A new phylogenetic tree model for fuzzy characters

Perfect phylogeny is one of the most popular character-based models. This model assumes the states of the characters are discrete. Although it provides a simple abstraction of characters, valuable information could be lost during the discretization of the experimental data. Indeed, fuzzy boundaries between species and degrees of character development are commonly found in nature. Therefore, we proposed the fuzzy perfect phylogeny model that extends the perfect phylogeny model to allow for a fuzzy membership of the characters. The properties of this model, such as uniqueness and backward compatibility, were then shown. We also showed how the fuzzy perfect phylogeny problem can be transformed to the perfect phylogeny problem in O(mv) time where m is the number of objects and v is the number of distinct value of characters. As a result, valuable information from the experimental data can be used without substantially increasing the problem complex.