(ε,δ)-Characteristic Fuzzy Sets Approach to the Ideal Theory of BCK/BCI-Algebras

Authors

  • G. Muhiuddin Department of Mathematics, University of Tabuk, Tabuk 71491
  • Shuaa Aldhafeeri Department of Mathematics, College of Basic Education, Public Authority for Applied Education and Training
  • K. P. Shum Institute of Mathematics, Yunnan University, Kunming 650091

DOI:

https://doi.org/10.26713/jims.v10i4.1130

Keywords:

(ε,δ)-characteristic fuzzy set, (Fuzzy) ideal, (α,β)-fuzzy ideal

Abstract

The notion of (ε,δ)-characteristic fuzzy sets is introduced. Given an ideal F of a BCK/BCI-algebra X, conditions for the (ε,δ)-characteristic fuzzy set in X  to be an (∈,∈∨q)-fuzzy ideal, an (∈,q)-fuzzy ideal, an (∈,∈∧q)-fuzzy ideal, a (q,q)-fuzzy ideal, a (q,∈)-fuzzy ideal, a (q,∈∨q)-fuzzy ideal and a (q,∈∧q)-fuzzy ideal are provided. Using the notions of (α,β)-fuzzy ideal μF(ε,δ), conditions for the F to be an ideal of X are investigated where (α,β) is one of (∈,∈∨q), (∈,∈∧q), (∈,q), (q,∈∨q), (q,∈∧q), (q,∈) and (q,q).

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References

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Published

2018-12-31
CITATION

How to Cite

Muhiuddin, G., Aldhafeeri, S., & Shum, K. P. (2018). (ε,δ)-Characteristic Fuzzy Sets Approach to the Ideal Theory of BCK/BCI-Algebras. Journal of Informatics and Mathematical Sciences, 10(4), 573–581. https://doi.org/10.26713/jims.v10i4.1130

Issue

Vol. 10 No. 4 (2018)

Section

Research Article

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