Fuzzy control and coherent functions

A fuzzy controller can be seen as an algorithm that, given a fuzzy set (input) and a set of linguistic rules, computes the degree of possibility of every control value. Using a valid and complete proof system for possibilistic logic, we prove that fuzzy controllers enjoy the following property: every possibility measure that satisfies the degrees of possibility of input and linguistic rules also satisfies, for every control value, the degree of possibility computed by the fuzzy controller. We call such a property coherence between input, task description and output. We give a general definition of coherent function and we show that coherent functions form a class of functions that properly contains fuzzy controllers. Moreover, we present an application of coherent functions to a task different from control, namely localization in mobile robotics.