Fuzzy constraints, choice, and utility

We revisit the notion of fuzzy revealed preference, with the intention of using it in decision making. A decision making agent manages resources that are priced, and it has a certain wealth. We review proposed fuzzifications of preference relations. Although they are well founded, they cannot deal well with decision making under fuzzy constraints. We introduce the fuzzy budget set as a general model of fuzzy constraints on resources. We then show that a general condition for rationality, the fuzzy axiom of revealed preference should not be an axiom anymore, but just a statement that is true to a certain degree. We show how to calculate this degree of truth. We define a fuzzy utility function, and show how it can be maximised, subject to fuzzy budget constraints.