Probability-Possibility Transformation under Perspective of Random-fuzzy
Dual Interpretation of Unknown Uncertainty
- Wei Mei ,
- Gan Li ,
- Yan Xu ,
- Lin Shi ,
- Gang Li ,
- Yan Xu
Abstract
Information-preservation is recognized as the only principle for
probability-possibility transformation in this work and the normalized
transformation is the right method. This is based on the viewpoint that
the reason we can transfer probability and possibility is that we
believe the uncertainty being handled can be information-equivalently
described by both probability and possibility. That viewpoint is
endorsed by the random-fuzzy dual interpretation of unknown uncertainty,
which says that unknown uncertainty being estimated could be interpreted
as either randomness or fuzziness, depending on the available prior
information and the perspective of cognition and modeling. Information
of uncertain variable is defined in this work as its distribution. The
suggested information-preservation principle is different from Klir's
principle, which is in fact an entropy-preservation principle. Then we
investigated the problem of information preservation and propagation in
parallel probability-possibility systems. By parallel, we mean the two
uncertainty systems have the same priori information. After uncertainty
propagation the two parallel systems will generally bifurcate, which
means information preservation only holds locally between the two
parallel systems. This observation accords with our intuition since
probability and possibility use different normalizations as well as
different disjunctive operators, which makes them two different
uncertainty systems appropriate for randomness and fuzziness,
respectively.