What is fuzzy logic?
1 Answer
Fuzzy logic is a generalisation of Boolean logic with truth values between true and false.
Explanation:
In ordinary Boolean logic, propositions are true or false.
In fuzzy logic you could consider propositions to have truth values in the range
There are several different systems of fuzzy logic used for different purposes in different areas of mathematics. These different systems have different rules for the truth values of logical operations.
If we write
#v(not P) = 1-v(P)#
#v(P ^^ Q) = v(P)*v(Q)#
#v(P vv Q) = v(not ((not P) ^^ (not Q)))#
#= 1-(1-v(P))(1-v(Q))#
These rules correspond to the way that probabilities of two independent events would combine.
What can we do if we don't know whether
Yet another alternative is to introduce the notion of relevance into logic, which typically has the side effect of splitting simple and's and or's into intrinsic and extrinsic conjunctions and disjunctions. Combined with fuzziness, this can have a similar effect to the modal operators.