PROCEEDINGS IPMU '08

Credibility Measure of Fuzzy Set and Applications

Xiang Li, Dan A. Ralescu.

In order to measure fuzzy event,
credibility measure is proposed as a
non-additive set function. In this
paper, this concept is extended to
fuzzy sets. First, a mean measure
is defined by Lebesgue integral
and some properties are investigated
such as the monotonicity theorem,
self-duality theorem and subadditivity
theorem. Furthermore, by using
Sugeno integral, an equilibrium
measure is proposed and studied.
Finally, these concepts are applied
to optimization problems, and the
mean measure maximization model
and equilibrium measure maximization
model are proposed.

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