Physical Sciences and Mathematics Commons^™

Why Fuzzy Control Is Often More Robust (And Smoother): A Theoretical Explanation, Orsolya Csiszar, Gábor Csiszar, Olga Kosheleva, Martine Ceberio, Vladik Kreinovich

Departmental Technical Reports (CS)

In many practical situations, practitioners use easier-to-compute fuzzy control to approximate the more-difficult-co-compute optimal control. As expected, for many characteristics, this approximate control is slightly worse than the optimal control it approximates, However, with respect to robustness or smoothness, the approximating fuzzy control is often better than the original one. In this paper, we provide a theoretical explanation for this somewhat mysterious empirical phenomenon.

Why Fractional Fuzzy, Mehran Mazandarani, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

In many practical situation, control experts can only formulate their experience by using imprecise ("fuzzy") words from natural language. To incorporate this knowledge in automatic controllers, Lotfi Zadeh came up with a methodology that translate the informal expert statements into a precise control strategy. This methodology -- and its following modifications -- is known as fuzzy control. Fuzzy control often leads to a reasonable control -- and we can get an even better control results by tuning the resulting control strategy on the actual system. There are many parameters that can be changes during tuning, so tuning usually is rather …

Shall We Use Logical Approach Or More Traditional Mamdani Approach In Fuzzy Control: Pragmatic Analysis, R. Noah Padilla, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

Fuzzy control methodology transforms the experts' if-then rules into a precise control strategy. From the logical viewpoint, an if-then rule means implication, so it seems reasonable to use fuzzy implication in this transformation. However, this logical approach is not what the first fuzzy controllers used. The traditional fuzzy control approach -- first proposed by Mamdani -- transforms the if-then rules into a statement that only contains and's and or's, and does not use fuzzy implication at all. So, a natural question arises: shall we use logical approach or the traditional approach? In this paper, we analyze this question on the …

How Accurate Are Fuzzy Control Recommendations: Interval-Valued Case, Juan Carlos Figueroa-Garcia, Vladik Kreinovich

Departmental Technical Reports (CS)

As a result of applying fuzzy rules, we get a fuzzy set describing possible control values. In automatic control systems, we need to defuzzify this fuzzy set, i.e., to transform it to a single control value. One of the most frequently used defuzzification techniques is centroid defuzzification. From the practical viewpoint, an important question is: how accurate is the resulting control recommendation? The more accurately we need to implement the control, the more expensive the resulting controller.

The possibility to gauge the accuracy of the fuzzy control recommendation follows from the fact that, from the mathematical viewpoint, centroid defuzzification is …