# On intuitionistic fuzzy INK-ideals of INK-algebras

VIT University

^{1}01 Nov 2017-Vol. 263, Iss: 4, pp 042142

About: The article was published on 2017-11-01 and is currently open access. It has received None citations till now.

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TL;DR: Various properties are proved, which are connected to the operations and relations over sets, and with modal and topological operators, defined over the set of IFS's.

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TL;DR: The notion of quadratic Q-algebra was introduced in this article, which is a generalization of the idea of BCH/BCI/BCK algebras.

Abstract: We introduce a new notion, called a Q-algebra, which is a generalization of the idea of BCH /BCI /BCK -algebras and we generalize some theorems discussed in BCI - algebras. Moreover, we introduce the notion of "quadratic" Q-algebra, and show that every quadratic Q-algebra (X; ∗ ,e) , e ∈ X, has a product of the form x ∗ y = x − y + e, where x, y ∈ X when X is a field with |X |≥ 3. 2000 Mathematics Subject Classification. 06F35, 03G25.

60 citations

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TL;DR: In this paper, the concept of fuzzy left (right) derivations BCC-ideals in BCC-algebras is introduced and then investigated their basic properties, and the authors studied how the image and the pre-image of fuzzy-left-right derivations under homomorphism became fuzzy-right-ideal.

Abstract: In the theory of rings, the properties of derivations are important. In [15], Jun and Xin applied the notion of derivations in ring and near-ring theory to BCI-algebras, and they also introduced a new concept called a regular derivation in BCI-algebras. They investigated some properties of its .In this manuscript, the concept of fuzzy left (right) derivations BCC-ideals in BCC-algebras is introduced and then investigate their basic properties. In connection with the notion of homomorphism, the authors study how the image and the pre-image of fuzzy left (right) derivations BCC-ideals under homomorphism of BCC-algebras become fuzzy left (right) derivations BCC-ideals. Furthermore, the Cartesian product of fuzzy left (right) derivations BCC-ideals in Cartesian product of BCC-algebras is introduced and investigated some related properties.

2 citations