Possibilities as cumulative subjective probabilities and a norm on the space of congruence classes of fuzzy numbers motivated by an expected utility functional
In our prior paper (Jamison and Lodwick.1996) we defined a fuzzy function and discussed the theory for optimizing unconstrained fuzzy functions. In that paper we described the need for a measure for comparing different possibility distributions in order to determine the decision makers preference for one distribution over another. In this paper we develop one such measure. We begin by developing possibility distributions from a set of axioms to show that possibility levels can be viewed as cumulative subjective probabilities. We use this development to motivate a norm on the vector space of congruence classes of fuzzy numbers. This norm is based on an expected utility functional. We show that our normed space is complete if the supports of our fuzzy numbers are contained within a bounded subset of the real line. (C) 2000 Published by Elsevier Science B.V. All rights reserved.
subjective probability fuzzy number possibility distribution normed space