Tensor based data classification has become increasingly popular in the domain of computer vision and face recognition, as the vector based model suffers from data topology and time efficiency due to the number of training parameters, which increases exponentially. Tensor-based model effectively utilizes the structural information inherent in the multidimensional features of an object. In order to enhance tensor model performance, variants of the Support tensor machines have been used in the past for tensor data classification. In our proposed approach, we have introduced the concept of granularity, for the development of the Granular Proximal Support Tensor Machine (GBPSTM), which leverages the granular ball generation method to form compact and meaningful representations of data, thereby improving classification performance and computational efficiency. Furthermore, to enhance robustness against noise and uncertainty, we incorporate fuzzy logic through an intuitionistic fuzzy approach, resulting in the Granular Ball Intuitionistic Fuzzy Proximal Support Tensor Machine (GBFPSTM). The effectiveness of the proposed models has been demonstrated through simulations on face detection and handwriting recognition datasets.