Linguistic variables

A phrase such as "seriously contaminate" is known as a linguistic variable it gives an indication of the magnitude of a parameter, but does not provide its exact value. Subjective knowledge is expressed by statements that contain vague terms, qualifications, probabilities, or judgmental data. Objects described by these vague statements are more difficult to fit into crisp sets. 

The relationships described form the concept (Fig. 5.68) of the FUZZY RULE SET. The membership-functions of the linguistic variables are derived from the experiments that have already been mentioned however, the plausibilities of the RULE SET have not been touched on so far. 

In general, a fuzzy system is any system whose variables (or, at least, some of them) range over states that are fuzzy numbers rather than real numbers. These fuzzy numbers may represent linguistic terms such as very small, medium, and so on, as interpreted in a particular context. If they do, the variables are called linguistic variables. 

One of the most important tools in applications of fuzzy set theory is the concept of linguistic variables (LV). These are groups of fuzzy sets with (partially) overlapping membership functions over a common (crisp) basic variable x. To represent several classes within an LV, the membership functions should cover all the relevant definition space of the basic variable x. The overlaps of these functions define the fuzziness. A linguistic variable L, classified by n fuzzy sets Aj, can be defined as... 

Fuzzification of crisp basic variables into linguistic variables (LVs)... 

B. Segmentation of Molecular Surfaces with Linguistic Variables... 

The segmentation of molecular surfaces can be carried out on the basis of different surface qualities.Here we shall focus on a segmentation with respect to topographical criteria. The shape analysis is based on the surface topography index (STI) described previously. Following Heiden and Brickmann, a six class linguistic variable... 

FIGURE 3 Membership functions for linguistic variables describing molecular shape. 

It has been demonstrated that an automatic segmentation of molecular surfaces into distinct domains can be performed with a dissimilarity measure for linguistic variables which have the form... 

In such rules, X and Y and Z are linguistic variables whose values, e.g., small, medium, and large, are words rather than numbers. In effect, the values of linguistic variables are labels for fuzzy sets. It is understood that the membership functions of these sets must be specified in context. Usually, the membership functions are assumed to be triangular or trapezoidal. 

The problem of interpolation may be described as follows. Assume that we have a collection of fuzzy if-then rules that express the dependency of the linguistic variable Y on the linguistic variables X, ...,X , with the ith rule having the form if Aj is A j and is A, , then Y is... 

Brickmann, J. (1997). Linguistic Variables in the Molecular Recognition Problem. In Fuzzy Logic in Chemistry (Rouvray, D.H., ed.). Academic Press, New York (NY), pp. 225-247. 

Linguistic Variables Verbal fuzzy expressions are described by fuzzy theory by means of linguistic variables for example, the solubility of a substance in water can be characterized by the fuzzy terms high and low. If the linguistic variables are further to be distinguished, the so-called modifiers are applied. 

Figure 8 0 Membership functions for the linguistic variable high" according to Eq. (8.40) together with different modifiers.

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