The Relative Gain Array (RGA) and the Niederlinski Index (NI) represent powerful tools for variable pairings selection to achieve minimum interaction subject to stability and integrity in decentralized control systems. Nevertheless, closed-loop integrity of the highest priority (against single loop failure) can not be guaranteed by variable pairing choice only, particularly when pairing on negative RGA elements becomes inevitable for a given process. In parallel to the Generalized Niederlinski Index (GNI) : a generalized integrity criterion based on steady state information of both the process and the controller is developed. Both the GNI and the generalized integrity criterion allow for joint consideration of variable pairing selection and controller design and reduce to the NI and RGA rules, thus representing more general tools than the NI and RGA for simultaneously ensuring closed-loop stability and integrity in decentralized control systems. The new criteria are particularly useful when it is impossible to find a pairing corresponding to all RGA elements positive. Guidelines for integrating variable pairing and controller design are offered. The inclusion of controller design imposes no considerable difficulty, since only directional change of individual controllers is important with no specific controller design actually required.