kappalab: Non-additive measure and integral manipulation functions , Kappalab, which stands for ”laboratory for capacities”, is an S4 tool box for capacity (or non-additive measure, fuzzy measure) and integral manipulation on a finite setting. It contains routines for handling various types of set functions such as games or capacities. It can be used to compute several non-additive integrals: the Choquet integral, the Sugeno integral, and the symmetric and asymmetric Choquet integrals. An analysis of capacities in terms of decision behavior can be performed through the computation of various indices such as the Shapley value, the interaction index, the orness degree, etc. The well-known Moebius transform, as well as other equivalent representations of set functions can also be computed. Kappalab further contains seven capacity identification routines: three least squares based approaches, a method based on linear programming, a maximum entropy like method based on variance minimization, a minimum distance approach and an unsupervised approach grounded on parametric entropies. The functions contained in Kappalab can for instance be used in the framework of multicriteria decision making or cooperative game theory. (Source: http://cran.r-project.org/web/packages)

References in zbMATH (referenced in 42 articles , 1 standard article )

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  1. Mayag, Brice; Bouyssou, Denis: Necessary and possible interaction between criteria in a 2-additive Choquet integral model (2020)
  2. Pelegrina, Guilherme Dean; Duarte, Leonardo Tomazeli; Grabisch, Michel; Travassos Romano, João Marcos: The multilinear model in multicriteria decision making: the case of 2-additive capacities and contributions to parameter identification (2020)
  3. Skibski, Oskar; Michalak, Tomasz: Fair division in the presence of externalities (2020)
  4. Destercke, Sébastien: A generic framework to include belief functions in preference handling and multi-criteria decision (2018)
  5. Alcantud, José Carlos R.; de Andrés Calle, Rocío: The problem of collective identity in a fuzzy environment (2017)
  6. Lourenzutti, Rodolfo; Krohling, Renato A.; Reformat, Marek Z.: Choquet based TOPSIS and TODIM for dynamic and heterogeneous decision making with criteria interaction (2017)
  7. Marrara, Stefania; Pasi, Gabriella; Viviani, Marco: Aggregation operators in information retrieval (2017)
  8. Zhang, Wenkai; Ju, Yanbing; Liu, Xiaoyue: Interval-valued intuitionistic fuzzy programming technique for multicriteria group decision making based on Shapley values and incomplete preference information (2017)
  9. Agahi, Hamzeh; Mesiar, Radko; Motiee, Mehran: On Hoeffding and Bernstein type inequalities for sums of random variables in non-additive measure spaces and complete convergence (2016)
  10. Anderson, Derek T.; Elmore, Paul; Petry, Fred; Havens, Timothy C.: Fuzzy Choquet integration of homogeneous possibility and probability distributions (2016)
  11. Angilella, Silvia; Bottero, Marta; Corrente, Salvatore; Ferretti, Valentina; Greco, Salvatore; Lami, Isabella M.: Non additive robust ordinal regression for urban and territorial planning: an application for siting an urban waste landfill (2016)
  12. Angilella, Silvia; Corrente, Salvatore; Greco, Salvatore: Stochastic multiobjective acceptability analysis for the Choquet integral preference model and the scale construction problem (2015)
  13. Murillo, J.; Guillaume, S.; Spetale, F.; Tapia, E.; Bulacio, P.: Set characterization-selection towards classification based on interaction index (2015)
  14. Sun, Hong-Xia; Yang, Hao-Xiong; Wu, Jian-Zhang; Ouyang, Yao: Interval neutrosophic numbers Choquet integral operator for multi-criteria decision making (2015)
  15. Bortot, Silvia; Marques Pereira, Ricardo Alberto: The binomial Gini inequality indices and the binomial decomposition of welfare functions (2014)
  16. Gong, Zengtai; Chen, Li; Duan, Gang: Choquet integral of fuzzy-number-valued functions: the differentiability of the primitive with respect to fuzzy measures and Choquet integral equations (2014)
  17. Greco, Salvatore; Mousseau, Vincent; Słowiński, Roman: Robust ordinal regression for value functions handling interacting criteria (2014)
  18. Wu, Jianzhang; Zhang, Qiang; Du, Qinjun; Dong, Zhiliang: Compromise principle based methods of identifying capacities in the framework of multicriteria decision analysis (2014)
  19. Lust, Thibaut; Rolland, Antoine: Choquet optimal set in biobjective combinatorial optimization (2013)
  20. Wu, Jianzhang; Chen, Fang; Nie, Cuiping; Zhang, Qiang: Intuitionistic fuzzy-valued Choquet integral and its application in multicriteria decision making (2013)

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