Fuzzy Logic Flashcards

Flashcards on Fuzzy Logic concepts and definitions.

What is Fuzzy Logic?

A mathematical language to express something with grammar, syntax, and semantics for communication, dealing with Fuzzy Sets.

Who first introduced Fuzzy Logic?

Lotfi Abdelli Zadeh (1965), University of California, Berkley, USA.

What is the antonym of fuzzy?

Crisp

What are the components of a fuzzy system?

Fuzzy element(s), Fuzzy set(s), Fuzzy rule(s), Fuzzy implication(s).

What is a fuzzy set?

A collection of ordered pairs.

What is the relationship between a Crisp set and a Fuzzy set?

A crisp set is a fuzzy set, but a fuzzy set is not necessarily a crisp set.

Give some examples of a fuzzy set.

High Temperature, Low Pressure, Color of Apple, Sweetness of Orange, Weight of Mango.

How is a Fuzzy set defined?

A = {(x, µA(x))|x ∈ X} where µA(x) is the membership function for the fuzzy set A.

What is the Support of a fuzzy set A?

The set of all points x ∈ X such that µA(x) > 0.

What is the Core of a fuzzy set A?

The set of all points x in X such that µA(x) = 1.

What is Normality in fuzzy sets?

A fuzzy set A is normal if its core is non-empty, meaning there exists a point x ∈ X such that µA(x) = 1.

What is a Crossover Point of a fuzzy set A?

A point x ∈ X at which µA(x) = 0.5.

What is a Fuzzy Singleton?

A fuzzy set whose support is a single point in X with µA(x) = 1.

How is the α-cut of a fuzzy set A defined?

Aα = {x | µA(x) ≥ α }

What is the condition for Convexity of a fuzzy set A?

µA (λx1 + (1 -λ)x2) ≥ min(µA(x1), µA(x2)).

What is Bandwidth?

For a normal and convex fuzzy set, the distance between the two unique crossover points.

What is Symmetry in Fuzzy Sets?

µA(x + c) = µA(x - c) for all x ∈ X.

What are open and closed fuzzy sets?

A fuzzy set is Open left If limx→−∞ µA(x) = 1 and limx→+∞ µA(x) = 0. Open right: If limx→−∞µA(x) = 0 and limx→+∞ µA(x) = 1. Closed If : limx→−∞ µA(x) = limx→+∞ µA(x) = 0

What does Fuzzy describe?

Certainty of a thing.

What does Probability describe?

Chance of an event to occur.

What is Prediction?

Guessing about things.

What is Forecasting?

Information from the past job and apply it to new job.

How is a fuzzy set characterized?

A fuzzy set is completely characterized by its membership function.

How is a Triangular Membership Function defined?

Specified by three parameters {a, b, c} and defined piecewise.

How is a Trapezoidal Membership Function defined?

Specified by four parameters {a, b, c, d} and defined piecewise.

How is a Gaussian Membership Function defined?

Specified by two parameters {c, σ} and defined by gaussian(x;c,σ) =e − 1 2 ( x−c σ )2.

How is a Generalized Bell Membership Function defined?

Specified by three parameters {a, b, c} and defined by bell(x; a, b, c)= 1 1+| x−c a |2b

How is a Sigmoidal Membership Functions defined?

Parameters: {a, c} ; where c = crossover point and a = slope at c; Sigmoid(x;a,c)= 1 1+e −[ a x−c ]

How is the Union of two fuzzy sets defined?

µA∪B(x) = max{µA(x), µB(x)}

How is the Intersection of two fuzzy sets defined?

µA∩B(x) = min{µA(x), µB(x)}

How is the Complement of a fuzzy set defined?

µAC(x) = 1-µA(x)

How is the Algebric product of two fuzzy sets defined?

µA•B(x) = µA(x) • µB(x)

How is the Scalar product of a fuzzy set defined?

µαA(x) = α · µA(x)

How is the Sum of two fuzzy sets defined?

µA+B(x) = µA(x) + µB(x) − µA(x) · µB(x)

What is the cartesian product of two fuzzy sets?

Cartesian Product (A × B): µA×B(x, y) = min{µA(x), µB(y)

What is Commutativity in fuzzy sets?

A∪B = B∪A and A∩B = B∩A

What is Associativity in fuzzy sets?

A ∪ (B ∪ C) = (A ∪ B) ∪ C and A ∩ (B ∩ C) = (A ∩ B) ∩ C

How can we generate more MFs?

Given a membership function of a fuzzy set representing a linguistic hedge, we can derive many more MFs representing several other linguistic hedges using the concept of Concentration and Dilation.