Systems of linear fuzzy constraints

Linear Fuzzy constraints are linear constraints where coefficients are fuzzy numbers. This paper demonstrates that two points of view can be considered to extend classical linear constraints: either tolerance constraints, or approximate (in)equality constraints can be obtained. Resolution of systems of linear fuzzy constraints is shown to be made easier by the use of fuzzy numbers analytically represented through a given type of membership function and three parameters. Solution methods are provided in the case of non fuzzy variables; as an illustration, some numerical examples are presented. The fuzzy variable case is also evoked.This paper is part of Purdue University Electrical Engineering technical report TR-EE 78-13.