Question

Question 4 Define a linguistic variable and its values. Explain its importance for implementing a fuzzy expert system.

Answer 1

A linguistic variable is a linguistic expression (one or more words) labeling an information granular. Its values are words or sentences in a natural or artificial language. For example a membership function is labeled by the expressions like “hot temperature” or “rich customer”.

A linguistic variable is characterized by a quintuple (X,T,U,G,M) where X is the name of the variable, T is the set of terms of X, U is the universe of discourse, G is a syntactic rule for generating the name of the terms, and M is a semantic rule for associating each term with its meaning, that is, a fuzzy set defined on U.

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

A variable, or label, that represents some characteristic of an element, such as “age” for persons or “temperature” for water.

It is a variable that takes words, known as linguistic terms as values.

Fuzzy Logic (FL) is a method of reasoning that resembles human reasoning. The approach of FL imitates the way of decision making in humans that involves all intermediate possibilities between digital values YES and NO.

Algorithm

• Define linguistic Variables and terms (start)
• Construct membership functions for them. (start)
• Construct knowledge base of rules (start)
• Convert crisp data into fuzzy data sets using membership functions. (fuzzification)
• Evaluate rules in the rule base. (Inference Engine)
• Combine results from each rule. (Inference Engine)
• Convert output data into non-fuzzy values. (defuzzification)

Linguistic variables are input and output variables in the form of simple words or sentences. For room temperature, cold, warm, hot, etc., are linguistic terms.

Temperature (t) = {very-cold, cold, warm, very-warm, hot}

Every member of this set is a linguistic term and it can cover some portion of overall temperature values.

LINGUISTIC VARIABLES AND HEDGES At the root of fuzzy set theory lies the idea of linguistic variables A linguistic variable is a fuzzy variable. For example, the statement "John is tall" implies that the linguistic variable John takes the linguistic value tall Example wind is strong IF sailing is good THEN project_duration is long IF THEN completion_risk is high speed is slow stopping_distance is short IF THEN