A lot of relevant works have been completed to provided different kinds of method to properly handle information offered which promotes the development of information industry. The representatives of the corresponding theories are soft theory [1-5], Z-numbers [6-9], D-numbers [10-14], fuzzy theory [15-18], Dempster-Shafer evidence theory [19-23] and some other mixed theories [24-26]. And the effectiveness of these theories are verified in many practical applications, like risk evaluation [27-29], pattern classification [30], optimization [31-34] and decision making [35-38]. Moreover, due to the rapid progress of quantum computing, some researchers come up with the idea that traditional information management can be transferred to the level of quantum. Some meaningful works about the topic are complex mass function [39-43] and quantum information theory [44-47]. In this paper, the proposed method is based on the quantum model of mass function [47]. In order to avoid the deviation which may caused by the original quantum evidences, a dual check system is designed to ensure the authenticity of the original judgments which utilizes the concept of Z-number [9]. Besides, because of the introduction of the time interval, a specially devised rule is proposed to appropriately decide the importance of different relationships of incidents, which is a kind of expert system under some restrictions. The contributions of the proposed method can be listed as: (1) The second dual check system can help avoid the deviation produced by the original evidences to help provide more effective results.

Quantum mass function has been applied in lots of fields because of its efficiency and validity of managing uncertainties in the form of quantum which can be regarded as an extension of classical Dempster-Shafer (D-S) evidence theory. However, how to handle uncertainties in the form of quantum is still an open issue. In this paper, a new method is proposed to dispose uncertain quantum information, which is called two-dimensional quantum mass function (TDQMF). A TDQMF is consist of two elements, TQ = (Qoriginal, Qindicative), both of the Qs are quantum mass functions, in which the Qindicative is an indicator of the reliability on Qoriginal. More flexibility and effectiveness are offered in handling uncertainty in the field of quantum by the proposed method compared with primary quantum mass function. Besides, some numerical examples are provided and some practical applications are given to verify its correctness and validity