Possibilities as cumulative subjective probabilities and a norm on the space of congruence classes of fuzzy numbers motivated by an expected utility functional

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