Abstract
In fuzzy theory, possibility valuation is defined as an extention of possibility measure for a fuzzy set, which is used as the valuation for the fuzzy set under possibilistic uncertainty. This definition is also regarded as a fuzzy integral of a membership function on possibility measure. However, various kinds of fuzzy integrals are poposed. Therefore, another possibility valuations can be defined. By the way, membership functions and possibility distribution functions are identified subjectively by decision makers. Therefore, the valur membership functions and possibility distribution functions should not be considered as cardinal value but ordinal value. In this paper, new definition of possibility valuation under uncertainty are proposed based on oridinal utility theory. And also, necessity valuation, which is a dual concept of possibility valuation, is proposed. Moreover, relationship between these definirions and identification of membership functions are discussed.
