Mixed-logic interpolation of differentiable functions

A great many logical implication operators have been proposed to represent the fuzzy if-then relation. Within a parameterized family of operators, these operators lead to differently-shaped interpolation functions which vary systematically according to the parameter. This shape can be summarized by a continuum from selection to consensus. The paper explores the use of this variation to build a fuzzy-logic model of a function when we know the value and slope of the function at selected points and must interpolate between the given points