Linguistic Description And Their Analytic Form

By Abu Horaira TarifCSE,CUET

1204058

REFERENCE

Fuzzy & Neural Approaches in EngineeringLofti A. Zadeh

• Fuzzy Sets• Fuzzy Relations• Implication Operators• Compositions

Analytical Form

• Variables• Propositions• If/then Rules• Algorithms• Inference

Linguistic Form

Linguistic Variable: Linguistic variable is an important concept in fuzzy logic and plays a key role in its applications, especially

in the fuzzy expert system.

Linguistic variable is a variable whose values are words in a natural language.

For example, “speed” is a linguistic variable, which can take the values as “slow”, “fast”, “very fast” and so on.

Linguistic variables collect elements into similar groups where we can deal with less precisely and hence we can handle more complex systems.

A linguistic variable is a variable whose values are words or sentences in a natural or artificial language.

It is a mathematical representation of semantic concepts that includes more than one term (fuzzy set).

It is a variable made up of a number of words (linguistic terms) with associated degrees of membership.

More About Linguistic Variable: Linguistic variable is a variable of higher order than fuzzy variable, and it take fuzzy variable as its values

A linguistic variable is characterized by: (x, T(x), U, M), x; name of the variable

T(x); the term set of x, the set of names or linguistic values assigned to x, with each value is a fuzzy variable defined in U

M; Semantic rule associate with each variable (membership)

For Example: x : “age” is defined as a linguistic variable

T(age) = {young, not young, very young, more or less old, old}

U: U={0, 100}

M: Defines the membership function of each fuzzy variable for example; M (young) = the fuzzy set for age below 25 years with membership of µyoung

Fuzzy Variable: A fuzzy variable is characterized by (X, U, R(X)), X is the name of the variable; U is the universe of

discourse; and R(X) is the fuzzy set of U.

For example: X = “old” with U = {10, 20, ..,80}, and R(X) = 0.1/20 + 0.2/30 + 0.4/40 + 0.5/50 + ….+ 1/80 is called a fuzzy membership of “old”

Fuzzy Proposition: A specific evaluation of a fuzzy variable is called fuzzy proposition.

Individual fuzzy propositions on either LHS or RHS of a rule may be connected by connectives such as AND & OR.

Individual if/then rules are connected with connective ELSE to form a fuzzy algorithm.

Propositions and if/then rules in classical logic are supposed to be either true or false.

In fuzzy logic they can be true or false to a degree.

Fuzzy Inference: Fuzzy proposition is computational procedures used for evaluating linguistic descriptions.

Two important inferring procedures are:

i. Generalized Modus Ponens(GMP)

ii. Generalized Modus Tollens(GMT)

(See Details From Book)

Modus Ponens vs Modus Tollens

Modus Ponens and Modus Tollens are forms of valid inferences.

By Modus Ponens, from a conditional statement and its antecedent, the consequent of the conditional statement is inferred: e.g. from “If John loves Mary, Mary is happy” and “John loves Mary,” “Mary is happy” is inferred.

By Modus Tollens, from a conditional statement and the negation of its consequent, the negation of the antecedent of the conditional statement is inferred: e.g. from “If today is Monday, then tomorrow is Tuesday” and “Tomorrow is not Tuesday,” “Today is not Monday” is inferred.

The validity of these inferences is widely recognized and they are incorporated into many logical systems.

Application Of Fuzzy Inference:Fuzzy inference systems have been successfully applied in fields such as: Automatic control Data classification Decision analysis Expert systems Computer vision.

Because of its multidisciplinary nature, fuzzy inference systems are associated with a number of names, such as: Fuzzy-rule-based systems Fuzzy expert systems Fuzzy modeling Fuzzy associative memory Fuzzy logic controllers Simply (and ambiguously) fuzzy systems.

Some Fuzzy Implication Operators

Interpretation of ELSE Under Various Implications

SEE TOPICS FROM BOOK Linguistic Values Linguistic Variables Primary Values Compound Values Implication Relation Fuzzy Inference & Composition Degree Of Fulfillment Area Cum Point Crisp Point Rules Of Inferences Fuzzy Algorithm

Modus Ponens And Modus Tollens (More Details Read From Discrete Mathematics)

THANK YOUVERY MUCH

Inspired By Miss Lamia Alam

Lecturer Of CUET,CSE DEPT