Approximating fuzzy control strategies via CRI

Authors:
Siegfried Gottwald;Vilem Novák;Irina Perfilieva
Affiliations:
Leipzig University, Institute for Logic, Leipzig, Germany;Ostrava University, IRAFM, Ostrava, Czech Republic;Ostrava University, IRAFM, Ostrava, Czech Republic
Venue:
IFSA'03 Proceedings of the 10th international fuzzy systems association World Congress conference on Fuzzy sets and systems
Year:
2003

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Abstract

We start from the observation that ZADEH's compositional rule of inference (CRI) is a strategy to determine approximately a roughly given control function. From this point of view the problem to solve a system of fuzzy relation equations also becomes the problem to determine approximately such a control strategy. This gives a natural interpretation for approximate solutions of unsolvable systems of relation equations. Therefore we discuss and generalize some approaches and results about approximate solutions of systems of relation equations. Finally we discuss here how a choice of the t-norm which is involved in the sup-t-composition modifies the solvability behavior.