模糊选择函数的合理性及拟传递合理性的刻画

The Characterization of Fuzzy Choice Functions' Rationality and Quasi-transitive Rationality

首先给出模糊选择函数合理性的一个充分必要条件。然后将普通情况下Schw artz所提出的收缩扩张公理模糊化,在选择集为正规模糊集的前提下,研究了模糊选择函数拟传递合理性的刻画问题。我们指出,该模糊化后的条件仍是选择函数拟传递合理的必要条件,但已不再是拟传递合理的充分条件(我们用例子说明了这一点)。因此,在文章的最后,给出了比较强的一个充分条件。

In this paper, we firstly present a necessary and sufficient condition for the characterization of transitive rationality in fuzzy case. Then we fuzzily some expansion and contraction axioms intro- duced by Schwartz in the study of crisp qusi-transitive rationality, and investigate the issue of charactering quasitransitive rationality in fuzzy case under the assumption that the involved choice sets are normal. We point out that the fuzzified axioms are necessary but not sufficient conditions any more in charactering quasi-transitive rationality in fuzzy case, which is illustrated through an example. In view of this, we propose a strong sufficient condition to guarantee the quasi-transitive rationality of choice functions towards the end of the paper.