Fuzzy Logic Flashcards
What is Fuzzy Logic?
“It is not logic that is fuzzy, but logic that is used to describe fuzziness.”
It is a set of mathematical expressions used in the knowledge representation of degree of membership of an object and not just based on crisp/classical membership.
Examples of Fuzzy Logic
- She is very tall
- He is very smart
- They are slightly alike
- We somewhat hate that cat
What is Boolean/Conventional Logic?
Boolean Logic is a set of rules that define a sharp distiction between the members of two sets (crisp membership)
Give another name for fuzzy logic
Multi-Valued Logic
Using Mathematics, describe classical set theory
x ∈ X
or
x ∉ X
Using Mathematics, describe Russell’s Paradox and how it contradicts classic set theory
Let R = {x|x ∉ x},
then R ∈R ⇔ R ∉ R
But in classical set theory,
R ∈ R or R ∉ R
Define fuzzy sets
A set that describes a gradual change across boundaries (fuzziness)
Define Universe of Discourse
The range of all possible values that can be assigned to a chosen variable
Using Mathematics, describe crisp sets (hint: use a piecewise function)
Let U be the Universal Discourse. Let a be a crisp set in U.
fₐ(x) = 1, if x ∈ a
fₐ(x) = 0, if x ∉ a
Using Mathematics, describe fuzzy sets (hint: use a piecewise function)
Let U be the Universal Discourse. Let a be a crisp set in U.
μₐ(x) = 1, if x ∈ a
μₐ(x) = 0, if x ∉ a
0 < μₐ(x) < 1, if x is partially in a
Describe linguistic variables
Have words instead numbers as their values
Are linguistic variables fuzzy variables?
Yes
Describes hedges as used with linguistic variables
These are liguistic modifiers. They modify the intended value of any linguistic variable e.g very, somewhat etc.
What are the uses of Hedges in fuzzy logic?
- Truth-values
- All purpose modifiers
- Probability
- Possibility
- Quantity
Give examples of Hedges you know, their mathematical expression, and their approximate graph
