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REGULARITY OF GENERALIZED DERIVATIONS IN BCI-ALGEBRAS
Muhiuddin, G. Korean Mathematical Society 2016 대한수학회논문집 Vol.31 No.2
In this paper we study the regularity of inside (or outside) (${\theta},{\phi}$)-derivations in BCI-algebras X and prove that let $d_{({\theta},{\phi})}:X{\rightarrow}X$ be an inside (${\theta},{\phi}$)-derivation of X. If there exists a ${\alpha}{\in}X$ such that $d_{({\theta},{\phi})}(x){\ast}{\theta}(a)=0$, then $d_{({\theta},{\phi})}$ is regular for all $x{\in}X$. It is also shown that if X is a BCK-algebra, then every inside (or outside) (${\theta},{\phi}$)-derivation of X is regular. Furthermore the concepts of ${\theta}$-ideal, ${\phi}$-ideal and invariant inside (or outside) (${\theta},{\phi}$)-derivations of X are introduced and their related properties are investigated. Finally we obtain the following result: If $d_{({\theta},{\phi})}:X{\rightarrow}X$ is an outside (${\theta},{\phi}$)-derivation of X, then $d_{({\theta},{\phi})}$ is regular if and only if every ${\theta}$-ideal of X is $d_{({\theta},{\phi})}$-invariant.
Some operations of anti-intuitionistic L-fuzzy soft b-ideals of BG-algebras
G. Muhiuddin,Mohamed E. A. Elnair,M. Balamurugan 원광대학교 기초자연과학연구소 2020 ANNALS OF FUZZY MATHEMATICS AND INFORMATICS Vol.20 No.2
In the present paper, the notion of anti-intuitionistic $L$-fuzzy soft set is applied to the $b$-ideals of $BG$-algebras. In fact, the notions of anti-intuitionistic $L$-fuzzy soft $b$-ideals of $BG$-algebras are introduced and their related properties are studied. Furthermore, some operations of anti-intuitionistic $L$-fuzzy soft $b$-ideals of $BG$-algebras are investigated. Finally, the products of anti-intuitionistic $L$-fuzzy soft $b$-ideals are discussed.
IVI-octahedron ideals and bi-ideals in semigroups
한상현,G. Muhiuddin,허걸,백종일 원광대학교 기초자연과학연구소 2022 ANNALS OF FUZZY MATHEMATICS AND INFORMATICS Vol.23 No.3
In this paper, we introduce the notions of IVI-octahedron ideals and bi-ideals, and obtain some of their properties. Also, we define an IVI-octahedron duo semigroup and give a characterization of a duo semigroup by it, and study some of its properties. Furthermore, we discuss some characterizations of a regular semigroup and a left [resp. right] regular semigroup by IVI-octahedron ideals and bi-ideals.
A novel generalization of fuzzy subsemigroups
전영배,Mehmet Ali Ozturk,G. Muhiuddin 원광대학교 기초자연과학연구소 2017 ANNALS OF FUZZY MATHEMATICS AND INFORMATICS Vol.14 No.4
The notion of $(\widetilde{\alpha},$ $\widetilde{\beta})$-fuzzy subsemigroups in semigroups is introduced, and related properties are investigated. Characterizations of $(\in,$ $\in\! \vee \, q^{\delta}_0)$-fuzzy subsemigroups are provided. Using a collection of subsemigroups with some conditions, an $(\in,$ $\in\! \vee \, q^{\delta}_0)$-fuzzy subsemigroup is constructed. An $(\in,$ $\in\! \vee \, q^{\delta}_0)$-fuzzy subsemigroup generated by the given fuzzy set with finite images is established.