Abstract
The rationality of a fuzzy choice function is a hot research topic in the study of fuzzy choice functions. In this paper, two common fuzzy sets are studied and analyzed in the framework of the Banerjee choice function. The complete rationality and bounded rationality of fuzzy choice functions are defined based on the two fuzzy sets. An assumption is presented to study the fuzzy choice function, and especially the fuzzy choice function with bounded rationality is studied combined with some rationality conditions. Results show that the fuzzy choice function with bounded rationality also satisfies some important rationality conditions, but not vice versa. The research gives supplements to the investigation in the framework of the Banerjee choice function.
Highlights
The rationality of a choice function is an important issue in the research of classical decision theory
Different from them, we study the rationality properties of the fuzzy choice function with bounded rationality by fuzzy preferences without the assumption that every involved choice set is normal
Proposition 30 indicates that the fuzzy choice function with bounded rationality satisfies Weak Fuzzy Congruence Axiom (WFCA) combined with other conditions; this is different from the conclusion under complete rationality
Summary
The rationality of a choice function is an important issue in the research of classical decision theory. The rationality has been widely studied in the context of preference modeling and choice functions To deal with this issue, various rationality conditions have been presented by a number of authors. The fuzzy preferences were modelled in the study of choice functions by Orlovsky in 1978 He argued that sometimes it was difficult for a decision maker to state definitely the preferences between alternatives. Wu et al [13] fuzzified some important rationality conditions of fuzzy choice functions in the framework of the Banerjee choice function and obtained some results under the assumption that every involved choice set is normal.
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