Discussion
Why is fuzzy membership not the same as probability?
Answer: A
Whether a definite man of definite height counts as tall is a question about the word, not about the world, and no amount of evidence resolves it. A probability that he is tall would presuppose a sharp boundary and uncertainty about which side he falls. Arithmetic, normalisation and application area are consequences or incidental. Identifying which kind of imperfection in knowledge a problem exhibits is what selects the right formalism rather than the fashionable one.
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