID AVERAGING OPERATOR AND ITS APPLICATION IN FINANCIAL DECISION MAKING** . In *Proceedings of the Tenth International Conference on Enterprise Information Systems - Volume 2: ICEIS,* ISBN 978-989-8111-37-1, pages 467-471. DOI: 10.5220/0001692204670471

#### in Bibtex Style

@conference{iceis08,

author={José M. Merigó and Montserrat Casanovas},

title={THE GENERALIZED HYBRID AVERAGING OPERATOR AND ITS APPLICATION IN FINANCIAL DECISION MAKING},

booktitle={Proceedings of the Tenth International Conference on Enterprise Information Systems - Volume 2: ICEIS,},

year={2008},

pages={467-471},

publisher={SciTePress},

organization={INSTICC},

doi={10.5220/0001692204670471},

isbn={978-989-8111-37-1},

}

#### in EndNote Style

TY - CONF

JO - Proceedings of the Tenth International Conference on Enterprise Information Systems - Volume 2: ICEIS,

TI - THE GENERALIZED HYBRID AVERAGING OPERATOR AND ITS APPLICATION IN FINANCIAL DECISION MAKING

SN - 978-989-8111-37-1

AU - M. Merigó J.

AU - Casanovas M.

PY - 2008

SP - 467

EP - 471

DO - 10.5220/0001692204670471