What nodes constitute the 'Markov Blanket' of a variable X in a Bayesian Network, rendering X conditionally independent of all other nodes in the network?
A node's Markov blanket consists of its parents, its children, and its children's other parents (spouses/co-parents); conditioning on these shields the node from the rest of the network.
In Bayesian network structure learning, what does 'd-separation' (directed separation) formally determine?
Judea Pearl's d-separation graphical criterion establishes whether variable sets X and Y are conditionally independent given evidence Z based on blocking linear, diverging, and converging v-structure collider paths.
What does Dempster-Shafer Theory model that standard Bayesian probability struggles to distinguish?
Dempster-Shafer evidence theory models epistemic ignorance directly by allocating probability masses across the power set of propositions (Belief and Plausibility).
In fuzzy set theory, if membership degree mu_A(x) = 0.8 and mu_B(x) = 0.4, what is the standard Zadeh Fuzzy Intersection (mu_(A cap B)(x))?
Zadeh's standard fuzzy intersection is defined by the minimum operator: min(mu_A(x), mu_B(x)) = min(0.8, 0.4) = 0.4.
In fuzzy set theory, if membership degree mu_A(x) = 0.7 and mu_B(x) = 0.3, what is the standard Zadeh Fuzzy Union (mu_(A cup B)(x))?
Zadeh's standard fuzzy union is defined by the maximum operator: max(mu_A(x), mu_B(x)) = max(0.7, 0.3) = 0.7.