Coverage and invariability in fuzzy systems

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

Invariability, orbits and fuzzy attractors

In this paper, we present a generalization of a new systemic approach to abstract fuzzy systems. Using a fuzzy relations structure will retain the information provided by degrees of membership. In addition, to better suit the situation to be modelled, it is advisable to use T-norm or T-conorm distinct from the minimum and maximum, respectively. This gain in generality is due to the completeness of the work on a higher level of abstraction. You cannot always reproduce the results obtained previously, and also sometimes different definitions with different views are obtained. In any case this approach proves to be much more effective when modelling reality

Fuzzy Structure of Complex Belief Systems: Fuzzy Relations and Fuzzy Belief Sets

In previous work, Nescolarde-Selva and Usó-Doménech (2014a Nescolarde-Selva, J. and J. L. Usó-Doménech. “Semiotic Vision of Ideologies.” Found Sci 19 (2014a): 263–282.[CrossRef], [Web of Science ®], b) discussed the theory that complex belief systems have a topological structure. In this article it is suggested that this structure is also fuzzy. We introduce the concepts of fuzzy sets in the context of beliefs (substantive and derived), and between derived beliefs themselves. Also introduced are the concepts of fuzzy covering and fuzzy invariance and the relationships between them