Abstract
Since the introduction of the ordered weighted averaging operator [18], the OWA has received great attention with applications in fields including decision making, recommender systems [8, 21], classification [10] and data mining [16] among others. The most important step in the calculation of the OWA is the permutation of the input vector according to the size of its arguments. In some applications, it makes sense that the inputs be reordered by values different to those used in calculation. For instance, if we have a number of mobile sensor readings, we may wish to allocate more importance to the reading taken from the sensor closest to us at a given point in time, rather than the largest reading.
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References
Beliakov, G., James, S.: Using Choquet integrals for kNN approximation and classification. In: Feng, G.G. (ed.) IEEE International Conference on Fuzzy Systems (FUZZ-IEEE 2008), pp. 1311–1317 (2008)
Beliakov, G., Pradera, A., Calvo, T.: Aggregation Functions: A Guide for Practitioners. Springer, Heidelberg (2007)
Calvo, T., Kolesárová, A., Komorníková, M., Mesiar, R.: Aggregation operators: properties, classes and construction methods. In: Calvo, T., et al. (eds.) Aggregation Operators: New Trends and Applications, pp. 3–104. Physica-Verlag, Heidelberg (2002)
Chiclana, F., Herrera-Viedma, E., Herrera, F., Alonso, S.: Induced ordered weighted geometric operators and their use in the aggregation of multiplicative preference relations. International Journal of Intelligent Systems 19, 233–255 (2004)
Chiclana, F., Herrera-Viedma, E., Herrera, F., Alonso, S.: Some induced ordered weighted averaging operators and their use for solving group decision-making problems based on fuzzy preference relations. European Journal of Operational Research 182, 383–399 (2007)
Grabisch, M., Murofushi, T., Sugeno, M.: Fuzzy Measures and Integrals: Theory and Applications. Physica-Verlag, Heidelberg (2000)
Grabisch, M., Marichal, J.-L., Mesiar, R., Pap, E.: Aggregation Functions. In: Encyclopedia of Mathematics and its Applications, vol. 127, Cambridge University Press, Cambridge (2009)
Herrera-Viedma, E., Peis, E.: Evaluating the informative quality of documents in SGML format from judgements by means of fuzzy linguistic techniques based on computing with words. Information Processing and Management 39, 233–249 (2003)
Marques Pereira, R.A., Ribeiro, R.A.: Aggregation with generalized mixture operators using weighting functions. Fuzzy Sets and Systems 137, 43–58 (2003)
Mathiassen, H., Ortiz-Arroyo, D.: Automatic categorization of patent applications using classifier combinations. In: Corchado, E., Yin, H., Botti, V., Fyfe, C. (eds.) IDEAL 2006. LNCS, vol. 4224, pp. 1039–1047. Springer, Heidelberg (2006)
Merigó, J.M., Gil-Lafuente, A.M.: The induced generalized OWA operator. Information Sciences 179, 729–741 (2009)
Mitchell, H.B., Estrakh, D.D.: A modified OWA operator and its use in lossless DPCM image compression. Journal of Uncertainty, Fuzziness and Knowledged-based Systems 5, 429–436 (1997)
Mitchell, H.B., Estrakh, D.D.: An OWA operator with fuzzy ranks. International Journal of Intelligent Systems 13, 59–81 (1998)
Mitchell, H.B., Schaefer, P.A.: Multiple priorities in an induced ordered weighted averaging operator. International Journal of Intelligent Systems 15, 317–327 (2000)
Pasi, G., Yager, R.R.: Modeling the concept of majority opinion in group decision making. Information Sciences 176, 390–414 (2006)
Torra, V.: OWA operators in data modeling and reidentification. IEEE Transactions on Fuzzy Systems 12(5), 652–660 (2004)
Torra, V., Narukawa, Y.: Modeling Decisions: Information Fusion and Aggregation Operators. Springer, Heidelberg (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.: The induced fuzzy integral aggregation operator. International Journal of Intelligent Systems 17, 1049–1065 (2002)
Yager, R.R.: Using fuzzy methods to model nearest neighbor rules. IEEE Transactions on Systems, Man, and Cybernetics – Part B: Cybernetics 32(4), 512–525 (2002)
Yager, R.R.: Noble reinforcement in disjunctive aggregation operators. IEEE Transactions on Fuzzy Systems 11(6), 754–767 (2003)
Yager, R.R.: Induced aggregation operators. Fuzzy Sets and Systems 137, 59–69 (2003)
Yager, R.R.: Choquet aggregation using order inducing variables. International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 12(1), 69–88 (2004)
Yager, R.R., Filev, D.P.: Induced ordered weighted averaging operators. IEEE Transactions on Systems, Man, and Cybernetics – Part B: Cybernetics 20(2), 141–150 (1999)
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Beliakov, G., James, S. (2011). Induced Ordered Weighted Averaging Operators. In: Yager, R.R., Kacprzyk, J., Beliakov, G. (eds) Recent Developments in the Ordered Weighted Averaging Operators: Theory and Practice. Studies in Fuzziness and Soft Computing, vol 265. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-17910-5_3
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DOI: https://doi.org/10.1007/978-3-642-17910-5_3
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