Fuzzy sets chirality measure

IV. FUZZY SYMMETRY DEFICIENCY MEASURES, FUZZY CHIRALITY MEASURES, AND FUZZY SYMMETRY GROUPS BASED ON THE MASS OF FUZZY SETS AND FUZZY HAUSDORFF-TYPE METRICS... [Pg.155]

Chirality, an important shape property of molecules, can be regarded as the lack of certain symmetry elements. Chirality measures are in fact measures of symmetry deficiency. These principles, originally used for crisp sets, also apply for fuzzy sets. Considering the case of three-dimensional chirality, the lacking point symmetry elements are reflection planes a and rotation-reflections 82 of even indices. Whereas the lacking symmetry elements can be of different nature in different dimensions, nevertheless, all the concepts, definitions, and procedures discussed in this section have straightforward generalizations for any finite dimension n. [Pg.161]

The fuzzy Hausdorff-type similarity measures can also be used for a direct comparison of a fuzzy set A and various extremal achiral fuzzy sets associated with it, providing alternative fuzzy chirality measures. [Pg.163]

Fuzzy chirality measures can also be defined in terms of a maximal achiral subset B, maximal mass achiral subset B, minimal achiral subset C, and minimal mass achiral subset C, of fuzzy set A, discussed in Section IV. If fuzzy set D denotes any one of these fuzzy sets, D e B, B ,C,C , then a fuzzy chirality measure A ts.o ) of fuzzy set A is provided by... [Pg.181]

Using the center of mass concept of fuzzy sets, the symmetry deficiency measure of finite continua, described in Section VIII, can be generalized for fuzzy sets. The chirality and more general symmetry deficiencies of fuzzy sets can be treated within a unified framework using the fuzzy metric FSNDSM diJ A,B). [Pg.184]

Molecular Similarity Measures and Chirality Measures Based on Resolution and Fuzzy Set Theory... [Pg.137]

THE FUZZY SETS APPROACH TO THE MEASUREMENT OF SYMMETRY AND CHIRALITY... [Pg.2897]

The external fuzzy chirality measure of a fuzzy set A is defined as xciA)=- I — m(A)/m(C) where C is a minimal mass achiral superset of fuzzy set A. [Pg.2899]

Fuzzy Measures of Molecular Shape and Size 197 (2) Any -chiral point set... [Pg.197]

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