Quasi-Transitivity Indicator And Its Application Study In Choice Functions

In this thesis, we define the quasi-transitivity indicator of a fuzzy relation, and discuss the relationships between this indicator and other indicators of a fuzzy relation. Then, we apply the quasi-transitivity indicator to the study of fuzzy choice functions, and investigate the connections between the indicator and the famous fuzzy δ-consistency indicator. The main research work is described in the following:Firstly, based on the similarity of fuzzy relations formulated by Belohlavek, we further discuss its properties. Secondly, we give the definition of the quasi-transitivity indicator of a fuzzy relation, and discuss its properties. Then, we investigate the relationships between the quasi-transitivity indicator and transitivity indicator, acyclicity indicator, negative-transitivity indicator. Finally, we introduce two indicators, the quasi-transitivity rationality indicator of a fuzzy choice function C and the fuzzy δ-consistency indicator. Under some conditions, we deal with the links between the quasi-transitivity rationality indicator and the fuzzy δ-consistency indicator.Through the discussion in this thesis, the research of quasi-transitivity is deepened, and some results relate to quasi-transitivity and quasi-transitivity rationality in the crisp and fuzzy cases are generalized.