Decompositions and range for additive fuzzy measures

Dan Butnariu

doi:10.1016/S0165-0114(83)80111-0

Decompositions and range for additive fuzzy measures

Dan Butnariu

Research output: Contribution to journal › Article › peer-review

Abstract

The aim of the present paper is to prove the existence of Hahn and Lebesgue decompositions for additive fuzzy measures in the sense of [3]. It is shown that the Radon-Nikodym theorem can be carried over from classical measures to additive fuzzy measures with their corresponding integrals. These results are applied to obtain a generalization of Liapounoff's convexity theorem [12] whose utility in the theory of fuzzy games is argued in the last section.

Original language	English
Pages (from-to)	135-155
Number of pages	21
Journal	Fuzzy Sets and Systems
Volume	10
Issue number	1-3
DOIs	https://doi.org/10.1016/S0165-0114(83)80111-0
State	Published - 1983
Externally published	Yes

Keywords

Additive fuzzy measure
Darboux property of an n-vector fuzzy measure
Fuzzy game
Fuzzy game with bounded variation
Hahn decomposition
Jordan decomposition
Lebesgue decomposition
n-vector fuzzy measure
σ-algebra of fuzzy sets

ASJC Scopus subject areas

Logic
Artificial Intelligence

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10.1016/S0165-0114(83)80111-0

Cite this

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abstract = "The aim of the present paper is to prove the existence of Hahn and Lebesgue decompositions for additive fuzzy measures in the sense of [3]. It is shown that the Radon-Nikodym theorem can be carried over from classical measures to additive fuzzy measures with their corresponding integrals. These results are applied to obtain a generalization of Liapounoff's convexity theorem [12] whose utility in the theory of fuzzy games is argued in the last section.",

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PY - 1983

Y1 - 1983

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AB - The aim of the present paper is to prove the existence of Hahn and Lebesgue decompositions for additive fuzzy measures in the sense of [3]. It is shown that the Radon-Nikodym theorem can be carried over from classical measures to additive fuzzy measures with their corresponding integrals. These results are applied to obtain a generalization of Liapounoff's convexity theorem [12] whose utility in the theory of fuzzy games is argued in the last section.

KW - Additive fuzzy measure

KW - Darboux property of an n-vector fuzzy measure

KW - Fuzzy game

KW - Fuzzy game with bounded variation

KW - Hahn decomposition

KW - Jordan decomposition

KW - Lebesgue decomposition

KW - n-vector fuzzy measure

KW - σ-algebra of fuzzy sets

UR - https://www.scopus.com/pages/publications/0346016672

U2 - 10.1016/S0165-0114(83)80111-0

DO - 10.1016/S0165-0114(83)80111-0

M3 - Article

AN - SCOPUS:0346016672

SN - 0165-0114

VL - 10

SP - 135

EP - 155

JO - Fuzzy Sets and Systems

JF - Fuzzy Sets and Systems

IS - 1-3

ER -

Decompositions and range for additive fuzzy measures

Abstract

Keywords

ASJC Scopus subject areas

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