Decomposition integral without alternatives, its equivalence to Lebesgue integral, and computational algorithms

• Autorzy: Šeliga Adam

Identyfikatory

DOI

10.14313/JAMRIS/3-2019/26

• Języki publikacji: EN

Abstrakty

EN

In this paper we present a new class of decomposition integrals called the collection integrals. from this class of integrals we take a closer look on two special types of collection integrals, namely the chain integral and the minmax integral. Superdecomposition version of collection integral is also defined and the superdecomposition duals for the chain and the min-max integrals are presented. Also, the condition on the collection that ensures the coincidence of the collection integral with the Lebesgue integral is presented. Lastly, some computational algorithms are discussed.

Słowa kluczowe

EN

decomposition integrals; nonlinear integrals; computational algorithms

• Wydawca: Łukasiewicz Industrial Research Institute for Automation and Measurements PIAP
• Czasopismo: Journal of Automation Mobile Robotics and Intelligent Systems
• Rocznik: 2019
• Tom: Vol. 13, No. 3
• Strony: 41--48
• Opis fizyczny: Bibliogr. 9 poz., rys

Twórcy

autor

Šeliga Adam

• Slovak University of Technology, Radlinského 11, 810 05 Bratislava, Slovakia, www: www.math.sk/seliga

Bibliografia

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• [4] Y. Even and E. Lehrer, “Decomposition-integral:unifying Choquet and the concave integrals”, Economic Theory, vol. 56, no. 1, 2014, 33–58, 10.1007/s00199-013-0780-0.
• [5] E. Lehrer, “A new integral for capacities”, Economic Theory, vol. 39, no. 1, 2009, 157–176,10.1007/s00199-007-0302-z.
• [6] R. Mesiar, J. Li, and E. Pap, “Superdecomposition integrals”, Fuzzy Sets and Systems, vol. 259, 2015,3–11, 10.1016/j.fss.2014.05.003.
• [7] R. Mesiar and A. Stupň anová , “Decomposition integrals”, International Journal of Approximate Reasoning, vol. 54, no. 8, 2013, 1252–1259,10.1016/j.ijar.2013.02.001.
• [8] N. Shilkret, “Maxitive measure and integration”,Indagationes Mathematicae (Proceedings), vol. 74,1971, 109–116, 10.1016/S1385-7258(71)80017-3.
• [9] Q. Yang, “The pan-integral on the fuzzy measure space”, Fuzzy Mathematics, vol. 3, 1985, 107–114.

Uwagi

Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2019).