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The relationships between choquet integral, pan‐integral, upper integral and lower integral
Author(s) -
Li Gang
Publication year - 2011
Publication title -
international journal of intelligent systems
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.291
H-Index - 87
eISSN - 1098-111X
pISSN - 0884-8173
DOI - 10.1002/int.20477
Subject(s) - choquet integral , mathematics , fuzzy measure theory , volume integral , daniell integral , measure (data warehouse) , riemann integral , fuzzy logic , multiple integral , riemann–stieltjes integral , functional integration , integral equation , calculus (dental) , mathematical analysis , fuzzy set , singular integral , fuzzy number , computer science , artificial intelligence , medicine , dentistry , database
Various types of integrals with respect to fuzzy measure on finite sets in the literature (Grabisch et al. , Fuzzy Measures and Integrals. Theory and Applications, Heidelberg, Germany, 2000; Wang et al ., Int J Intell Syst 2006; 21:1073–1092; Wang and Klir, Int J Uncertainty, Fuzziness knowl‐based Syst 1997;5(2):163–175; Wang and Klir, Fuzzy Measures Theory, New York; Plenum, 1992) have been proposed, including Choquet integral, pan‐integral, the upper integral, and the lower integral. In this paper, we present the relationships between these different types of integrals. The sufficient and necessary conditions for the equality between these integrals are discussed. © 2011 Wiley Periodicals, Inc.