p-ideals of BCI-algebras based on neutrosophic N-structures

Article type: Research Article

Authors: Muhiuddin, G.^{; *}

Affiliations: Department of Mathematics, University of Tabuk, Tabuk, Saudi Arabia

Correspondence: [*] Corresponding author. G. Muhiuddin, Department of Mathematics, University of Tabuk, Tabuk 71491, Saudi Arabia. E-mail: chishtygm@gmail.com.

Abstract: In this paper, neutrosophic N -structures are applied to p-ideals of BCI-algebras. In fact, we introduce the notion of neutrosophic N -p-ideal in BCI-algebras, and investigate several properties. Further, we present characterizations of neutrosophic N -p-ideal. Moreover, we consider relations between a neutrosophic N -ideal and a neutrosophic N -p-ideal. Also, we provide conditions for a neutrosophic N -ideal to be a neutrosophic N -p-ideal. Furthermore, it is proved that the neutrosophic N -structure QNG over Q is a neutrosophic Np -ideal of Q ⇔ G is a p-ideal of Q where G is a non-empty subset of a BCI-algebras Q.

Keywords: BCI-algebra, p-ideal, neutrosophic set, neutrosophic 𝒩-ideal, neutrosophic 𝒩_p-ideal

DOI: 10.3233/JIFS-201309

Journal: Journal of Intelligent & Fuzzy Systems, vol. 40, no. 1, pp. 1097-1105, 2021