This paper extends the previous works to further explore the role of the first order polarization tensor in electro-sensing by the weakly electric fish specifically for object discrimination and characterization. The first order polarization tensor for few objects used in the considered experiment are calculated and discussed to identify whether there are other evidences to suggest that a weakly electric fish able to recognize the tensor when choosing or rejecting an object. Our findings in this study suggest that all fish during most of the experiments face difficulties to discriminate two objects when their first order polarization tensors are almost similar depending on the types of training given to them.