A Study On Rationality And Normality Indicators In The Sense Of Georgescu Fuzzy Choice Functions

In this thesis, under two weaker assumption conditions H1*and H2*, we systematically investigate the relationships among two rationality indicators, two normality indicators and the strongly complete rationality indicator.Firstly, we simply review the definitions and the related connections of rationality and normality in the cases of crisp choice functions and fuzzy choice functions. At the same time, we discuss the relationships between the rationality and normality of fuzzy choice functions under the weaker assumption conditions H1*and H2*. As a result, several new results are obtained.Secondly, we carry out the research on the rationality indicators in the framework of the Georgescu fuzzy choice functions. We study on the relationships between the rationality indicators and normality indicators of fuzzy choice functions and obtain some results related to these rationality indicators. Our main results are:The G-rationality indicator is less than or equal to the indicator of that the fuzzy revealed preference relation R is included in the fuzzy preference relation Q if the involved t-norm is a general t-norm. However, the G-rationality indicator is less than or equal to the indicator of that the fuzzy revealed preference relation R is equivalent to the fuzzy preference relation Q under the involved t-norm is a minimum t-norm and two weaker assumption conditions H1*and H2*. Based on the weaker assumption conditions H1*and H2*, the G-rationality indicator is less than or equal to the indicator of the strong completeness of the fuzzy preference relation Q. For a general t-norm, it is true that the M-rationality indicator is less than or equal to the G-rationality indicator. It should be pointed out that it is not necessarily sure that the M-rationality indicator is less than or equal to the G-rationality indicator. For this reason, we give a example to illustrate this fact. Afterwards, we make a further study to the relationships between two normality indicators combined with the strong completeness of the fuzzy revealed preference relation R and give a conclusion that they are equal under the weaker assumption conditions H1*and H2*Then, we discuss the relationships between the G-rationality indicator and the G-normality indicator under the weaker assumption conditions H1*and H2*and prove that they are not equal for a general t-norm. Meanwhile, we find an inferior limit of the G-normality indicator.Finally, we give a definition of the strongly complete rationality indicator if the involved t-norm is the minimum t-norm and show that the strongly complete rationality indicator is equal to the above rationality indicators of fuzzy choice function under the weaker assumption conditions H1*and H2*...