The extension of Buckley-Feuring solutions for non-polynomial fuzzy partial differential equations. Application to microeconomics utility theory

This paper presents the natural extension of Buckley-Feuring method proposed in for solving fuzzy partial differential equations (FPDE) in a nonpolynomial relation, such as the operator phi(D
_x1
,D
_x2
), which maps to the quotient between both partials. The new assumptions and conditions proceedings from this consideration given in this document, have been developed for a concrete application: a new method for building consumer fuzzy utility functions from marginal rates of substitution (MRS).