Abstract
The generalized Bonferroni mean is able to capture some interaction effects between variables and model mandatory requirements. We present a number of weights identification algorithms we have developed in the R programming language in order to model data using the generalized Bonferroni mean subject to various preferences. We then compare its accuracy when fitting to the journal ranks dataset.
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References
Beliakov, G.: fmtools package, version 1.0 (2007), http://www.deakin.edu.au/~gleb/aotool.html
Beliakov, G.: Construction of aggregation functions from data using linear programming. Fuzzy Sets and Systems 160, 65–75 (2009)
Beliakov, G., James, S.: Citation based journal rankings: an application of fuzzy measures. In: Proc. of the 5th Intl Summer School of Aggregation Operators AGOP 2009, Palma de Mallorca, Spain, July 6-11 (2009)
Beliakov, G., James, S.: Using Choquet integrals for evaluating citation indices in journal ranking. In: Proc. Eurofuse Workshop 2009, Pamplona, Spain, September 16-18 (2009)
Beliakov, G., James, S.: Citation-based journal ranks: The use of fuzzy measures. Fuzzy Sets and Systems 167, 101–119 (2011)
Beliakov, G., James, S.: Defining Bonferroni means over lattices. In: Proc. of FUZZIEEE, Brisbane, Austarlia (2012)
Beliakov, G., James, S.: On extending generalized Bonferroni means to Atanassov orthopairs in decision making contexts. Fuzzy Sets and Systems (in press, 2012), doi: 10.1016/j.fss.2012.03.018
Beliakov, G., James, S., Mordelová, J., Rückschlossová, T., Yager, R.R.: Generalized Bonferroni mean operators in multi-criteria aggregation. Fuzzy Sets and Systems 161, 2227–2242 (2010)
Beliakov, G., Pradera, A., Calvo, T.: Aggregation Functions: A Guide for Practitioners. Springer, Heidelberg (2007)
Bloomfield, P., Steiger, W.L.: Least Absolute Deviations. Theory, Applications and Algorithms. Birkhauser, Boston (1983)
Bonferroni, C.: Sulle medie multiple di potenze. Bollettino Matematica Italiana 5, 267–270 (1950)
Dujmovic, J.J.: Continuous preference logic for system evaluation. IEEE Trans. on Fuzzy Systems 15, 1082–1099 (2007)
Grabisch, M., Kojadinovic, I., Meyer, P.: A review of methods for capacity identification in Choquet integral based multi-attribute utility theory: Applications of the Kappalab R package. European Journal of Operational Research 186, 766–785 (2008)
Grabisch, M., Marichal, J.-L., Mesiar, R., Pap, E.: Aggregation Functions. Cambridge University press, Cambridge (2009)
Mordelová, J., Rückschlossová, T.: ABC-aggregation functions. In: Proc. of the 5th Intl. Summer School on Aggregation Operators, Palma de Mallorca, Spain (2009)
R Development Core Team. R: A Language and Environment for Statistical Computing. R Foundation for Statistical Computing, Vienna, Austria (2011), http://www.R-project.org/
Torra, Y., Narukawa, V.: Modeling Decisions. Information Fusion and Aggregation Operators. Springer (2007)
Xia, M., Xu, Z., Zhu, B.: Generalized intuitionistic fuzzy Bonferroni means. International Journal of Intelligent Systems 27, 23–47 (2011)
Xu, Z.: Uncertain Bonferroni mean operators. International Journal of Computational Intelligence Systems 3(6), 761–769 (2010)
Xu, Z., Yager, R.R.: Intuitionistic fuzzy Bonferroni means. IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics 41, 568–578 (2011)
Yager, R.: On generalized Bonferroni mean operators for multi-criteria aggregation. International Journal of Approximate Reasoning 50, 1279–1286 (2009)
Yager, R., Beliakov, G., James, S.: On generalized Bonferroni means. In: Proc. Eurofuse 2009 Conference, Pamplona, Spain (2009)
Yager, R.R.: On ordered weighted averaging aggregation operators in multicriteria decision making. IEEE Trans. on Systems, Man and Cybernetics 18, 183–190 (1988)
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Beliakov, G., James, S. (2012). Using Linear Programming for Weights Identification of Generalized Bonferroni Means in R. In: Torra, V., Narukawa, Y., López, B., Villaret, M. (eds) Modeling Decisions for Artificial Intelligence. MDAI 2012. Lecture Notes in Computer Science(), vol 7647. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-34620-0_5
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DOI: https://doi.org/10.1007/978-3-642-34620-0_5
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