Abstract
In this paper we propose a joint grid-based and stochastic search for parameters elicitation in the case of WOWA aggregation functions. The method uses a grid search approach to determine the parameter of a monotonic quantifier, and for each of the values, a stochastic search in the space of the criteria weights minimizes the sum of the quadratic error between the computed and the real output of a learning set. A simulated application is proposed in the case of transportation risk assessment, using an ad hoc questionnaire applied to risk matrices.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Beliakov, G., Pradera, A., Calvo, T.: Aggregation Functions: a guide for practitioners. STUDFUZZ, vol. 221. Springer, Heidelberg (2007)
Calvo, T., Mayor, G., Mesiar, R.: Aggregation Operators: new trends and applications. STUDFUZZ, vol. 91. Springer, Heidelberg (2002)
Filev, D., Yager, R.R.: On the issue of obtaining OWA operator weights. Fuzzy Sets and Systems 94, 157–169 (1998)
Grabisch, M., Roubens, M.: Application of the Choquet integral in multicriteria decision making. In: Grabisch, M., Murofushi, T., Sugeno, M. (eds.) Fuzzy Measures and Integrals Theory and Applications, pp. 348–374. Physica Verlag (2000)
Henningsen, A., Henningsen, G.: Om estimation of the CES production function - Revisited. Economic Letters 115, 67–69 (2012)
Klement, E.P., Mesiar, R., Pap, E.: Triangular Norms. Kluwer Academic Publishers (2000)
Llamazares, B.: On generalization of weighet means and OWA operators. In: Proc. of EUSLAT-LFA 2011 (2011)
Marichal, J.: An axiomatic approach of the discrete Choquet integral as a tool to aggregate interacting criteria. The IEEE Transactions on Fuzzy Systems 8(6), 800–807 (2000)
Palomares, I.: Applying OWA Operators and RIM Quantifiers to measure Consensus with Large Group of Experts. In: Proc. 6th International Summer School on Aggregation Operators - AGOP 2011 (2011)
Pérez, R., Alonso, P., Daz, I., Montes, S.: Aggregation of Risk Assesment Matrices for Umnao Reliability in Transportation Systems. In: De Baets, B., Fodor, J., Montes, S. (eds.) Proc. of EUROFUSE20- Uncertainty and Imprecision Modelling in Decision Making, pp. 225–232. Ediciones de la Universidad de Oviedo (2013)
Pinar, M., Cruciani, C., Giove, S., Sostero, M.: Constructing the FEEM sustainability index: A Choquet integral application. Ecological Indicator 39, 189–202 (2014)
Torra, V., Lv, Z.: On the WOWA operator and its interpolation function. International Journal of Intelligent Systems 24, 1039–1056 (2009)
Torra, V.: The weighted OWA operator. International Journal of Intelligent Systems 12, 153–166 (1997)
Torra, V., Narukawa, Y.: Modeling Decisions. Springer (2007)
Yager, R.R.: On ordered weighted averaging aggregation operators in multicriteria decision making. IEEE Trans. on Systems, Man and Cybernetics 18, 183–190 (1988)
Yager, R.R.: Applications and extensions of OWA aggregation, Internat. Journal Man Machine Studies 37, 103–132 (1992)
Yager, R.R.: Families of OWA operators. Fuzzy Sets and Systems 59, 125–148 (1993)
Yager, R.R., Kacprzyk, J. (eds.): The ordered Weighted Averaging Operators, Theory and Applications. Kluwer Academic Publisher (1997)
Yager, R.R.: Quantifier guided aggregation using OWA operators. International Journal of Intelligent Systems 11, 49–73 (1996)
Yager, R.R., Kacprzyk, J., Beliakov, G. (eds.): Recent Developments in the Ordered Weighted Averaging Operators: Theory and Practice. STUDFUZZ, vol. 265. Springer, Heidelberg (2011)
Xu, Z.S., Da An, Q.L.: overview of operators for aggregation informations. International Journal of Intelligent Systems 18, 953–969 (2003)
Wang, Y.M., Parkan, C.: A minimax disparity approach for obtaining OWA operator weights. Inform. Sci. 175, 20–29 (2005)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2015 Springer International Publishing Switzerland
About this chapter
Cite this chapter
Cardin, M., Giove, S. (2015). A Grid-Based Optimization Algorithm for Parameters Elicitation in WOWA Operators: An Application to Risk Assesment. In: Bassis, S., Esposito, A., Morabito, F. (eds) Advances in Neural Networks: Computational and Theoretical Issues. Smart Innovation, Systems and Technologies, vol 37. Springer, Cham. https://doi.org/10.1007/978-3-319-18164-6_20
Download citation
DOI: https://doi.org/10.1007/978-3-319-18164-6_20
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-18163-9
Online ISBN: 978-3-319-18164-6
eBook Packages: EngineeringEngineering (R0)