Xu, Zeshui Choquet integrals of weighted intuitionistic fuzzy information. (English) Zbl 1186.68469 Inf. Sci. 180, No. 5, 726-736 (2010). Summary: The Choquet integral is a very useful way of measuring the expected utility of an uncertain event [G. Choquet, Ann. Inst. Fourier 5, 131–295 (1953/54; Zbl 0064.35101)]. In this paper, we use the Choquet integral to propose some intuitionistic fuzzy aggregation operators. The operators not only consider the importance of the elements or their ordered positions, but also can reflect the correlations among the elements or their ordered positions. It is worth pointing out that most of the existing intuitionistic fuzzy aggregation operators are special cases of our operators. Moreover, we propose the interval-valued intuitionistic fuzzy correlated averaging operator and the interval-valued intuitionistic fuzzy correlated geometric operator to aggregate interval-valued intuitionistic fuzzy information, and apply them to a practical decision-making problem involving the prioritization of information technology improvement projects. Cited in 76 Documents MSC: 68T37 Reasoning under uncertainty in the context of artificial intelligence 28E10 Fuzzy measure theory 94D05 Fuzzy sets and logic (in connection with information, communication, or circuits theory) Keywords:Choquet integral; intuitionistic fuzzy set; interval-valued intuitionistic fuzzy set; intuitionistic fuzzy aggregation operator; interval-valued intuitionistic fuzzy aggregation operator; correlation Citations:Zbl 0064.35101 PDFBibTeX XMLCite \textit{Z. Xu}, Inf. Sci. 180, No. 5, 726--736 (2010; Zbl 1186.68469) Full Text: DOI References: [1] Atanassov, K., Intuitionistic fuzzy sets, Fuzzy Sets and Systems, 20, 87-96 (1986) · Zbl 0631.03040 [2] Atanassov, K., Intuitionistic Fuzzy Sets: Theory and Applications (1999), Physica-Verlag: Physica-Verlag Heidelberg · Zbl 0939.03057 [3] Atanassov, K.; Gargov, G., Interval valued intuitionistic fuzzy sets, Fuzzy Sets and Systems, 31, 343-349 (1989) · Zbl 0674.03017 [4] Bustince, H.; Herrera, F.; Montero, J., Fuzzy Sets and Their Extensions: Representation, Aggregation, and Models (2007), Springer-Verlag: Springer-Verlag Heidelberg [5] Choquet, G., Theory of capacities, Annales de l’institut Fourier, 5, 131-295 (1953) · Zbl 0064.35101 [6] De, S. K.; Biswas, R.; Roy, A. R., Some operations on intuitionistic fuzzy sets, Fuzzy Sets and Systems, 114, 477-484 (2000) · Zbl 0961.03049 [7] Deschrijver, G., Arithmetic operators in interval-valued fuzzy set theory, Information Sciences, 177, 2906-2924 (2007) · Zbl 1120.03033 [8] Deschrijver, G.; Kerre, E. E., On the relationship between some extensions of fuzzy set theory, Fuzzy Sets and Systems, 133, 227-235 (2003) · Zbl 1013.03065 [9] Deschrijver, G.; Kerre, E. E., Implicators based on binary aggregation operators in interval-valued fuzzy set theory, Fuzzy Sets and Systems, 153, 229-248 (2005) · Zbl 1090.03024 [10] Deschrijver, G.; Kerre, E. E., On the position of intuitionistic fuzzy set theory in the framework of theories modelling imprecision, Information Sciences, 177, 1860-1866 (2007) · Zbl 1121.03074 [11] Grabisch, M., Fuzzy integral in multicriteria decision making, Fuzzy Sets and Systems, 69, 279-298 (1995) · Zbl 0845.90001 [12] Hung, W. L.; Yang, M. S., On the \(J\)-divergence of intuitionistic fuzzy sets with its application to pattern recognition, Information Sciences, 178, 1641-1650 (2008) · Zbl 1134.68489 [13] Jiang, Y. C.; Tang, Y.; Wang, J.; Tang, S., Reasoning within intuitionistic fuzzy rough description logics, Information Sciences, 179, 2362-2378 (2009) · Zbl 1192.68672 [14] Ngwenyama, O.; Bryson, N., Eliciting and mapping qualitative preferences to numeric rankings in group decision-making, European Journal of Operational Research, 116, 487-497 (1999) · Zbl 1009.90518 [15] Torra, V., The weighted OWA operator, International Journal of Intelligent Systems, 12, 153-166 (1997) · Zbl 0867.68089 [16] Torra, V., Information Fusion in Data Mining (2003), Springer: Springer Berlin · Zbl 1030.68100 [17] Wang, Z.; Klir, G., Fuzzy Measure Theory (1992), Plenum Press: Plenum Press New York [18] Xu, Z. S., Intuitionistic preference relations and their application in group decision making, Information Sciences, 177, 2363-2379 (2007) · Zbl 1286.91043 [19] Xu, Z. S., Intuitionistic fuzzy aggregation operators, IEEE Transactions on Fuzzy Systems, 15, 1179-1187 (2007) [20] Xu, Z. S., Intuitionistic Fuzzy Information: Aggregation Theory and Applications (2008), Science Press: Science Press Beijing [22] Xu, Z. S.; Chen, J.; Wu, J. J., Clustering algorithm for intuitionistic fuzzy sets, Information Sciences, 178, 3775-3790 (2008) · Zbl 1256.62040 [23] Xu, Z. S.; Yager, R. R., Some geometric aggregation operators based on intuitionistic fuzzy sets, International Journal of General Systems, 35, 417-433 (2006) · Zbl 1113.54003 [24] Zadeh, L. A., Fuzzy sets, Information and Control, 8, 338-353 (1965) · Zbl 0139.24606 [25] Zadeh, L. A., Toward a generalized theory of uncertainty (GTU)-an outline, Information Sciences, 172, 1-40 (2005) · Zbl 1074.94021 [26] Zadeh, L. A., Is there a need for fuzzy logic?, Information Sciences, 178, 2751-2779 (2008) · Zbl 1148.68047 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.