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A Fuzzy Generating Set of 2D-Space Groups

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Abstract

Minimal generating sets for 17 2D-space (plane) groups have been derived. The concept of fuzzy generating set of a group is introduced. The considered groups are compared with respect to the degree of fuzziness of their generating sets.

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REFERENCES

  1. P. M. Zorky, J. Mol. Struct. 374, 9 (1996).

    ADS  Google Scholar 

  2. A. M. Banaru, Moscow Univ. Chem. Bull. 64, 80 (2009).

    Article  Google Scholar 

  3. H. S. M. Coxeter and W. O. J. Moser, Generators and Relations for Discrete Groups (Springer, New York, 1980).

    Book  MATH  Google Scholar 

  4. E. Lord, Generators and Relations for Space Groups (Bangalore, 2010).

    Google Scholar 

  5. E. A. Lord and A. M. Banaru, Moscow Univ. Chem. Bull. 67, 50 (2012).

    Article  Google Scholar 

  6. International Tables for Crystallography, Vol. A: Space-Group Symmetry (Springer, 2005).

  7. L. A. Zadeh, Inf. Control 8, 338 (1965).

    Article  Google Scholar 

  8. A. Rosenfeld, J. Math. Anal. Appl. 35, 512 (1971).

    Article  MathSciNet  Google Scholar 

  9. A. P. Ryzhov, Elements of the Theory of Fuzzy Sets and Its Applications (Dialog–MGU, Moscow, 1998) [in Russian].

    Google Scholar 

  10. A. de Luca and S. Termini, Inf. Control 20, 301 (1972).

    Article  Google Scholar 

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Correspondence to A. M. Banaru.

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Translated by Yu. Sin’kov

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Banaru, A.M. A Fuzzy Generating Set of 2D-Space Groups. Crystallogr. Rep. 63, 1071–1076 (2018). https://doi.org/10.1134/S1063774518070040

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  • DOI: https://doi.org/10.1134/S1063774518070040

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