Discrete pseudo-integrals

Authors:
Radko Mesiar;Jun Li;Endre Pap
Affiliations:
Faculty of Civil Engineering, Slovak University of Technology, Radlinského 11, 813 68 Bratislava, Slovakia and UTIA CAS, Pod Vodárenskou věží 4, 182 08 Prague, Czech Repub ...;School of Sciences, Communication University of China, Beijing 100024, China;Faculty of Natural Sciences and Mathematics, 21 000 Novi Sad, Serbia and Obuda University, H-1034 Budapest, Hungary
Venue:
International Journal of Approximate Reasoning
Year:
2013

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Abstract

Integration of simple functions is a corner stone of general integration theory and it covers integration over finite spaces discussed in this paper. Different kinds of decomposition and subdecomposition of simple functions into basic functions sums, as well as different kinds of pseudo-operations exploited for integration and sumation result into several types of integrals, including among others, Lebesgue, Choquet, Sugeno, pseudo-additive, Shilkret, PAN, Benvenuti and concave integrals. Some basic properties of introduced discrete pseudo-concave integrals are discussed, and several examples of new integrals are given.