Positive implicative ideals of BCK-algebras based on neutrosophic sets and falling shadows

Hashem Bordbar (Avtor), Xiao Long Xin (Avtor), Rajab Ali Borzooei (Avtor), Young Bae Jun (Avtor)

Povzetek

Neutrosophy is introduced by F. Smarandache in 1980 which studies the origin, nature, and scope of neutralities, as well as their interactions with different ideational spectra. Neutrosophy considers a proposition, theory, event, concept, or entity, ”A” in relation to its opposite, ”Anti-A” and that which is not A, ”Non-A”, and that which is neither ”A” nor ”Anti-A”, denoted by ”Neut-A”. Neutrosophy is the basis of neutrosophic logic, neutrosophic probability, neutrosophic set, and neutrosophic statistics. In this article, we apply the notion of neutrosophic set theory to (positive implicative) ideals in BCK-algebras by using the concept of falling shadows. The notions of a positive implicative (∈, ∈)-neutrosophic ideal and a positive implicative falling neutrosophic ideal are introduced, and several properties are investigated. Characterizations of a positive implicative (∈, ∈)-neutrosophic ideal are considered, and relations between a positive implicative (∈, ∈)-neutrosophic ideal and an (∈, ∈)-neutrosophic ideal are discussed. Conditions for an (∈, ∈)-neutrosophic ideal to be a positive implicative (∈, ∈)-neutrosophic ideal are provided, and relations between a positive implicative (∈, ∈)-neutrosophic ideal, a falling neutrosophic ideal and a positive implicative falling neutrosophic ideal are studied. Conditions for a falling neutrosophic ideal to be positive implicative are provided.

Ključne besede

neutrosophic random set;neutrosophic falling shadow;neutrosophic ideal;falling neutrosophic ideal;

Podatki

Jezik:	Angleški jezik
Leto izida:	2022
Tipologija:	1.01 - Izvirni znanstveni članek
Organizacija:	UNG - Univerza v Novi Gorici
UDK:	512
COBISS:	110636803
ISSN:	2331-6055
Št. ogledov:	691
Št. prenosov:	0
Ocena:	0 (0 glasov)
Metapodatki:

Ostali podatki

URN:	URN:SI:UNG
Strani:	str. 9-30
Zvezek:	ǂVol. ǂ48
Čas izdaje:	2022
DOI:	10.5281/zenodo.6041290
ID:	15553573