Artificial Intelligence: Fuzzy Logic (Part I)

Practice flashcards covering the fundamental concepts, membership functions, operations, and the Tsukamoto method of Fuzzy Logic as presented in the lecture notes.

Prof. Lotfi Astor Zadeh

The individual who introduced Fuzzy Logic in 1962.

Fuzzy Logic

A problem-solving control system methodology that is suitable for implementation on systems.

Variabel Fuzzy (Fuzzy Variable)

The specific variables discussed and analyzed within a fuzzy system.

Himpunan Fuzzy (Fuzzy Set)

A group representing a specific state or condition within a fuzzy variable.

Semesta Pembicaraan (Universe of Discourse)

The entire range of values permitted to be operated upon within a fuzzy variable.

Domain Himpunan Fuzzy

All values allowed in the universe of discourse that can be operated on within a particular fuzzy set.

Fungsi Keanggotaan (Membership Function)

A graph representing the magnitude of the membership degree ($\mu(x)$) of each input variable within the interval $0$ and $1$.

$$\mu(x)$$

The symbol used to denote the degree of membership of an element in a fuzzy set.

Grafik Keanggotaan Kurva Linear Naik

A fuzzy set increase starting at a domain value with membership degree $0$ moving right to a higher membership degree, defined as $\mu[x] = \frac{x - a}{b - a}$ for $a \le x \le b$.

Grafik Keanggotaan Kurva Linear Turun

A fuzzy set decrease starting from the highest degree on the left and moving down to a lower membership degree on the right, defined as $\mu[x] = \frac{b - x}{b - a}$ for $a \le x \le b$.

Grafik Keanggotaan Kurva Segitiga (Triangular Curve)

A membership function resulting from the combination of two linear lines, where the degree is $1$ only at point $b$ and $0$ at points $a$ and $c$.

Grafik Keanggotaan Kurva Trapesium (Trapezoidal Curve)

Similar to a triangular curve, but with multiple points having a membership value of $1$ between domain values $b$ and $c$.

Grafik Keanggotaan Kurva Bentuk Bahu (Shoulder Curve)

A curve used to terminate a fuzzy area where the membership degree remains constant at $1$.

Grafik Keanggotaan Kurva-S (Sigmoid)

A curve defined by parameters $a$, $b$, and $c$, where $b$ represents the inflection point.

Titik Infleksi (Inflection Point)

The specific point on a Sigmoid S-curve where the degree of membership is exactly $0.5$.

Kurva-S PERTUMBUHAN (Growth S-curve)

A Sigmoid curve moving from left to right that transitions from a membership degree of $0$ up to $1$.

Kurva-S PENYUSUTAN (Shrinkage S-curve)

A Sigmoid curve moving from left to right that transitions from a membership degree of $1$ down to $0$.

Operasi Gabungan (Union)

Also known as the MAX operator, expressed as $\mu_{A \cup B}(x) = \max \{ \mu_A(x), \mu_B(x) \}$.

Operasi Irisan (Intersection)

Also known as the MIN operator, expressed as $\mu_{A \cap B}(x) = \min \{ \mu_A(x), \mu_B(x) \}$.

Operasi Komplemen (Complement)

The NOT operator for fuzzy sets, expressed as $\mu_{A^C}(x) = 1 - \mu_A(x)$.

Basis Pengetahuan Fuzzy (Fuzzy Knowledge Base)

A collection of fuzzy rules formulated as IF…THEN statements.

Fuzzifikasi (Fuzzification)

The process of converting crisp system input values into linguistic variables using membership functions.

Mesin Inferensi (Inference Engine)

The process of converting fuzzy input into fuzzy output by following IF…THEN rules defined in the knowledge base.

Defuzzifikasi (Defuzzification)

The process of converting fuzzy output from the inference engine back into crisp (tegas) values.

Metode Tsukamoto

An extension of monotonic reasoning where each rule's consequent is a monotonic fuzzy set and the final output is a weighted average based on $\alpha$-predicates.

$\alpha$-predikat (Fire Strength)

The crisp value resulting from the fuzzy inference of a single rule, used in determining the overall crisp output.