Research on lean management and innovation capability evaluation of technological small and medium sized enterprises under probabilistic hesitant fuzzy sets

The lean management and innovation capability evaluation of technological small and medium sized enterprises is a classical multi-attributes group decision-making (MAGDM). Recently, the probabilistic hesitant fuzzy sets (PHFSs) have been extended to apply in many fields. However, the existing models don’t evaluate the alternative considering the psychological factors. Thus, in this paper, an extended probabilistic hesitant fuzzy grey relational analysis (PHF-GRA) method is proposed to reduce the restrictions of GRA method by combining with cumulative prospect theory (CPT), considering the psychological preference. In addition, the PHFSs assigns probability values to different degrees of hesitancy, which shows its superiority in complex environment. At the same time, the weight vectors of each attribute are calculated by the entropy values of different foreground decision elements. Then, probabilistic hesitant fuzzy GRA (PHF-GRA) model based on CPT model is constructed for MAGDM under PHFSs. Finally, a practical example study for lean management and innovation capability evaluation of technological small and medium sized enterprises is constructed to validate the proposed GRA (PHF-GRA) model based on model CPT and some comparative studies are constructed to verify the applicability.