In fuzzy set theory, there are many types of fuzzy sets extensions, such as intuitionistic fuzzy sets, interval valued fuzzy sets, ambiguous sets, etc. We apply the notion of a bipolar fuzzy n-fold KU-ideal of KU-algebras in this chapter. We introduce the notion of a KU-ideal bipolar fuzzy n-fold and investigate some properties. Bipolar-valued fuzzy sets are an extension of fuzzy sets whose range of membership degrees is extended between [0 , 1] and [-1, 1]. We also have connections between a KU-ideal bipolar fuzzy n-fold and a KU-ideal n-fold. The bipolar fuzzy n-fold KU-ideals image and inverse image in KU-algebras are defined and how the bipolar fuzzy n-fold KU-ideals image and inverse image in KU-algebras are studied to become bipolar fuzzy n-fold KU-ideals. In addition, the Cartesian product of bipolar fuzzy n-fold KU-ideals is included in the Cartesian product of KU-algebras.
Samy M. Mostafa
Department of Mathematics, Faculty of Education, Ain Shams University, Roxy, Cairo, Egypt.
Fatema F. Kareem
Department of Mathematics, Ibn-Al-Haitham College of Education, University of Baghdad, Iraq.
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