Abstract
In this paper we introduce the notion of obstinate filter in BL-algebra A and we state and prove some theorems which determine the relationship between this notion and other types of filters of a BL-algebra and by some examples we show that this notion is different. Also, we prove that if F is an obstinate filter, then F is a Boolean filter hence A/F is a Boolean algebra. Finally, we construct some algorithms for studying the structure of the finite BL-algebras and filters in finite BL-algebras.