TL-filters of IL-algebras

The aim of this study is to present some generalizations of the concept of fuzzy filter which is introduced by Islam, Sanyal, and Sen in IL-algebras and to investigate which of the results obtained about fuzzy filters are also provided in these generalizations. This study consists of two parts. In the first part, basic information about filters in BL-algebras is given. In the rest of the same section, some definitions and theorems about IL-algebras, filters of IL-algebras and fuzzy filters of IL-algebras are presented in order to provide a basis for the second part of the study. In the second part, the concepts of L-filter and TL-filter as two different generalizations of the concept of fuzzy filter in IL-algebras are introduced and some algebraic properties of them are investigated. Some theorems determining the relationship between these filters are proved.