Fuzzy Derivations BCC-Ideals on BCC-Algebras

Abstract

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 BCCideals 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.

Neutrosophic Q-Ideals of Neutrosophic Q-Algebra

“…Definition 2.10. [13] An intuitionistic fuzzy set Y={(c,T Y (c),F Y (c)): c∈W} over a Q-algebra W is called the intuitionistic fuzzy Q-ideal if it satisfies the following inequalities:…”

“…[11] presented some new types of ideals in Q-algebra. [12] grounded the idea of fuzzy Q-ideals in Q-algebras. [13] also introduced the notion of intuitionistic fuzzy Q-ideals of Q-algebra.…”

“…[12] grounded the idea of fuzzy Q-ideals in Q-algebras. [13] also introduced the notion of intuitionistic fuzzy Q-ideals of Q-algebra. In 2005, [14] presented the neutrosophic set as an extension of IFS.…”

Quotient TM-algebras

“…Megalai and Tamilarasi [4] introduced the notion of TM-algebras, which is a generalization of BCH /BCI/BCK/Q-algebras. In [7], Mostafa et al introduced the notion of fuzzy TM-ideals in TM-algebras, and investigate related properties. In this paper, we establish construct the quotient MT-algebras via an ideal, and we have the fundamental theorem of homomorphism for TMalgebras as a consequence.…”