Lecture 7 - Fuzzy logic Flashcards
Fuzzy logic
mathematical theory used to transform numerical representations into symbolic ones
Why do we need fuzzy logic?
Because KBs cannot handle numerical representations
Numerical quantities
they provide an exact quantification to the problem we are modeling: they provide precision.
Precision
the level of detail we will use to model the problem, related to sub-symbolic AI
Significance
the relevant information we will use to model the problem
Discretization
the process of converting numerical knowledge representations into symbolic ones.
Uncertainty
lack of sureness about something: degree of uncertainty.
Inconsistent information
two similar situations lead to different outcomes
Incomplete information
problem domain is only partially described
Imprecise information
problem domain is not well described
Aristotelian logic
An object can only be related to a single object
Linguistic variable
same as a symbolic variable, for example, “age”
Linguistic term
the fuzzy sets contained in the linguistic variable, i.e., young, middle-age, old
Formal definition of “fuzzy set”
Let X denote the universe of discourse such that its elements are represented by x, then a fuzzy set A in X is defined as a set of ordered paired with the form
A = ( x, miu(x) | x e X ).
Membership function
Quantifies how much x belongs to the fuzzy set A
Fuzzification
mapping numerical input to fuzzy sets with a membership degree
No overlap between fuzzy sets
Equivalent to binary partition
Granularity level
Number of symbolic terms we will use to model a certain linguistic variable
Triangular membership function
3 parameters, only one maximal value
Trapezoidal membership function
4 parameters, not single maximal value
Gaussian membership function
Softer, more flexibility
Difference between membership values and probabilities
Membership values:
Fuzzy logic relies on degrees of truth as a mathematical model of vagueness and imprecision
Probabilities/Confidence:
are a mathematical model of ignorance (with probabilities, we are partially ignorant: if we say that there is a 50% of rain, we are 50% ignorant about the situation, whereas membership values do not represent ignorance because we know where all values belong, but they belong to different fuzzy sets to different extents).
