Gaussian Fuzzy Number for STR-DNA Similarity Calculation Involving Familial and Tribal Relationships

Abstract

We performed locus similarity calculation by measuring fuzzy intersection between individual locus and reference locus and then performed CODIS STR-DNA similarity calculation. The fuzzy intersection calculation enables a more robust CODIS STR-DNA similarity calculation due to imprecision caused by noise produced by PCR machine. We also proposed shifted convoluted Gaussian fuzzy number (SCGFN) and Gaussian fuzzy number (GFN) to represent each locus value as improvement of triangular fuzzy number (TFN) as used in previous research. Compared to triangular fuzzy number (TFN), GFN is more realistic to represent uncertainty of locus information because the distribution is assumed to be Gaussian. Then, the original Gaussian fuzzy number (GFN) is convoluted with distribution of certain ethnic locus information to produce the new SCGFN which more represents ethnic information compared to original GFN. Experiments were done for the following cases: people with family relationships, people of the same tribe, and certain tribal populations. The statistical test with analysis of variance (ANOVA) shows the difference in similarity between SCGFN, GFN, and TFN with a significant level of 95%. The Tukey method in ANOVA shows that SCGFN yields a higher similarity which means being better than the GFN and TFN methods. The proposed method enables CODIS STR-DNA similarity calculation which is more robust to noise and performed better CODIS similarity calculation involving familial and tribal relationships.