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-...
| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
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De Gruyter
2019-09-01
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| Series: | Journal of Intelligent Systems |
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| Online Access: | https://doi.org/10.1515/jisys-2017-0258 |
| _version_ | 1818733837208780800 |
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| author | Khan Faiz Muhammad Khan Hidayat Ullah Mukhtar Safyan Khan Asghar Sarmin Nor Haniza |
| author_facet | Khan Faiz Muhammad Khan Hidayat Ullah Mukhtar Safyan Khan Asghar Sarmin Nor Haniza |
| author_sort | Khan Faiz Muhammad |
| collection | DOAJ |
| 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, (β̄, ᾱ)-fuzzy bi-ideals, and (β̄, ᾱ)-fuzzy interior ideals, where α, β∈{∈γ, qδ, ∈γ∨qδ, ∈γ∧qδ} and ᾱ, β̄∈{⋶γ, q̄δ, ⋶γ∨q̄δ, ⋶γ∧q̄δ}, with α≠∈γ∧qδ and β̄≠⋶γ∧q̄δ. 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 [(∈γ, ∈γ∨qδ)-fuzzy bi-ideals, (∈γ, ∈γ∨qδ)-fuzzy interior ideals]. Special attention is given to (∈γ, ∈γ∨qδ)-fuzzy bi-ideals and (⋶γ, ⋶γ∨q̄δ) -fuzzy bi-ideals. |
| first_indexed | 2024-12-17T23:55:48Z |
| format | Article |
| id | doaj.art-a58cf3ed179b4ea0af68c3e529b47849 |
| institution | Directory Open Access Journal |
| issn | 0334-1860 2191-026X |
| language | English |
| last_indexed | 2024-12-17T23:55:48Z |
| publishDate | 2019-09-01 |
| publisher | De Gruyter |
| record_format | Article |
| series | Journal of Intelligent Systems |
| spelling | doaj.art-a58cf3ed179b4ea0af68c3e529b478492022-12-21T21:28:04ZengDe GruyterJournal of Intelligent Systems0334-18602191-026X2019-09-0128464966710.1515/jisys-2017-0258Some Innovative Types of Fuzzy Ideals in AG-GroupoidsKhan Faiz Muhammad0Khan Hidayat Ullah1Mukhtar Safyan2Khan Asghar3Sarmin Nor Haniza4Department of Mathematics and Statistics, University of Swat, Khyber Pakhtunkhwa, PakistanDepartment of Mathematics, University of Malakand at Chakdara, Dir (L), Khyber Pakhtunkhwa 18800, PakistanDepartment of Mathematics, Bacha Khan University Charsadda, Khyber Pakhtunkhwa, PakistanDepartment of Mathematics, Abdul Wali Khan University Mardan, Khyber Pakhtunkhwa, Mardan, PakistanDepartment of Mathematical Sciences, Faculty of Science, Universiti Teknologi Malaysia, 81310 UTM Johor Bahru, Johor, MalaysiaAG-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, (β̄, ᾱ)-fuzzy bi-ideals, and (β̄, ᾱ)-fuzzy interior ideals, where α, β∈{∈γ, qδ, ∈γ∨qδ, ∈γ∧qδ} and ᾱ, β̄∈{⋶γ, q̄δ, ⋶γ∨q̄δ, ⋶γ∧q̄δ}, with α≠∈γ∧qδ and β̄≠⋶γ∧q̄δ. 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 [(∈γ, ∈γ∨qδ)-fuzzy bi-ideals, (∈γ, ∈γ∨qδ)-fuzzy interior ideals]. Special attention is given to (∈γ, ∈γ∨qδ)-fuzzy bi-ideals and (⋶γ, ⋶γ∨q̄δ) -fuzzy bi-ideals.https://doi.org/10.1515/jisys-2017-0258ag-groupoids(∈γ, ∈γ∨qδ)-fuzzy bi-ideals(∈γ, ∈γ∨qδ)-fuzzy interior ideals(⋶γ, ⋶γ∨q̄δ)-fuzzy bi-ideals, (⋶γ, ⋶γ∨q̄δ)-fuzzy interior ideals20m1020n99 |
| spellingShingle | Khan Faiz Muhammad Khan Hidayat Ullah Mukhtar Safyan Khan Asghar Sarmin Nor Haniza Some Innovative Types of Fuzzy Ideals in AG-Groupoids Journal of Intelligent Systems ag-groupoids (∈γ, ∈γ∨qδ)-fuzzy bi-ideals (∈γ, ∈γ∨qδ)-fuzzy interior ideals (⋶γ, ⋶γ∨q̄δ)-fuzzy bi-ideals, (⋶γ, ⋶γ∨q̄δ)-fuzzy interior ideals 20m10 20n99 |
| title | 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_short | Some Innovative Types of Fuzzy Ideals in AG-Groupoids |
| title_sort | some innovative types of fuzzy ideals in ag groupoids |
| topic | ag-groupoids (∈γ, ∈γ∨qδ)-fuzzy bi-ideals (∈γ, ∈γ∨qδ)-fuzzy interior ideals (⋶γ, ⋶γ∨q̄δ)-fuzzy bi-ideals, (⋶γ, ⋶γ∨q̄δ)-fuzzy interior ideals 20m10 20n99 |
| url | https://doi.org/10.1515/jisys-2017-0258 |
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