The US National Oceanic and Atmospheric Administration (NOAA) considers the range between 26 and 32 degrees as 'caution' and identifies ranges further up the temperature scale as 'dangerous' and 'extremely dangerous.' If we adhere to this definition, we can imagine the bounds of a hot day drawn by NOAA. Can we consider today a hot day? What does a precise thermometer reading tell us about the day, and how should we regulate our behaviour based on this reading? Let us suppose that today's temperature is 25 degrees Celcius, or 77 Ferenheight.
We start this discussion by restating the motivation behind the fuzzy set theory. We will base this discussion on "Type-2 Fuzzy Sets made Simple" by Robert John and Jerry Mendel, possibly the best paper to learn about type-2 fuzzy sets and logic. This post will look at the basic concepts behind type-2 fuzzy sets. In these cases, type-2 fuzzy sets provide the necessary framework to formalize and work with this information. We can extend this concept when the circumstances are so fuzzy that we have trouble deciding the membership grade as a number in. In a previous post, we have seen how we use a fuzzy set of type-1 when we cannot determine the membership of an element as 0 or 1.
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