Indicators of fuzzy relations

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.