Graphical fuzzy algebra applied to schedulability analysis of real time systems

Abstract

This paper proposes a graphical representation for the computation of fuzzy number operations, based on the theory of evidence. The proposed method has been compared with the theory of falling shadows [Wang 1992] with similar results for the AND operation. It is shown, as already remarked in [Dubois & Prade 1989], that no general correspondence between grades of membership correlation, and t-norms when the extension principle is applied, can be established. Some new interpretations based on imprecise observations [Dubois & Prade 1991] are provided. The proposed representation is easier to apply to the computation of complex function with fuzzy arguments. An example is provided where it is graphically shown that interval computations can be performed to solve fuzzy real-time schedulability analysis, reducing the number of time consuming simulations.