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Martin Sleziak
Martin Sleziak
8:47 AM
@AliTaghavi I would guess that if you create a chatroom and post nothing there, it is very likely that other users won't know what is a purpose of that room. (And moreover, if you don't post anything there, nobody can ping you in that room.)
But perhaps you have created that room by mistake?
chat.stackexchange.com/rooms/154374/analyticobjects
chat.stackexchange.com/rooms/info/154374/analyticobjects
 
12 hours later…
Ben Hocking
Ben Hocking
8:34 PM
Is this a good place to discuss fuzzy logic? I came up with a set of propositions that are paradoxical in classical logic, but which allow a solution of (1/3, 1/3, 2/3) in fuzzy logic:
x = y xor z
y = x and z
z = not x and not y
In fuzzy (or classical) logic, these can be rewritten as:
x = |y - z|
y = min(x, z)
z = min(1-x, 1-y)
The values of (1/3, 1/3, 2/3) provide the only valid solution to this.
What I'm wondering is (a) whether this is the simplest set of propositions that contain 1/3 as a solution to one of the propositions, (b) whether there is a general means for constructing such se…
Ben Hocking
Ben Hocking
8:44 PM
For those who are interested in the trivial (classically non-paradoxical) example, here's the simplest version I can think of:
x = y and not z
y = (not x) and z
z = x and not y
In fuzzy (or classical) logic, these can be rewritten as:
x = min(y, 1-z)
y = min(1-x, z)
z = min(x, 1-y)
And for any alpha between 0 and 0.5 inclusive, x=y=z=alpha is a solution.
Oh wait, there's an even more trivial example: x = x and not x. As before, letting x be false is a perfectly valid solution, but if we convert it to fuzzy logic, any value between 0 and 0.5 (inclusive) works.

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