  This paper is to consider the problems of estimation and recognition from the
perspective of sigma-max inference (probability-possibility inference), with a
focus on discovering whether some of the unknown quantities involved could be
more faithfully modeled as fuzzy uncertainty. Two related key issues are
addressed: 1) the random-fuzzy dual interpretation of unknown quantity being
estimated; 2) the principle of selecting sigma-max operator for practical
problems, such as estimation and recognition. Our perspective, conceived from
definitions of randomness and fuzziness, is that continuous unknown quantity
involved in estimation with inaccurate prior should be more appropriately
modeled as randomness and handled by sigma inference; whereas discrete unknown
quantity involved in recognition with insufficient (and inaccurate) prior could
be better modeled as fuzziness and handled by max inference. The philosophy was
demonstrated by an updated version of the well-known interacting multiple model
(IMM) filter, for which the jump Markovian System is reformulated as a hybrid
uncertainty system, with continuous state evolution modeled as usual as
model-conditioned stochastic system and discrete mode transitions modeled as
fuzzy system by a possibility (instead of probability) transition matrix, and
hypotheses mixing is conducted by using the operation of "max" instead of
"sigma". For our example of maneuvering target tracking using simulated data
from both a short-range fire control radar and a long-range surveillance radar,
the updated IMM filter shows significant improvement over the classic IMM
filter, due to its peculiarity of hard decision of system model and a faster
response to the transition of discrete mode.
