Abstract
In this work we propose a new multicriteria decision making algorithm for interval-valued fuzzy preference relations based on the use on a appropriate definition of interval-valued Choquet integrals. This algorithm allows to recover some of the best known usual fuzzy algorithms when the considered intervals are reduced to a single point. Since a key point in every decision making problem is that of the ordering, we propose a method to build orders based on the use of aggregation functions that, on one hand, allows to define several different total orders and, on the other hand, recovers some of the most commonly used total orders between intervals.
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References
Aumann, R.J.: Integrals of set–valued functions. J. Math. Anal. Appl. 12, 1–12 (1965)
Beliakov, G., Bustince, H., Goswami, D.P., Mukherjee, U.K., Pal, N.R.: On averaging operators for Atanassovs intuitionistic fuzzy sets. Inform. Sci. 181, 1116–1124 (2010)
Bustince, H., Barrenechea, E., Pagola, M., Fernandez, J.: Interval-valued fuzzy sets constructed from matrices: Application to edge detection. Fuzzy Sets Syst. 160, 1819–1840 (2009)
Choquet, G.: Theory of capacities. Ann. Inst. Fourier (Grenoble) 5, 131–292 (1953-1954)
Grabisch, M., Marichal, J.–L., Mesiar, R., Pap, E.: Aggregation functions. Cambridge University Press, Cambridge (2009)
Herrera, F., Herrera-Viedma, E.: Linguistic decision analysis:steps for solving decision problems under linguistic information. Fuzzy Sets and Systems 115, 67–82 (2000)
Jang, L.C.: Interval–valued Choquet integrals and their applications. J. Appl. Math. and Computing 16, 429–443 (2004)
Moore, R.E.: Interval Analysis. Prentice-Hall, Englewood Cliffs (1966)
Tan, C., Chen, X.: Intuitionistic fuzzy Choquet integral operator for multi-criteria decision making. Expert Systems with Appl. 37, 149–157 (2010)
Xu, Z.S.: Choquet integrals of weighted intuitionistic fuzzy information. Information Sciences 180, 726–736 (2010)
Ye, J.: Fuzzy decision-making method based on the weighted correlation coefficient under intuitionistic fuzzy environment. European Journal of Operational Research 205, 202–204 (2010)
Zadeh, L.A.: Probability measures of fuzzy events. J. Math. Anal. Appl. 23, 421–427 (1968)
Zadeh, L.A.: The concept of a linguistic variable and its applications to approximate reasoning. Inform. Sci. 8, Part I, 199–251, Part II pp. 301–357, Inform. Sci. 9, Part III pp. 43–80 (1975)
Zhang, D., Wang, Z.: On set–valued fuzzy integrals. Fuzzy Sets and Systems 56, 237–247 (1993)
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Bustince, H., Fernandez, J., Sanz, J., Galar, M., Mesiar, R., Kolesárová, A. (2011). Multicriteria Decision Making by Means of Interval-Valued Choquet Integrals. In: Melo-Pinto, P., Couto, P., Serôdio, C., Fodor, J., De Baets, B. (eds) Eurofuse 2011. Advances in Intelligent and Soft Computing, vol 107. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-24001-0_25
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DOI: https://doi.org/10.1007/978-3-642-24001-0_25
Publisher Name: Springer, Berlin, Heidelberg
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