I was skimming through Kees Van Deemter’s book Not Exactly: In Praise of Vagueness (Oxford University Press, 2010) when I came across the following diagram:
It displays our intuitive answer to the question: When is a person tall? We know that all heights below a certain value definitely don’t qualify as tall and all those above another value unequivocally count as tall. That leaves a grey area. Van Deemter suggests that the following function might be suitable (where v stands for degree of truth):
0 if x < 150
1 if x > 190
We have three intervals—two horizontal lines--0 below 150 cm and 1 above 190 cm—with a diagonal line in between. Welcome to the world of fuzzy membership functions.
If we shift the binary functions 0 and 1 to defined negative and positive values and think in terms of financial instruments, what do we have? Well, yes, a bull call option spread.
(compliments of OIC)
There’s the maximum profit, the maximum loss, and all that fuzzy stuff in between.
And the point, you ask? Actually, I’m not sure there is any. But isn’t it interesting?