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FUZZ-IEEE’2013 Panel Presentation

Fuzzy techniques are valued for their ease of use, yet there are compelling reasons to explore more complex methods. First, more sophisticated approaches can provide a more accurate representation of uncertainty in expert opinions, utilizing type-2 fuzzy sets to better articulate degrees of vagueness. Second, while complexity might seem counterintuitive, it can lead to faster computations—examples include optimization over ellipsoids versus boxes. Lastly, translating intuitive fuzzy language into computer-usable forms remains a challenge, which could ultimately simplify operations without sacrificing accuracy.

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FUZZ-IEEE’2013 Panel Presentation

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  1. FUZZ-IEEE’2013 Panel Presentation Title: Since one of the main advantages of fuzzy techniques is easiness-of-use, why make them more complicated? Presenter: Vladik Kreinovich

  2. An advantage of fuzzy is easiness-of-use, so why use more complicated techniques? • First answer: this leads to a more adequate description of uncertainty • We need fuzzy in situations when an expert cannot describe an exact value of x, only “small” or “high” • The usual [0,1]-based fuzzy techniques describe the expert’s uncertainty by a number d from [0,1] • If an expert cannot describe an exact value of x, she cannot describe her degree d exactly either • A more adequate description is to say, e.g., that 0.7 is a possible degree, and 0.6 is somewhat possible • This means using type-2 fuzzy sets

  3. An advantage of fuzzy is easiness-of-use, so why use more complicated techniques? • Second answer: representation complexity often leads to faster computations • Example 1: ellipsoids are more complex than boxes, but optimization over ellipsoids is faster • Example 2: complex numbers are more complex than reals, but optimization and integration are faster • For this reason, complex numbers are used in processing real-valued signals (e.g., FFT) • In applications like fuzzy control, complex numbers are sometimes computationally more efficient

  4. An advantage of fuzzy is easiness-of-use, so why use more complicated techniques? • Third answer: representations are complex because we describe them in computer-usable terms • On the intuitive level, we can easily manipulate “fuzzy” words like “small” or “large” • We want computers to manipulate these words, but computers were designed for crisp notions • This is similar to the need to translate from decimal to binary – since binary is the computer language • Ideally, we should teach computers how to deal with words directly • This will make seemingly complicated representations easier – but it’s a great challenge

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