In order to better solve the multi-attribute decision-making (MADM) issues in real life, this paper proposes the probabilistic spherical hesitant fuzzy set (PSHFS) theory based on spherical HFS (SHFS) and probabilistic HFS (PHFS). Firstly, PSHFS is developed, and its basic operations of PHSF element (PSHFE) are proposed. Secondly, generalized PSHF weighted averaging (GPSHFWA) and generalized PSHF weighted geometric (GPSHFWG) operators are constructed, and their excellent properties and some special forms are investigated. Thirdly, for MADM problems with different priorities of related evaluation criteria, we propose generalized PSHF prioritized weighted averaging (GPSHFPWA) and geometric (GPSHFPWG) operators, and investigate their excellent properties and some special operators. Fourthly, two new MADM techniques are constructed dependent on the proposed two types of operators in practical MADM problems. Finally, the effectiveness of the two MADM techniques constructed is tested through an application example of the green enterprise credit selection (GECS). The sensitivity analysis of parameter shows the influence on different values of parameter on the optimal alternatives by setting different parameter values, and shows the flexibility of the proposed MADM techniques. Meanwhile, the two MADM techniques are compared with several existing MADM techniques to prove the advantages of the two MADM techniques.
Ning et al. (Thu,) studied this question.