Fuzzy measure of fuzzy events defined by fuzzy integrals
Fuzzy Sets and SystemsPublished 1 September 1992
Michel Grabisch, Toshiaki Murofushi, Michio Sugeno
Citations119
SJR quartileQ1
SJR score0.75
SNIP1.25
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TL;DR
This work proposes a general definition of fuzzy measure of fuzzy events, which is compatible with previous definitions of Zadeh, and possesses all properties of a fuzzy measure, in particular the duality property.
Abstract
We define the concept of fuzzy measure of a fuzzy event by using a general form of fuzzy integral proposed by Murofushi, called fuzzy t-conorm integral, encompassing previous definitions. Zadeh defined the probability measure of a fuzzy event, and later the possibility measure of fuzzy event. Using a duality property of fuzzy t-conorm integral, we propose a general definition of fuzzy measure of fuzzy events, which is compatible with previous definitions of Zadeh, and possesses all properties of a fuzzy measure, in particular the duality property. Using our definition, we examine the case of decomposable measures and belief functions. A comparison with previous works is provided.
Keywords
MathematicsDecision SciencesEngineering
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