On the equivalence of sequences dependent on fuzzy ideals in the BCI-algebra

Document Type : Original Article

Authors

1 Department of mathematics, Payame Noor University, P.O. Box 19395-4697, Tehran, Iran

2 Department Mathematics, Payame Noor University, Tehran, Iran.

3 Department of Mathematics, Technical and Vocational University(TVU), Yazd, Iran

4 Department of Mathematics, Ashtian Branch, Islamic Azad University, Iran

Abstract

Murali and Makamba (2001) introduced an equivalence of fuzzy subgroups. Dudek and Jun (2004) studied the equivalence defined by Murali and Makamba in fuzzy ideals of a BCI-algebra. In this paper, we obtained a sequence of fuzzy ideals of a BCI-algebra X from a fuzzy ideal on X. We will show that, if two fuzzy ideals are equivalent, then the sequence of fuzzy ideals obtained from them are equivalent. We show that there is a relationship between a fuzzy ideal with BCI-algebra X and a fuzzy ideal with adjoint BCI-algebra A, where A is an Abelian subgroup of Autµ(X).

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