Differential calculus of fuzzy multi-variable functions and its applications to fuzzy partial differential equations

Abstract In this study, we deal with the concept of directional derivatives for fuzzy multi-variable functions and give explicit expressions for their directional derivatives. We give some applications of this concept as Green's identity for fuzzy multi-variable functions and Neumann boundary value problems. The fuzziness variations of a fuzzy multi-variable function according to the changing of the directions at a given point are examined. Moreover, we provide solutions to wave equations with fuzzy initial values. Some examples are presented to illustrate the results.

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