Abstract
Abstract In this paper, we apply the concept of fuzzy sets to Novikov algebras, and introduce the concepts of L-fuzzy ideals and L-fuzzy subalgebras. We get a sufficient and neccessary condition such that an L-fuzzy subspace is an L-fuzzy ideal. Moreover, we show that the quotient algebra A/μ of the L-fuzzy ideal μ is isomorphic to the algebra A/Aμ of the non-fuzzy ideal Aμ. Finally, we discuss the algebraic properties of surjective homomorphic image and preimage of an L-fuzzy ideal.
Highlights
In this paper, we apply the concept of fuzzy sets to Novikov algebras, and introduce the concepts of L-fuzzy ideals and L-fuzzy subalgebras
We show that the quotient algebra A/μ of the L-fuzzy ideal μ is isomorphic to the algebra A/Aμ of the non-fuzzy ideal Aμ
Since Rosenfeld [1] introduced fuzzy sets in the realm of the group theory, many researchers are engaged in extending the concepts and results of abstract algebra to the boarder framework of the fuzzy set
Summary
Since Rosenfeld [1] introduced fuzzy sets in the realm of the group theory, many researchers are engaged in extending the concepts and results of abstract algebra to the boarder framework of the fuzzy set. Abstract: In this paper, we apply the concept of fuzzy sets to Novikov algebras, and introduce the concepts of L-fuzzy ideals and L-fuzzy subalgebras. The concept of a fuzzy subspace is extended to a Novikov algebra. [3] Let V be a vecter space over a eld F, an L-fuzzy subset μ : V → L is an L-fuzzy subspace if and only if
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