Coverage and invariability in fuzzy systems

Abstract This paper presents a new complex system systemic. Here, we are working in a fuzzy environment, so we have to adapt all the previous concepts and results that were obtained in a non-fuzzy environment, for this fuzzy case. The direct and indirect influences between variables will provide the basis for obtaining fuzzy and/or non-fuzzy relationships, so that the concepts of coverage and invariability between sets of variables will appear naturally. These two concepts and their interconnections will be analyzed from the viewpoint of algebraic properties of inclusion, union and intersection (fuzzy and non-fuzzy), and also for the loop concept, which, as we shall see, will be of special importance.