Intuitionistic Fuzzy Set Theory Applied to BCK - algebras
Lamyaa Bakor Badhurays · 2016
The subject of this thesis depends on intuitionistic fuzzy BCK - algebras. In the first chapter we recalled some elementary basic definitions and results on intuitionistic fuzzy sets. The second chapter is devoted to study the concept of BCK- algebras and we investigated the fuzzification of BCK-algebras and discussed some of its properties. In the third chapter we studied the intuitionistic fuzzy ideals of BCK-algebras, and we introduced the notion of intuitionistic fuzzy BCK-submodules and investigated further related properties. We introduced the notion of intuitionistic (T,S) -fuzzy BCK- submodules by using triangular norms. Also, we presented some basic results on intuitionistic fuzzy BCK-submodules with respect to triangular norms and we have investigated various properties. The concept of interval-valued intuitionistic fuzzy BCK-submodules and (∈,∈⋁q)-interval-valued intuitionistic fuzzy BCK-submodules of BCK-algebra were presented and some of their properties were investigated. These concepts and results were submitted as an articles to scientific journals, and we obtained an acceptance to publish one of these articles.