In this section, the definition and examples of linguistic variables are given first. Then we explain two interpretations of fuzzy if-then rules and how to obtain a fuzzy relation that represents the meaning of a given fuzzy rule.

Linguistic Variables

As was pointed out by Zadeh [1], conventional techniques for system analysis are intrinsically unsuited for dealing with humanistic system, whose behavior is strongly influenced by human judgment, perception, and emotions. This is a manifestation of what might be called the principle of incompatibility "As the complexity of a system increases, our ability to make precise and yet significant statements about its behavior diminishes until a threshold is reached beyond which precision and significance become almost mutually exclusive characteristics". It was because of this belief that Zadeh proposed the concept of linguistic variables as an alternative approach to model human thinking. This is an approach that, in an approximate manner, serves to summarize information and express it in terms of fuzzy sets in stead of crisp numbers.