Minimal achiral superset

A fuzzy set C is a minimal achiral superset of a fuzzy set A if fuzzy set C is achiral, AzC, and if no achiral fuzzy set C" exists such that C" cC, C C", and A [Pg.161]

For more general objects, several chirality measures have been proposed based on the concepts of maximal achiral subsets and minimum achiral supersets [240]. A maximal achiral subset of an object is a subset that cannot be increased within the object without becoming chiral, and a minimal achiral superset of an object cannot be decreased while containing the object and staying achiral. Note that for some objects neither the maximal achiral subset nor the minimal achiral superset is necessarily unique, and their collection gives a fairly detailed chirality characterization [240], for example, by measuring the deviation of their volumes from that of the original object and from one another. 

Fuzzy set C is a minimal mass achiral superset of fuzzy set A if the... 

If fuzzy set A is achiral, then both the minimal achiral fuzzy superset B and the minimal mass achiral fuzzy superset C are unique and B = C=A. 

Here fuzzy set is a maximal achiral subset, fuzzy set 5 is a maximal mass achiral subset, fuzzy set C is a minimal achiral fuzzy superset, and fuzzy set C is a minimal mass achiral superset of fuzzy set A. 

If M(x, Mr, Not, and Nr are maximal volume achiral subset, maximal volume R-subset, minimal volume achiral superset, and minimal volume R-superset of a set T, respectively, then... 

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