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Technical Report: UTEP-CS-23-02a


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 time-consuming. many parameters. Recently, it was empirically shown that in many cases, quite good results can be attained by using a special 1-parametric tuning procedure called fractional fuzzy inference -- we get up to 40% improvements just by selecting the proper value of a single parameter. In this paper, we provide a theoretical explanation of why fractional fuzzy inference works so well.

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