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A study of entropy/clarity of genetic sequences using metric spaces and fuzzy sets. (English) Zbl 1410.92084
Summary: The study of genetic sequences is of great importance in biology and medicine. Sequence analysis and taxonomy are two major fields of application of bioinformatics. In the present paper we extend the notion of entropy and clarity to the use of different metrics and apply them in the case of the fuzzy polynuclotide space (FPS). Applications of these notions on selected polynucleotides and complete genomes both in the $$I^{12\times k}$$ space, but also using their representation in FPS are presented. Our results show that the values of fuzzy entropy/clarity are indicative of the degree of complexity necessary for the description of the polynucleotides in the FPS, although in the latter case the interpretation is slightly different than in the case of the $$I^{12\times k}$$ hypercube. Fuzzy entropy/clarity along with the use of appropriate metrics can contribute to sequence analysis and taxonomy.

##### MSC:
 92D20 Protein sequences, DNA sequences 03E72 Theory of fuzzy sets, etc.
##### Keywords:
polynucleotides; fuzzy sets; metric spaces; entropy; clarity
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