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Some innovative types of fuzzy ideals in AG-groupoids

AG-groupoids (non-associative structure) are basic structures in Flocks theory. This theory mainly focuses on distance optimization, motion replication, and leadership maintenance with a wide range of applications in physics and biology. In this paper, we define some new types of fuzzy ideals of AG-...

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Main Authors: Khan, F. M., Khan, H. U., Mukhtar, S., Khan, A., Sarmin, N. H.
Format: Article
Published: Walter de Gruyter GmbH 2017
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QA Mathematics
Online Access:http://eprints.utm.my/id/eprint/77186/
https://www.scopus.com/inward/record.uri?eid=2-s2.0-85037633628&doi=10.1515%2fjisys-2017-0258&partnerID=40&md5=e657e6c5e73f171014b34e8832b230bf
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spelling my.utm.771862018-05-31T09:50:21Z http://eprints.utm.my/id/eprint/77186/ Some innovative types of fuzzy ideals in AG-groupoids Khan, F. M. Khan, H. U. Mukhtar, S. Khan, A. Sarmin, N. H. QA Mathematics AG-groupoids (non-associative structure) are basic structures in Flocks theory. This theory mainly focuses on distance optimization, motion replication, and leadership maintenance with a wide range of applications in physics and biology. In this paper, we define some new types of fuzzy ideals of AG-groupoids called (α, β)-fuzzy bi-ideals, (α, β)-fuzzy interior ideals, (β, α)-fuzzy bi-ideals, and (β, α)-fuzzy interior ideals, where α, β ϵ{ ϵγ, qσ, ϵγ ∨ qσ, ϵγ ∧ qσ} and α, β ϵ{ϵγ, qσ, ϵγ ∨ qσ, ϵγ ∧ qσ}, with α ≠ ϵγ ∧ qσ and β ≠ ϵγ ∧ qσ. An important milestone achieved by this paper is providing the connection between classical algebraic structures (ordinary bi-ideals, interior ideals) and new types of fuzzy algebraic structures [(ϵγ, ϵγ ∨ qσ)-fuzzy bi-ideals, (ϵγ, ϵγ ∨ qσ)-fuzzy interior ideals]. Special attention is given to (ϵγ, ϵγ ∨ qσ)-fuzzy bi-ideals and (ϵγ, ϵγ ∨ qσ ) -fuzzy bi-ideals. Walter de Gruyter GmbH 2017 Article PeerReviewed Khan, F. M. and Khan, H. U. and Mukhtar, S. and Khan, A. and Sarmin, N. H. (2017) Some innovative types of fuzzy ideals in AG-groupoids. Journal of Intelligent Systems . ISSN 0334-1860 (In Press) https://www.scopus.com/inward/record.uri?eid=2-s2.0-85037633628&doi=10.1515%2fjisys-2017-0258&partnerID=40&md5=e657e6c5e73f171014b34e8832b230bf DOI:10.1515/jisys-2017-0258
institution Universiti Teknologi Malaysia
building UTM Library
collection Institutional Repository
continent Asia
country Malaysia
content_provider Universiti Teknologi Malaysia
content_source UTM Institutional Repository
url_provider http://eprints.utm.my/
topic QA Mathematics
spellingShingle QA Mathematics
Khan, F. M.
Khan, H. U.
Mukhtar, S.
Khan, A.
Sarmin, N. H.
Some innovative types of fuzzy ideals in AG-groupoids
description AG-groupoids (non-associative structure) are basic structures in Flocks theory. This theory mainly focuses on distance optimization, motion replication, and leadership maintenance with a wide range of applications in physics and biology. In this paper, we define some new types of fuzzy ideals of AG-groupoids called (α, β)-fuzzy bi-ideals, (α, β)-fuzzy interior ideals, (β, α)-fuzzy bi-ideals, and (β, α)-fuzzy interior ideals, where α, β ϵ{ ϵγ, qσ, ϵγ ∨ qσ, ϵγ ∧ qσ} and α, β ϵ{ϵγ, qσ, ϵγ ∨ qσ, ϵγ ∧ qσ}, with α ≠ ϵγ ∧ qσ and β ≠ ϵγ ∧ qσ. An important milestone achieved by this paper is providing the connection between classical algebraic structures (ordinary bi-ideals, interior ideals) and new types of fuzzy algebraic structures [(ϵγ, ϵγ ∨ qσ)-fuzzy bi-ideals, (ϵγ, ϵγ ∨ qσ)-fuzzy interior ideals]. Special attention is given to (ϵγ, ϵγ ∨ qσ)-fuzzy bi-ideals and (ϵγ, ϵγ ∨ qσ ) -fuzzy bi-ideals.
format Article
author Khan, F. M.
Khan, H. U.
Mukhtar, S.
Khan, A.
Sarmin, N. H.
author_facet Khan, F. M.
Khan, H. U.
Mukhtar, S.
Khan, A.
Sarmin, N. H.
author_sort Khan, F. M.
title Some innovative types of fuzzy ideals in AG-groupoids
title_short Some innovative types of fuzzy ideals in AG-groupoids
title_full Some innovative types of fuzzy ideals in AG-groupoids
title_fullStr Some innovative types of fuzzy ideals in AG-groupoids
title_full_unstemmed Some innovative types of fuzzy ideals in AG-groupoids
title_sort some innovative types of fuzzy ideals in ag-groupoids
publisher Walter de Gruyter GmbH
publishDate 2017
url http://eprints.utm.my/id/eprint/77186/
https://www.scopus.com/inward/record.uri?eid=2-s2.0-85037633628&doi=10.1515%2fjisys-2017-0258&partnerID=40&md5=e657e6c5e73f171014b34e8832b230bf
_version_ 1643657522573213696
score 13.244404

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