New score functions based on risk preference in vague set theory

The characters and disadvantages of some main present score functions in the vague set theory are analyzed. The meaning and essence of score functions are discussed and the concept of vague valuepsilas equilibrium point is introduced. From the risk preference point of view and regarding uncertainty information as potential risk, three risk type score functions are defined. A risk aversion type score function and a risk proneness type score function are constructed which can reflect risk aversion decision makerspsila preference and maintain it consistency. The character of these new score functions are detailed discussed and proved.