Intuitionistic Fuzzy Ideals With Thresholds(?,?) Of BCI-Algebras

In this diplomarbeit, we apply the theories of intuitionistic fuzzy sets to BCI-algebras and introduce the concepts of intuitionistic fuzzy subalgebra, intuitionistic fuzzy ideal, intuitionistic fuzzy implicative ideal, intuitionistic fuzzy positive implicative ideal, intuitionistic fuzzy commutative ideal and intuitionistic fuzzy p-ideal with thresholds (?,?) of BCI-algebras. Some characterizations and properties of intuitionistic fuzzy ideals with thresholds (?,?) are investigated. This diplomarbeit enriches and develops the theories of fuzzy BCI-algebras and fuzzy algebra system which have been existed. The results of this diplomarbeit are listed as follows:1. Introducing the concepts of intuitionistic fuzzy subalgebras, intuitionistic fuzzy ideals and intuitionistic fuzzy closed ideals with thresholds (?,?) of BCI-algebras; discussing the relations between intuitionistic fuzzy subalgebras, intuitionistic fuzzy ideals and intuitionistic fuzzy closed ideals with thresholds (?,?) of BCI-algebras; giving the necessary and sufficient conditions about that an intuitionistic fuzzy subset on BCI-algebra is an intuitionistic fuzzy ideal with thresholds (?,?) of BCI-algebras and proving that the intersection and direct product of intuitionistic fuzzy ideals with thresholds (?,?) of BCI-algebras is still an intuitionistic fuzzy ideal with thresholds (?,?) of it.2. Giving the definitions of intuitionistic fuzzy implicative ideals, intuitionistic fuzzy positive implicative ideals, intuitionistic fuzzy commutative ideals and intuitionistic fuzzy p-ideals with thresholds (?,?) of BCI-algebras and discussing some properties of them. We discuss the relations among various intuitionistic fuzzy ideals and show that an intuitionistic fuzzy ideal with thresholds (?,?) of BCI-algebras is an intuitionistic fuzzy implicative ideal with thresholds (?,?) of BCI-algebras if and only if it is both an intuitionistic fuzzy positive implicative ideal and an intuitionistic fuzzy commutative ideal with thresholds (?,?) of BCI-algebras.