Bustince, Humberto; Fernandez, Javier; Kolesárová, Anna; Mesiar, Radko Fusion functions and directional monotonicity. (English) Zbl 1415.68227 Laurent, Anne (ed.) et al., Information processing and management of uncertainty in knowledge-based systems. 15th international conference, IPMU 2014, Montpellier, France, July 15–19, 2014. Proceedings. Part III. Cham: Springer. Commun. Comput. Inf. Sci. 444, 262-268 (2014). Summary: After introducing fusion functions, the directional monotonicity of fusion functions is introduced and studied. Moreover, in special cases the sets of all vectors with respect to which the studied fusion functions are increasing (decreasing) are completely characterized.For the entire collection see [Zbl 1385.68008]. Cited in 3 Documents MSC: 68T37 Reasoning under uncertainty in the context of artificial intelligence Keywords:aggregation function; fusion function; directional monotonicity; piecewise linear function PDFBibTeX XMLCite \textit{H. Bustince} et al., Commun. Comput. Inf. Sci. 444, 262--268 (2014; Zbl 1415.68227) Full Text: DOI References: [1] Baczynski, M., Jayaram, B.: Fuzzy Implications. STUDFUZZ, vol. 231. Springer, Heidelberg (2008) · Zbl 1147.03012 [2] Beliakov, G., Pradera, A., Calvo, T.: Aggregation Functions: A Guide for Practitioners. Springer, Heidelberg (2007) · Zbl 1123.68124 [3] Choquet, G.: Theory of capacities. Ann. Inst. Fourier 5, 131-295 (1953) · Zbl 0064.35101 [4] Fujimoto, K., Sugeno, M., Murofushi, T.: Hierarchical decomposition of Choquet integrals models. Int. J. Uncertainty, Fuzziness and Knowledge-Based Systems 3, 1-15 (1995) · Zbl 1232.93010 [5] Grabisch, M.: Fuzzy integral in multicriteria decision making. Fuzzy Sets and Systems 69, 279-298 (1995) · Zbl 0845.90001 [6] Grabisch, M., Marichal, J.-L., Mesiar, R., Pap, E.: Aggregation Functions. Cambridge University Press, Cambridge (2009) · Zbl 1196.00002 [7] Klement, E.P., Mesiar, R., Pap, E.: Triangular Norms. Kluwer Academic Publishers, Dordrecht (2000) · Zbl 0972.03002 [8] Mesiar, R., Vivona, D.: Two-step integral with respect to a fuzzy measure. Tatra Mount. Math. Publ. 16, 358-368 (1999) · Zbl 0948.28015 [9] Shilkret, N.: Maxitive measure and integration. Indag. Math. 33, 109-116 (1971) · Zbl 0218.28005 [10] Sugeno, M.: Theory of Fuzzy Integrals and Applications. PhD Thesis, Tokyo Inst. of Technology, Tokyo (1974) [11] Torra, V., Narukawa, Y.: Twofold integral and multistep Choquet integral. Kybernetika 40, 39-50 (2004) · Zbl 1249.28027 [12] Wilkin, T., Beliakov, G.: Weakly monotone aggregation functions. Fuzzy Sets and Systems (2013) (submitted) · Zbl 1415.68244 [13] 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.