Buckley-feuring solutions for non-polynomial fuzzy partial differential equations. Application to utility theory

This paper presents the natural extension of Buckley-Feuring method proposed in (Buckley and Feuring, 2002) for solving fuzzy partial differential equations (FPDE) in a non-polynomial relation, such as the operator phi(D_{x 1}, D_{x 2}), which maps to the quotient between both partials. The new assumptions and conditions proceedings from this consideration, have been developed for a concrete application: a new method for building consumer fuzzy utility functions from marginal rates of substitution (MRS). Finally, the consumer decision problem is tackled in its fuzzy mathematical programming form.