The fuzzy polynucleotide space revisited

A theory of fuzzy polynucleotides, including an n-dimensional metric fuzzy polynucleotide space, has been previously introduced by the present author for fuzzy-theoretical analysis of nucleic acids [Sadegh-Zadeh K. Fuzzy genomes. Artif Intell Med 2000;18:1-28; Sadegh-Zadeh K. Ein Verfahren zur Fuzzydecodierung und Fuzzydechiffrierung von Informationen. Offenlegungsschrift DE 199 36 925 A 1. Deutsches Patent- und Markenamt; 2001]. The conceptual framework of that theory has been used by Nieto et al. [Nieto JJ, Torres A, Vázquez-Trasande MM. A metric space to study differences between polynucleotides. Appl Math Lett 2003;16:1289-94; Nieto JJ, Torres A, Georgiou DN, Karakasidis TE. Fuzzy polynucleotide spaces and metrics. Bull Math Biol 2006;68:703-25] and Torres et al. [Torres A, Nieto JJ. The fuzzy polynucleotide space: basic properties. Bioinformatics 2003;19:587-92; Torres A, Nieto JJ. Fuzzy logic in medicine and bioinformatics. J Biomed Biotechnol 2006;1-7 [Article ID 91908]] to create a completely different, 12-dimensional metric space which they have also called 'the fuzzy polynucleotide space'. In the present paper both spaces are compared.

Both metric spaces are briefly outlined. Similarity and dissimilarity relationships between polynucleotide strings are measured in both spaces to compare their performance.

Nieto et al.'s and Torres et al.'s metric space measures the relationships between polynucleotide chains incorrectly. Structurally highly different polynucleotide sequences are misclassified as highly similar ones, and completely different sequences are misclassified as identical ones. For this reason their construct is to be considered as a device of misdiagnosis that bears "fuzzy polynucleotide space" as a misnomer.