On fuzzy interpolation

This note intends to discuss several connections between interpolative reasoning and fuzzy sets and the role played by the extension principle in this connection. It is first recalled how gradual rules can encode linear or non-linear interpolation between precisely known points and can exactly reconstruct any single-input monotonic real function when the membership functions of the fuzzy sets involved in the rules are suitably chosen. Then linear interpolation between fuzzy points is investigated. The interest of gradual rules as opposed to other approximation schemes is singled out.