PROBABILITIES, POSSIBILITIES, AND FUZZY-SETS

A formal analysis of probabilities, possibilities, and fuzzy sets is presented in this paper. A number of theorems proved show the above measures have equal representational power when their domains are infinite. However, for finite domains, it is proved that probabilities have a higher representational power than both possibilities and fuzzy sets. The cost of this increased power is high computational complexity and reduced computational efficiency. The resulting trade-off of high complexity and representational power versus computational efficiency is discussed under the spectrum of experimental systems and applications.