Expected utility theorem had been used to explain reasonable selection of consumer or efficient decision-making of producer that under the assumption which maximize economical efficiency as that subjective preference of individual selects the optimum alternative among the various selection alternative. But, Preference which influence in decision-making have the several problems that Reference is subjective fairly, and can be changed according to size of probability, decision-making frame, scale of gains or loss amount of money. Therefore this research investigates application possibility of Non-expected utility theory that used betweenness property to solve these problem that was involved in expected utility theorem, also analyzed and compare with expected utility theorem. Analysis showed that Non-expectation utility theory fill up a shortage of expected utility theorem. And it looked that application possibility of Non-expected utility theory in decision-making is enough as that proving the experiment example which presented in existing research.