Abstract: In order to describe quantitatively the degree of possessing the unascertained nature or the degree of being in the unascertained state, a concept of unascertained measure satisfying measure criteria in the measurable space is defined. Then it is used as a membership function, and based on it, the concept of unascertained set in domain is introduced, the operations of the unascertained set are defined. The usefulness of the new uncertainty set is illustrated via discussing the relationship and essential difference between the unascertained set and the fuzzy set. On the basis of unascertained set, an unascertained logic system is set up, and it can be used to deal with the uncertain information. A new concept, weight of index classification. is defined, its calculation method is given, and is applied to the reasoning algorithm in the unascertained logic system, which makes the complex reliability well explicable. Finally, an example in fault diagnosis is presented to show the effectiveness of the proposed unascertained logic syste