In Fuzzy Logic, the Defuzzification method that calculates the center of gravity of the aggregated fuzzy output membership area is:
The Centroid method computes crisp output z* = ∫ $\mu (z) z dz / ∫ \mu (z) dz, finding$ the center of gravity of the fuzzy set.
How does a Sugeno Fuzzy Inference System differ from a Mamdani Fuzzy System?
Sugeno systems use crisp linear or constant equations in rule consequents (THEN $y = ax + b$), making defuzzification computationally simpler.
In Reinforcement Learning, the equation that recursively breaks down the value of a state into expected immediate reward plus discounted future value is:
The Bellman Equation defines V(s) = R(s) + $\gamma * max_a \Sigma P(s'|s,a) V(s'), anchoring dynamic programming$ and Q-learning algorithms.
In Constraint Satisfaction Problems (CSPs), Arc Consistency (AC-3) enforces consistency between two variables $X_{i}$ and $X_{j}$ by:
AC-3 makes arc ($X_{i}$, $X_{j}$) consistent by deleting any value x ∈ $D_{i}$ for which no value y ∈ $D_{j}$ satisfies the constraint between $X_{i}$ and $X_{j}$.
In CSP Backtracking Search, the Minimum Remaining Values (MRV) heuristic chooses the next variable to assign based on:
MRV ('most constrained variable' or 'fail-first' heuristic) picks the variable with the smallest domain to detect failures early.