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When defining a linguistic variable, it is customary to specify minimum and maximum values. For example, when defining a Temperature variable, someone might specify -40C and +85C as the range of that variable. The members of the fuzzy set (e.g. Cold, Lukewarm, Hot) are then defined within the variable's overall range.

In a real-world application, what happens if the variable's value goes out of range? For example, if the variable and its membership functions are defined for the range (-40, +85), would an actual temperature reading of -45 cause any problems? If all membership functions have values of either (0) or (1) at the endpoints of the range, why not just extend those values to infinity and treat an out-of-range value just like any other value?

If the fuzzy logic "works" for out-of-range values, then what is the purpose for defining a range in the first place?

user2979790
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I cannot see any other reason than that it may be practical to have a defined range if you, for instance, want to display membership functions graphically, or if you want to force the values to be realistic. As you say, the last membership value (0 or 1 in your case) would be the one that is used "off range". ("Open" sets, i.e. sets with membership functions that have a non-zero end value, are problematic if used in conclusions, since the area below the curve is unlimited. Maybe a defined range could be useful there?)

palun
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