Mesh construction of PLF and its approximation process in Mamdani fuzzy system

摘要

A piecewise linear function (PLF) plays a key role in the study of approximation of fuzzy system to an unknown function. PLF is not only the extension of unitary piecewise linear function under multi-variant conditions but also an important bridge between fuzzy system and approximation function. In this paper, a specific PLF is first constructed by the mesh subdivision of a polyhedron, and its analytical expression is obtained. Secondly, we verify that a PLF has the approximation performance to a continuous function based on the maximum norm and matrix norm, and the Mamdani fuzzy system can also approximate to arbitrary accuracy with respect to the maximum norm.