Intelligent Systems II · M2 · revision
The final revision: methods, theory and common mistakes
Last-day revision
A compact read after the worked lessons.
Q1: short calculations and definitions
| Asked for | Write |
|---|---|
| Union / intersection | Same element, max / min respectively. |
| Complement / difference | 1−μA / min(μA,1−μB). |
| Triangle membership | Locate x; rising (x−a)/(b−a), falling (c−x)/(c−b), 0 outside, 1 at peak. |
| Swarm intelligence | Collective problem-solving emerging from interacting simple agents; explain PSO through position, velocity, pbest and gbest. |
GA: the table to make in the exam
Individual → current x → bit string → fitness → selected parent → crossover child → mutated child → decoded x → new fitness. Use this resulting population as the input to the second generation. The cut position and flipped bit are counted from the stated end; this guide counts from the left.
Do not change the mutation instruction midway because an answer looks worse. Without elitism, fitness can worsen. Do not confuse a mating-pool index with the decimal x value.
PSO: the table to make in the exam
Particle → old position → old velocity → pbest → gbest → inertia/personal/social terms → new velocity → new position → new objective → retained pbest. After all particles, update gbest. For synchronous updates, freeze the old gbest throughout one iteration.
At initialisation pbest=x, hence personal pull=0. In iteration 2 it need not be zero. For minimisation, smaller objective wins; a worse move must not overwrite a better memory.
Fuzzy controller: five operations
- Calculate input memberships using the specified graphs.
- Apply AND=min or the supplied connective to obtain rule strengths.
- Clip consequents using min-implication.
- Combine output sets by max-aggregation.
- Use the named defuzzification method. MoM, full area centroid and peak-weighted average are different operations.
Three short theory answers to revise
Mamdani: crisp inputs → fuzzifier → knowledge base and inference engine → aggregation → defuzzifier → crisp output. Rules are interpretable, but require careful membership/rule design and can grow in number.
GA: population search inspired by evolution, using evaluation, selection, crossover, mutation and replacement. Flexible and derivative-free, but may be expensive or converge prematurely.
PSO: particles move using inertia, personal best and swarm best. Simple and derivative-free, but parameter-dependent and not guaranteed to find a global optimum.
Calculator and rounding
Enter a fraction as (whole numerator) ÷ (whole denominator). For a negative square use parentheses: (−2)²=4. Retain full calculator precision through iterations and round only the displayed result. Binary place values 8,4,2,1 can be checked manually without a special calculator mode.
Yaad rakho: Question ki instruction follow karo; answer ko sundar banane ke liye data ya operator mat badlo.