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Title:Positive implicative ideals of BCK-algebras based on neutrosophic sets and falling shadows
Authors:Bordbar, Hashem (Author)
Long Xin, Xiao (Author)
Borzooei, Rajab Ali (Author)
Jun, Young Bae (Author)
Files:This document has no files. This document may have a phisical copy in the library of the organization, check the status via COBISS. Link is opened in a new window
Work type:Unknown ()
Tipology:1.01 - Original Scientific Article
Organization:UNG - University of Nova Gorica
Abstract: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.
Keywords:neutrosophic random set, neutrosophic falling shadow, neutrosophic ideal, (positive implicative) falling neutrosophic ideal
Year of publishing:2022
Number of pages:str. 9-30
Numbering:Vol. 48, 1
COBISS_ID:110636803 Link is opened in a new window
ISSN on article:2331-6055
DOI:10.5281/zenodo.6041290 Link is opened in a new window
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Title:Neutrosophic sets and systems
Shortened title:Neutrosophic sets syst.
Publisher:Department of Mathematics and Science, University of New Mexico
COBISS.SI-ID:526970905 New window