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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.
Square root fuzzy sub-implicative ideals of $KU$-algebras
허걸,Ola W. Abd El-Baseer,Jong Il Baek,Samy M. Mostafa 원광대학교 기초자연과학연구소 2023 ANNALS OF FUZZY MATHEMATICS AND INFORMATICS Vol.26 No.2
In real life problems, square roots are used in finance (rates of return over 2 years), normal distributions (probability density functions), lengths and distances (Pythagorean Theorem), quadratic formula (height of falling objects), radius of circles, simple harmonic motion (pendulums and springs), and standard deviation. There are many reasons from which we inspire to explore further algebraic structure in a fuzzy setting. The following are the key reasons from which we have motivated: It is seen that the use of fuzzy sets is more convenient in real life problem than ordinary sets, and so it is important in the case of algebraic structures. As a result, an effort has been made to further examine square root structure in a fuzzy situation. In this paper, we consider the square root fuzzy sub-implicative (sub-commutative) ideals in $KU$-algebras, and investigate some related properties. We give conditions for a square root fuzzy of ideal to be a square root fuzzy sub-implicative (sub-commutative) ideal. We show that any square root fuzzy sub-implicative (sub-commutative) ideal is a square root fuzzy ideal, but the converse is not true. Using a level set of a fuzzy set in a $KU$-algebra, we give a characterization of a square root fuzzy sub-implicative (sub-commutative) ideal.
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.