Lecture 8 Flashcards
(25 cards)
What is the difference between uncertainty and vagueness?
Uncertainty arises from incomplete or unreliable information, while vagueness refers to imprecise definitions or gradations in meaning.
How does fuzzy logic handle vagueness?
Fuzzy logic assigns degrees of truth between 0 and 1, rather than just true or false.
What is a fuzzy set?
A set where elements have degrees of membership between 0 and 1, rather than just being in or out.
How is fuzzy membership different from classical set membership?
Classical sets have strict membership (0 or 1), whereas fuzzy sets allow partial membership between 0 and 1.
What is an example of a real-world fuzzy set?
Height classifications (e.g., ‘tall’ people) where membership gradually changes rather than having a strict cutoff.
Why do we normalize fuzzy membership values between 0 and 1?
To allow comparisons within a formalism and standardize calculations.
What is an example of a fuzzy function?
A function defining ‘nearly full’ for a glass of water, where the membership value is high around half-full but decreases for empty and completely full states.
How do fuzzy relations extend classical relations?
Fuzzy relations allow degrees of association between elements rather than strict binary relationships.
Why is uncertainty an obstacle for rational agents?
It makes decision-making difficult by introducing unknown factors into an agent’s environment.
How does uncertainty affect an autonomous taxi agent?
The agent must handle unpredictable elements like traffic, road conditions, and signal changes.
What are three sources of uncertainty in data?
Unreliable data, incomplete data, and imprecise measurements.
How does propositional logic handle uncertainty?
It uses declarative statements to define what is known and unknown but struggles with probabilistic reasoning.
What are the two major schools of thought in probability?
Frequentism and Bayesianism.
How does frequentist probability interpret probabilities?
It defines probability as the frequency of an event occurring over many trials.
How does Bayesian probability interpret probabilities?
It defines probability as a measure of belief based on prior knowledge and evidence.
What is an atomic event in probability?
A single possible outcome in a sample space.
What is a sample space?
The set of all possible outcomes in an experiment.
What is an event in probability?
A subset of the sample space representing one or more outcomes.
How is probability assigned to atomic events?
By dividing the number of favorable outcomes by the total number of possible outcomes.
What is the probability of rolling an even number on a fair six-sided die?
3/6 or 1/2, since there are three even numbers out of six total outcomes.
What is a probability distribution?
A function assigning probabilities to all possible values of a random variable.
What is a random variable?
A function that assigns numerical values to outcomes in a probability space.
What is the probability of a Boolean random variable being true?
It depends on the given probability distribution; typically, P(A) + P(¬A) = 1.
How do we express probabilities for Boolean, discrete, and continuous variables?
Using P(X=x) notation, where X is the variable and x is its assigned value.
