Bulletin of Mathematical Biology (2006) 68: 703–725 DOI 10.1007/s11538-005-9020-5 ORIGINAL ARTICLE Fuzzy Polynucleotide Spaces and Metrics Juan J. Nieto a,∗ , A. Torres b , D.N. Georgiou c , T.E. Karakasidis d a Departamento de An ´ alisis Matem´ atico, Facultad de Matem ´ aticas, Universidad de Santiago de Compostela, 15782 Spain b Departamento de Psiquiatr´ ıa Radiolog´ ıa y Salud P ´ ublica, Facultad de Medicina, Universidad de Santiago de Compostela, 15782 Spain c Department of Mathematics, University of Patras, 265 00 Patras, Greece d Department of Civil Engineering, University of Thessaly, 383 34 Volos, Greece Received: 26 October 2004 / Accepted: 14 March 2005 / Published online: 7 April 2006 C  Society for Mathematical Biology 2006 Abstract The study of genetic sequences is of great importance in biology and medicine. Mathematics is playing an important role in the study of genetic se- quences and, generally, in bioinformatics. In this paper, we extend the work con- cerning the Fuzzy Polynuclotide Space (FPS) introduced in Torres, A., Nieto, J.J., 2003. The fuzzy polynuclotide Space: Basic properties. Bioinformatics 19(5); 587– 592 and Nieto, J.J., Torres, A., Vazquez-Trasande, M.M. 2003. A metric space to study differences between polynucleotides. Appl. Math. Lett. 27:1289–1294, by studying distances between nucleotides and some complete genomes using several metrics. We also present new results concerning the notions of similarity, differ- ence and equality between polynucleotides. The results are encouraging since they demonstrate how the notions of distance and similarity between polynucleotides in the FPS can be employed in the analysis of genetic material. Keywords DNA · RNA · Polynucleotides · Fuzzy sets · Metric spaces 1. Introduction Nucleic acids DNA and RNA are the genetic material of living organisms. There are two basic techniques used in the analysis of genetic material with applications in diagnosis and taxonomy: (a) sequence analysis which is used to determine the building blocks of a nucleic acid, i.e., its building blocks (nucleotides) and their order in the molecular chain, and ∗ Corresponding author. E-mail addresses: amnieto@usc.es (Juan J. Nieto), mrtorres@usc.es (A. Torres), georgiou@ math.upatras.gr (D.N. Georgious), e-mail: thkarak@uth.gr (T.E. Karakasidis).