Linguistic expression

In some applications, membership functions can easily be determined by clearly recognized prototypes and suitable similarity functions. In other applications, neural networks can be employed for constructing membership functions by learning from data exemplifying the linguistic expression involved. Many other methods for constructing membership functions are described in the literature, but this topic is beyond the scope of this chapter. 

Contrary to their classical counterparts, operations on fuzzy sets are not unique. This is a natural consequence of the fact—well-established by numerous psychological experiments—that logical connectives (not, and, or, etc.) in linguistic expressions have different meanings when applied by... 

Fuzzy sets on [R that satisfy these requirements capture various linguistic expressions, describing approximate numbers or intervals, such as numbers that are close to a given real number or numbers that are around a given interval of real numbers. Moreover, we can define meaningful arithmetical operations on these fuzzy sets via the a-cut representation. At each a-cut, these operations are the standard arithmetical operations on closed intervals ... 

Fuzzy logic deals with propositions expressed in natural language. The linguistic expressions involved may contain fuzzy linguistic terms of any of the following types ... 

Thoughts are loaded onto the linguistic expressions, which aid to translate thoughts into words for refined understanding ... 

Engineers must perform their productivity by simple and fast ideas in addition to economical solutions not only in the materialistic sense but also in the thinking domain. Productive knowledge and inventions can be shared by other individuals through linguistic expressions rather than equations or formulations, and hence, language is the initial means for such explanations. 

The fuzzy logic can express all the subjectivity in human thinking and natural linguistic expressions in a comparatively undistorted manner. The foUowing points lead to the necessity of fuzzy logic concepts use in the modeling. 

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