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Tropical (Idempotent) Algebras as a Way to Optimize Fuzzy Control
Jaime Nava, University of Texas at El PasoFollow
6-2011
Technical Report: UTEP-CS-11-33
To appear in International Journal of Innovative Management, Information & Production (IJIMIP), 2011, Vol. 2, No. 3.
Fuzzy control is a methodology that transforms control rules (described by an expert in words of a natural language) into a precise control strategy. There exist several versions of this transformation. The main difference between these versions is in how they interpret logical connectives "and" and "or", i.e., in other words, what reasoning method a version uses. Which of these versions should we choose? It turns out that on different stages of control, different reasoning methods lead to better control results. In this paper, we describe the choice of reasoning methods that optimize control results in terms of smoothness and stability. It turns out that reasoning methods which are optimal on each stage correspond to tropical algebras -- algebras isomorphic to the set of real numbers with operations plus and maximum.
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Technical Report: UTEP-CS-11-33
To appear in International Journal of Innovative Management, Information & Production (IJIMIP), 2011, Vol. 2, No. 3.