A Study On Relationships Between Traces Of A Fuzzy Relation And Its Property Indicators

In this thesis, we concentrate on the characterization of various property indicators of fuzzy relations by means of the traces of fuzzy relations. As a result, the relationships between the traces and some property indicators of a fuzzy relation are revealed.Firstly, we give an overview of some indicators of fuzzy relations in the literature including reflexivity indicator, irreflexivity indicator,S-asymmetry indicator, strong S-completeness indicator, T-transitivity indicator, negative S-transitivity indicator, TS-Semitransitivity indicator, T-S-Ferrers indicator etc. and the related research results on characterizing these properties by means of their traces.Afterwards, we proceed to investigate the relationships between the traces and property indicators of fuzzy relations. Under the condition that the involved t-norm is left-continuous, we characterize reflexivity and T-transitivity indicators of fuzzy relations. Meanwhile, under the assumptions that the involved logic connectives form a De Morgan triple with a left-continuous t-norm and the generated implication satisfies contrapositive symmetry, we present the characterizations of other property indicators by means of the traces of fuzzy relations, including reflexivity indicators, T-asymmetry indicators, strong S-completeness indicators, negative S-transitivity indicators, T-S-Semitransitivity indicators, T-S-Ferrers indicators. With our research, some results in the literature on the relationships between the traces and some properties of fuzzy relations are extended and improved.