• Journal of the Chungcheong Mathematical Society
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• v.10 no.1
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• pp.9-15
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• 1997

The main goal of this paper is to investigate some properties of a quotient fuzzy seminorm ${\rho}_q$ induced by a fuzzy seminorm ${\rho}={\chi}_{B_{{\parallel}{\cdot}{\parallel}}}$ on a normed linear space X.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 2004.04a
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• pp.510-514
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• 2004

In this paper, we introduce Fuzzy Beppo Levi's Theorem in which we use the supremum instead of addition in the expression of Beppo Levi's Theorem. That holds under the conditions which are continuity of t-seminorm ┬and the fuzzy additivity of a fuzzy measure g.

• 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.7
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• pp.934-938
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• 2004

In this paper, we introduce the seminormed fuzzy co-integral as a complementary concept of seminormed fuzzy integral, and investigate its properties. Furthermore we propose an application of this new integral for decision making problems.

• 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].

• The Journal of the Korea Contents Association
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• v.2 no.2
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• pp.91-97
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• 2002

Let (X, F, g) be a fuzzy measure space. Then for any h$\in$ $L^{0}$ (X) , a$\in$[0 , 1] , and $A\in$F ∫$_{A}$aㆍh($\chi$)┬g＝aㆍ∫$_{A}$h($\chi$)┬g with the t-seminorm ┬(x, y)= xy. And we prove that the Seminormed fuzzy integral has some linearity properties only for ｛0,1｝-classes of fuzzy measure as follow, For any f, h$\in$ $L^{0}$ ($\chi$), any a, b$\in$R+: af＋bh$\in$ $L^{0}$ ($\chi$)⇒ ∫$_{A}$(af＋bh)┬g＝a∫$_{A}$f┬g＋b∫$_{A}$h┬g; if and only if g is a probability measure fulfilling g(A) $\in$｛0, 1｝ for all $A\in$F.n$F.