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

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

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

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