×

Symmetry vs. asymmetry. (English) Zbl 1212.26070

Summary: Symmetry, jointly with its “opposite”, antisymmetry, may be considered as two sides of the same coin: total symmetry, or total asymmetry, relative to a pattern object, without intermediate situations. But this dychotomical classification suffer a lack of necessary and realistic grades. For this reason, it is convenient to introduce “shade regions” modulating the degrees (a fuzzy concept). So, we analyze here the asymmetry problem, with its different approaches of description (from physics, by techniques as group theory), searching for an efficient algorithm, by the introduction of asymmetry/symmetry level functions.

MSC:

26E50 Fuzzy real analysis
28E10 Fuzzy measure theory
68T30 Knowledge representation
68T01 General topics in artificial intelligence
PDFBibTeX XMLCite
Full Text: EuDML