Primitive Fuzzy Concept

Just as hot, young, rich, tall, and hirsute may be expressed by compatibility functions fxCC), /i,(years), /i( ), /x(cm), and ju.(no. of hairs), so the fuzzy chiral may be expressed on the scalar of a numerically valued variable that quantitatively expresses some manifestation of chirality, e.g., optical rotation, chemical shift difference, or rate constant, with the appropriate domain understood. It is therefore permissible to speak of degrees of chirality and to compare molecules or molecular ensembles by 

The ranking of chiral systems such as the foregoing by their structures and associated properties is intuitively obvious, and is arrived at independently of any theory that accounts for these properties. For this reason we are led to the conclusion that chirality in a real system is a primitive fuzzy concept.  

To conclude it is natural to abandon two-valued logic in science because, when one deals with the phenomena of nature, one enters a stage in logic in which we recognize the utility of imprecision . The vagueness of chiral and achiral, when used with reference to a chemical system, should therefore be regarded as a virtue rather than as a defect. 

We saw that it is natural to attach a quantitative meaning to the chirality of molecular structures and that it is possible to rank the chirality of closely related structures. There is no reason not to apply measures of chirality as welt to geometrical objects, including geometrical models of 

We have seen that different chirality measures give incommensurable values for the shape and the relative degree of chirality of a given object. In short, there is no such thing as a unique scale by which chirality can be measured. If a choice among the numerous chirality measures that have been discussed in the literature is to have any relevance to the world of observables, it must be predicated on the measure s ability to correlate the calculated degree of chirality with some experimentally determined chirality property. That is, the measure must successfully model some pseudoscalar physical or chemical property. As will be discussed subsequently, this goal may prove to be elusive. 

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