Mesiar, R.; Kolesárová, A.; Bustince, H.; Dimuro, G. P.; Bedregal, B. C. Fusion functions based discrete Choquet-like integrals. (English) Zbl 1346.91057 Eur. J. Oper. Res. 252, No. 2, 601-609 (2016). Summary: In this paper, we generalize a formula for the discrete Choquet integral by replacing the standard product by a suitable fusion function. For the introduced fusion functions based discrete Choquet-like integrals we discuss and prove several properties and also show that our generalization leads to several new interesting functionals. We provide a complete characterization of the introduced functionals as aggregation functions. For \(n = 2\), several new aggregation functions are obtained, and if symmetric capacities are considered, our approach yields new generalizations of OWA operators. If \(n>2\), the introduced functionals are aggregation functions only if they are Choquet integrals with respect to some distorted capacity. Cited in 2 ReviewsCited in 14 Documents MSC: 91B06 Decision theory 28E10 Fuzzy measure theory Keywords:multi-criteria analysis; aggregation function; Choquet integral; fusion function; pre-aggregation function PDFBibTeX XMLCite \textit{R. Mesiar} et al., Eur. J. Oper. Res. 252, No. 2, 601--609 (2016; Zbl 1346.91057) Full Text: DOI References: [1] Aczél, J., Lectures on functional equations and their applications (1966), Academic Press: Academic Press New York · Zbl 0139.09301 [2] Baczynski, M.; Jayaram, B., Fuzzy implications, Studies in fuzziness and soft computing series, Vol. 231 (2008), Springer-Verlag: Springer-Verlag Heidelberg · Zbl 1147.03012 [3] Bedregal, B. C.; Dimuro, G. P.; Bustince, H.; Barrenechea, E., New results on overlap and grouping functions, Information Sciences, 249, 148-170 (2013) · Zbl 1335.68264 [4] Beliakov, G.; Bustince, H.; Calvo, T., A practical guide to averaging functions (2016), Springer: Springer Heidelberg, Berlin/New York [5] Beliakov, G.; Pradera, A.; Calvo, T., Aggregation functions: a guide for practitioners (2007), Springer: Springer Heidelberg, Berlin/New York · Zbl 1123.68124 [6] Bustince, H.; Fernandez, J.; Kolesárová, A.; Mesiar, R., Directional monotonicity of fusion functions, European Journal of Operational Research, 244, 300-308 (2015) · Zbl 1346.26004 [7] Bustince, H.; Fernandez, J.; Mesiar, R.; Montero, J.; Orduna, R., Overlap functions, Nonlinear Analysis: Theory, Methods & Applications, 72, 1488-1499 (2010) · Zbl 1182.26076 [8] Bustince, H.; Galar, M.; Bedregal, B.; Kolesárová, A.; Mesiar, R., A new approach to interval-valued choquet integrals and the problem of ordering in interval-valued fuzzy set applications, IEEE Transactions on Fuzzy Systems, 21, 6, 1150-1162 (2013) [9] Bustince, H.; Pagola, M.; Mesiar, R.; Hüllermeier, E.; Herrera, F., Grouping, overlap, and generalized bientropic functions for fuzzy modeling of pairwise comparisons, IEEE Transactions on Fuzzy Systems, 20, 405-415 (2012) [10] Calvo, T.; Kolesárová, A.; Komorníková, M.; Mesiar, R., Aggregation operators: properties, classes and construction methods, (Calvo, T.; Mayor, G.; Mesiar, R., Aggregation operators. New trends and applications (2002), Physica-Verlag: Physica-Verlag Heidelberg), 3-107 · Zbl 1039.03015 [11] Choquet, G., Theory of capacities, Annales de l’institut Fourier, 5, 131-295 (1953) · Zbl 0064.35101 [12] Denneberg, D., Non-additive measure and integral (1994), Kluwer Academic Publishers Group: Kluwer Academic Publishers Group Dordrecht · Zbl 0826.28002 [13] Durante, F.; Sempi, C., Semicopulae, Kybernetika, 41, 315-328 (2005) · Zbl 1249.26021 [14] Genest, C.; Molina, J. J.Q.; Rodríguez-Lallena, J. A.; Sempi, C., A characterization of quasi-copulas, Journal of Multivariate Analysis, 69, 193-205 (1999) · Zbl 0935.62059 [15] Grabisch, M., Fuzzy integral in multicriteria decision making, Fuzzy Sets and Systems, 69, 279-298 (1995) · Zbl 0845.90001 [16] Grabisch, M.; Marichal, J.-L.; Mesiar, R.; Pap, E., Aggregation functions (2009), Cambridge University Press: Cambridge University Press Cambridge [17] Klement, E. P.; Mesiar, R.; Pap, E., Triangular norms (2000), Kluwer Academic Publishers: Kluwer Academic Publishers Dordrecht · Zbl 0972.03002 [18] Klement, E. P.; Mesiar, R.; Pap, E., A universal integral as common frame for Choquet and Sugeno integral, IEEE Transactions on Fuzzy Systems, 18, 178-187 (2010) [19] Klement, E. P.; Mesiar, R.; Spizzichino, F.; Stupňanová, A. S., Universal integrals based on copulas, Fuzzy Optim. Decis. Making, 13, 273-289 (2014) · Zbl 1428.28024 [20] Lehrer, E., A new integral for capacities, Economic Theory, 39, 157-176 (2009) · Zbl 1156.91334 [21] Lucca, G.; Sanz, J. A.; Dimuro, G. P.; Bedregal, B.; Mesiar, R.; Kolesárová, A.; Bustince, H., Pre-aggregation functions, IEEE Transactions on Fuzzy Systems (2016) [22] Mesiar, R., Choquet-like integrals, Journal of Mathematical Analysis and Applications, 194, 477-488 (1995) · Zbl 0845.28010 [23] Šipoš, J., Integral with respect to a pre-measure, Mathematica Slovaca, 29, 141-155 (1979) · Zbl 0423.28003 [24] Wilkin, T.; Beliakov, G., Weakly monotone aggregation functions, International Journal of Intelligent Systems, 30, 144-165 (2015) [25] Yager, R., On ordered weighted averaging aggregation operators in multi-criteria decision making, IEEE Transactions on Systems, Man and Cybernetics, 18, 183-190 (1988) · Zbl 0637.90057 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.