The use of revealed preference in a fuzzy setting: some preliminary results

The Weak Axiom of Revealed Preference (WARP) is an important axiom in microeconomic theory. This paper discusses the topic in a fuzzy setting. Using simple concepts of fuzzy mathematics, we show that although we violate WARP we can still be declared rational up to some degree. This is a useful result. The paper discusses how we could properly define, within a fuzzy setting, a ‘Greatest set’. The choice function is defined and equated to the nearest Maximal set or to the nearest Greatest set, both of which are ‘crisp’ sets. A simple formulation is proposed, which may enable us to assert degrees of rationality even though we violate WARP.