Identyfikatory
Warianty tytułu
Języki publikacji
Abstrakty
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
Rocznik
Tom
Strony
41--48
Opis fizyczny
Bibliogr. 9 poz., rys
Twórcy
autor
- Slovak University of Technology, Radlinského 11, 810 05 Bratislava, Slovakia, www: www.math.sk/seliga
Bibliografia
- [1] G. Choquet, “Theory of capacities”, Annales de l’Institut Fourier, vol. 5, 1954, 131–295.
- [2] C. Davis, “Theory of Positive Linear Dependence”, American Journal of Mathematics, vol. 76, no. 4, 1954, 733–746, 10.2307/2372648.
- [3] A. Szeliga, “A note on the computational complexity of Lehrer integral”. In: Advances in Architectural, Civil and Environmental Engineering: 27th Annual PhD Student Conference on Applied Mathematics, Applied Mechanics, Geodesy and Cartography, Landscaping, Building Technology, Theory and Structures of Buildings, Theory and Structures of Civil Engineering Works, Theory and Environmental Technology of Buildings, Water Resources Engineering, 2017, 62–65.
- [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).
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-b2946d45-6ac3-490d-aeff-e861753ac538