A Study On The Expansion-contraction Conditions For Sequential Fuzzy Choice Functions

The investigation of rationality conditions is one of the most important research topics in the theory of choice functions.In this paper,we carry out a detailed study of expansion-contraction conditions for sequential fuzzy choice functions.The conditions involved include the ?-like conditions(?,?2),?-like conditions(?,?2,?',?+),the con-ditions ?,CA and AA.Firstly,in the crisp case,we investigate whether the sequential choice function C2 o C1 still satisfies the condition provided that the both choice functions C1 and C2 satisfy a certain condition.The following main results are obtained:(1)If both C1 and C2 satisfy the conditions ?,?2,?',AA,then the sequential choice function C2 oC1 satisfies these rationality conditions respectively;(2)If C1 satisfies AA and C2 satisfies?,?2,?+ CA,then C2 o C1 also satisfies these conditions respectively.Secondly,based on the above results,we carry out a similar investigation into fuzzy choice functions.We show that the results concerning the conditions ?,?,?',?+,?,AA in the crisp case can be completely extended to the sequential fuzzy choice functions.However,for the conditions ?2,?2?CA,the extensions are not so direct.As a result,we strengthen some conditions to obtain the similar results.For instance,under the conditions for C1 to meet F?2?we show that if the requirement of C2 is strengthened to FAA?then C2 o C1 still satisfies F?2.Through the study,we have a clear understanding of the relationships between the expansion-contraction properties of the sequential choice function C2 o C1 and those of C1 and C2.