Lecture 7 - Fuzzy logic

Question 1

Fuzzy logic

Answer 1

mathematical theory used to transform numerical representations into symbolic ones

Question 2

Why do we need fuzzy logic?

Answer 2

Because KBs cannot handle numerical representations

Question 3

Numerical quantities

Answer 3

they provide an exact quantification to the problem we are modeling: they provide precision.

Question 4

Precision

Answer 4

the level of detail we will use to model the problem, related to sub-symbolic AI

Question 5

Significance

Answer 5

the relevant information we will use to model the problem

Question 6

Discretization

Answer 6

the process of converting numerical knowledge representations into symbolic ones.

Question 7

Uncertainty

Answer 7

lack of sureness about something: degree of uncertainty.

Question 8

Inconsistent information

Answer 8

two similar situations lead to different outcomes

Question 9

Incomplete information

Answer 9

problem domain is only partially described

Question 10

Imprecise information

Answer 10

problem domain is not well described

Question 11

Aristotelian logic

Answer 11

An object can only be related to a single object

Question 12

Linguistic variable

Answer 12

same as a symbolic variable, for example, “age”

Question 13

Linguistic term

Answer 13

the fuzzy sets contained in the linguistic variable, i.e., young, middle-age, old

Question 14

Formal definition of “fuzzy set”

Answer 14

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 ).

Question 15

Membership function

Answer 15

Quantifies how much x belongs to the fuzzy set A

Question 16

Fuzzification

Answer 16

mapping numerical input to fuzzy sets with a membership degree

Question 17

No overlap between fuzzy sets

Answer 17

Equivalent to binary partition

Question 18

Granularity level

Answer 18

Number of symbolic terms we will use to model a certain linguistic variable

Question 19

Triangular membership function

Answer 19

3 parameters, only one maximal value

Question 20

Trapezoidal membership function

Answer 20

4 parameters, not single maximal value

Question 21

Gaussian membership function

Answer 21

Softer, more flexibility

Question 22

Difference between membership values and probabilities

Answer 22

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).