Research On The Characterizations Of Properties Of Fuzzy Relations By Means Of Traces

In this thesis, we concentrate on the characterizations of various properties of fuzzy relations by means of their traces. On one hand, we attempt to reformulate the results related to the traces of fuzzy relations obtained by Fodor under some weakened conditions. Meanwhile, we present some new characterizations of properties of fuzzy relations.Our main research and results are summarized as follows.Firstly, we review the related results of the characterizations of various properties of relations in the crisp case by means of their traces and present some new characterization results on properties of relations. The involved properties include mainly asymmetry, completeness, transitivity, negative transitivity, semitransitivity and Ferrers property.Secondly, we give an overview of the characterization results on various properties of fuzzy relations in terms of traces, which are obtained by Fodor. Then comes our main research work. We first carry out an improvement on the results obtained by Fodor under a strong De Morgan triple. We show that the same results are still valid if the involved fuzzy connectives form a De Morgan triple with a left-continuous t-norm and contrapositive symmetry, and thus the characterization results of Fodor are extended. Meanwhile, we carry out a further research on the characterization of properties of fuzzy relations based on the results with crisp relations. The involved properties include mainly T-asymmetry, S-strongly completeness, T-S-semitransitivity and T-S-Ferrers property. Our investigation improves and deepens the study on properties of fuzzy relations.