In this paper, first we give the definitions of various indicators of fuzzy relations and their basic properties. Then we investigate the relationships between these indicators, particularly between those of T-transitivity, negative S-transitivity, T-S-semitransitivity and T-S-Ferrers property. The investigation is divided into three parts: results in the general case, results under a condition proposed by Peng et al., and results under special t-norms and t-conorms. On account of our research, certain results on fuzzy relations in the literature are extended to the degree description.