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: | , , , , |
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| Format: | Article |
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Walter de Gruyter GmbH
2017
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| Subjects: | |
| 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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| Summary: | 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. |
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