i dont think very many ppl will know the answer to this, but its late at night and i thought it would be fun to ask anyways. i just bought a text on fuzzy set theory and logic and im waiting for it to arrive. but im really curious, what mathematics are done on fuzzy sets? whats the algebraic structure, or the topological structure on fuzzy sets? can you define a fuzzy norm so that it resembles a banach space enabling you to do calculus? is there a meaningful way to define measures? the thing is that all of axiomatic set theory (and hence all of classical mathematics) depends on the implicit undefined notion of sets and set membership, so disposing of this, i cant think of how to proceed to define meaningful concepts of 'topology' or 'algebra' on fuzzy sets. anyways, if you have no idea what im talking about, why dont you just tell me what the meaning of life is?
math question (fuzzy logic)
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Eat, shit, and sleep. Throw some sex in there and some social visits with friends and you're good to go. Oh, and make sure 75% of all that time is taken up by working your ass off for peanuts a day.
That's the meaning of life.
That's the meaning of life.
I'm not that familiar with fuzzy set theory as such - fuzzy logic is traditionally more of a Computer Science concept, and I'd say has been more or less superceded in practice by using probabilistic reasoning rather than continuum-valued logics - but I'd assume that in revising the notion of set, most of the subsequent revision to the rest of mathematics would be algebraic?careful said:
I don't off the top of my head see much reason for worry as long as we can accept that yes, you may see very wide impact in mathematics, but a great many relationally defined theories in maths will be essentially isomorphic in fuzzy set theory to their ZFC counterparts.