Zy. Wang et al., FUZZY MEASURES DEFINED BY FUZZY INTEGRAL AND THEIR ABSOLUTE CONTINUITY, Journal of mathematical analysis and applications, 203(1), 1996, pp. 150-165
Given a measurable space (X,J), a fuzzy measure mu on (X,J), and a non
negative function f on X that is measurable with respect to J, we can
define a new set function nu on (X,J) by the fuzzy integral. It is kno
wn that nu is a lower semicontinuous fuzzy measure on (X,J) and, moreo
ver, if mu is finite, then nu is a finite fuzzy measure as well. In th
is paper, we generalize in several different ways the concept of absol
ute continuity of set functions, as defined in classical measure theor
y. In addition, we investigate the relationship among these generaliza
tions by using the structural characteristics of set functions such as
null-additivity and autocontinuity, and determine which types of abso
lute continuity of fuzzy measures are possessed by the fuzzy measure (
or the lower semicontinuous fuzzy measure) obtained by the fuzzy integ
ral. (C) 1996 Academic Press, Inc.