Fuzzy Aspects Associated with Biological Inheritance

Genetics explores the mechanisms of heredity and trait variation across organisms, with foundational principles established by Gregor Mendel through experiments on monohybrid and dihybrid crosses. The mathematical framework of hypergroups can effectively describe these classical genetic models. This study examines the interaction between genetic hybridization models and fuzzy set theory. It focuses on the fuzzy function that relates to phenotype classes made from simple dominance in dihybrid, trihybrid, and polyhybrid crosses. The methods use fuzzy logic to model phenotype distributions. The results show a clear link between the structure of the fuzzy function and the number of distinct phenotype classes in each hybridization case. This article presents a general form for the fuzzy function, and it always follows the same order relation. The number of phenotypes in each class determines this relation. Therefore, each class is associated with a string that serves as a row in the matrix describing the respective hybridization. Studies have shown that the eigenvalues of this matrix coincide with its elements.