FUZZ-IEEE’2013 Panel Presentation

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