Stock selection for effective investment decisions is a valuable and attractive research interest for many years. Owing to the uncertainty and complexity of the stock market, many fuzzy multicriteria decision-making (MCDM) methods were proposed to solve stock selection problems. However, these methods have difficulty in characterizing unreliable information, which is widespread in the stock market, and handling the non-compensation among multiple criteria. In this paper, an innovative method is developed from the perspectives of information reliability and criterion non-compensation to manage stock selection problems. First, the Z-number, which is a powerful tool for describing real-life information and identifying information reliability, is introduced to depict stock evaluation information. Second, the outranking degree of Z-numbers is defined based on the fuzzy and probability information. Subsequently, some outranking aggregation and exploitation procedures are presented based on the idea of Elimination and Choice Translating Reality (ELECTRE) I to handle the non-compensation among stock evaluation criteria. By integrating the above studies, a Z-number ELECTRE I MCDM method is developed. Finally, a stock investment object selection problem is solved, and some discussions and analyses are conducted to testify the applicability and validity of this method.

Z-number is the general representation of real-life information with reliability, and it has adequate description power from the point of view of human perception. This study develops an innovative method for addressing multicriteria group decision-making (MCGDM) problems with Z-numbers under the condition that the weight information is completely unknown. Processing Z-numbers requires effective support of reliable tools. Then, the normal cloud model can be employed to analyze the Z-number construct. First, the potential information involved in Z-numbers is invoked, and a novel concept of normal Z+-value is proposed with the aid of the normal cloud model. The operations, distance measurement, and power aggregation operators of normal Z+-values are defined. Moreover, an MCGDM method is developed by incorporating the defined distance measurement and power aggregation operators into the MultiObjective Optimization by Ratio Analysis plus the Full Multiplicative Form. Finally, an illustrative example concerning air pollution potential evaluation is provided to demonstrate the proposed method. Its feasibility and validity are further verified by a sensitivity analysis and comparison with other existing methods.