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Samy M. Mostafa,Ola W. Abd El-Baseer,D. L. Shi,Amany M. Menshawy,Kul Hur 원광대학교 기초자연과학연구소 2024 ANNALS OF FUZZY MATHEMATICS AND INFORMATICS Vol.27 No.2
A picture fuzzy set is one of the generalizations of Atanassove's (IFSs) fuzzy set. Under this environment, in this manuscript, we familiarize a new type of extensions of fuzzy sets called cubic root fuzzy sets (briefly, $\sqrt[3]{\cdot}$-Fuzzy sets) and Fermatean fuzzy sets to contrast $(3,3,\sqrt[3]{\cdot})$-picture sets. We introduce the notion of $(3,3,\sqrt[3]{\cdot})$-picture fuzzy $BCC$-ideals of $BCC$-algebras. After then, we study the homomorphic image and inverse image of $(3,3,\sqrt[3]{\cdot})$-picture fuzzy $BCC$-ideals under homomorphism of $BCC$-algebras. Moreover, the Cartesian product of $(3,3,\sqrt[3]{\cdot})$-picture fuzzy $BCC$-ideals of $BCC$-algebras is given. Finally, we introduce the concept of correlation for $(3,3,\sqrt[3]{\cdot})$-picture fuzzy sets, which is a new extension of the correlation of Atanassove's IFSs and investigated several properties.
Ola W. Abd El-Baseer,Jeong Gon Lee,Young Bae Jun,Amany M. Menshawy,Kul Hur,Samy M. Mostafa 원광대학교 기초자연과학연구소 2023 ANNALS OF FUZZY MATHEMATICS AND INFORMATICS Vol.25 No.1
In this paper, the concepts of cubic Pythagorean $KU$-ideals are introduced and several properties are investigated. Also, relations between cubic Pythagorean $KU$-ideals and cubic Pythagorean ideals are given. The pre-image of cubic Pythagorean $KU$-ideals under homomorphism of $KU$-algebras are defined and how the pre-image of cubic Pythagorean $KU$-ideals under homomorphism of $KU$-algebras become cubic Pythagorean $KU$-ideal are studied. Moreover, the Cartesian product of cubic Pythagorean $KU$-ideals in Cartesian product $KU$-algebras is given. Finally, novel new correlation coefficient between two cubic Pythagorean fuzzy sets are also studied.