\((\varepsilon,\delta)\)-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:

\((\varepsilon, \delta)\)-characteristic fuzzy set, (Fuzzy) ideal, \((\alpha, \beta)\)-fuzzy ideal

Abstract

The notion of \((\varepsilon,\delta)\)-characteristic fuzzy sets is introduced. Given an ideal \(F\) of a \(BCK/BCI\)-algebra \(X\), conditions for the \((\varepsilon,\delta)\)-characteristic fuzzy set in \(X\)  to be an \((\in, \in \! \vee \, {q})\)-fuzzy ideal, an \((\in, {q})\)-fuzzy ideal, an \((\in, \in \! \wedge \, {q})\)-fuzzy ideal, a \((q,q)\)-fuzzy ideal, a \((q, \in)\)-fuzzy ideal, a \((q, \in \! \vee \, {q})\)-fuzzy ideal and a \((q, \in \! \wedge \, {q})\)-fuzzy ideal are provided. Using the notions of \((\alpha, \beta)\)-fuzzy ideal \(\mu_F^{(\varepsilon,\delta)}\), conditions for the \(F\) to be an ideal of \(X\) are investigated where \((\alpha, \beta)\) is one of \((\in, \in \! \vee \, {q})\), \((\in, \in \! \wedge \, {q})\), \((\in,q)\), \((q,\in \! \vee\, {q})\), \((q,\in \! \wedge \,{q})\), \((q, \in)\) 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). \((\varepsilon,\delta)\)-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 Articles

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