抄録
This paper decomposes every gain gamble into a risky gamble and a certain gain, and develops an axiom system for a weighted additive model with certainty equivalent. A concatenation operation is introduced not only to give a formal expression (segregation expression) to the decomposition but also to enable an extension of the expression (extended segregation expression) in the sense that the risky part includes the concatenations of risky gambles. The certainty equivalent of a gamble can be decomposed into the sum of a conditional certainty equivalent of the risky gamble and the certain gain. Two conditions---segregation monotonicity and segregation equivalence---are provided for such limited extended segregation expressions as the risky part consists of the concatenations of gambles having the same chance event to make the conditional certainty equivalent in the multiplicative form; that is, multiplication of the usual certainty equivalent by a weight that depends on an event partition and the amount of certain gain.
