• East Asian mathematical journal
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• v.17 no.2
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• pp.253-264
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• 2001

• The Journal of the Korea Contents Association
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• v.2 no.4
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• pp.99-103
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• 2002

In this paper, we investigate for how to define a fuzzy measure by using the semi-normed fuzzy integral of a given measurable function with respect to another given fuzzy measure when t-seminorm is continuous. Let (X, F, g) be a fuzzy measure space, h$\in$L$^\circ$(X), and $\top$ be a continuous t-seminorm.. Then the set function $\nu$ defined by $\nu$(A)=$\int _A$h$\top$g for any $A\in$F is a fuzzy measure on (X, F).

• Journal of the Korean Institute of Intelligent Systems
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• v.14 no.3
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• pp.262-266
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• 2004

In general, the fuzzy integral lacks some important properties that Lebesgue integral possesses. One of them is linearity. In this paper, we introduce fuzzy linearity in which we use the supremum and the infimum instead of additon and scalar multiplication in the expression of linearity and show that the fuzzy linearity of the seminormed fuzzy integrals of interval-valued functions when the fuzzy measure g is fuzzy additive, the continuous t-seminorm is saturated and measurable functions satisfy the condition[Max].