Ordered Semigroups Based on ∈,∈∨qkδ-Fuzzy Ideals
A new trend of using fuzzy algebraic structures in various applied sciences is becoming a central focus due to the accuracy and nondecoding nature. The aim of the present paper is to develop a new type of fuzzy subsystem of an ordered semigroup S. This new type of fuzzy subsystem will overcome the d...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2018-01-01
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| Series: | Advances in Fuzzy Systems |
| Online Access: | http://dx.doi.org/10.1155/2018/5304514 |
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| _version_ | 1849407562809606144 |
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| author | Faiz Muhammad Khan Nie Yufeng Hidayat Ullah Khan Bakht Muhammad Khan |
| author_facet | Faiz Muhammad Khan Nie Yufeng Hidayat Ullah Khan Bakht Muhammad Khan |
| author_sort | Faiz Muhammad Khan |
| collection | DOAJ |
| description | A new trend of using fuzzy algebraic structures in various applied sciences is becoming a central focus due to the accuracy and nondecoding nature. The aim of the present paper is to develop a new type of fuzzy subsystem of an ordered semigroup S. This new type of fuzzy subsystem will overcome the difficulties faced in fuzzy ideal theory of an ordered semigroup up to some extent. More precisely, we introduce ∈,∈∨qkδ-fuzzy left (resp., right, quasi-) ideals of S. These concepts are elaborated through appropriate examples. Further, we are bridging ordinary ideals and ∈,∈∨qkδ-fuzzy ideals of an ordered semigroup S through level subset and characteristic function. Finally, we characterize regular ordered semigroups in terms of ∈,∈∨qkδ-fuzzy left (resp., right, quasi-) ideals. |
| format | Article |
| id | doaj-art-489d5a38aaa54e47b4227449f4ecfbc2 |
| institution | Kabale University |
| issn | 1687-7101 1687-711X |
| language | English |
| publishDate | 2018-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Advances in Fuzzy Systems |
| spelling | doaj-art-489d5a38aaa54e47b4227449f4ecfbc22025-08-20T03:36:01ZengWileyAdvances in Fuzzy Systems1687-71011687-711X2018-01-01201810.1155/2018/53045145304514Ordered Semigroups Based on ∈,∈∨qkδ-Fuzzy IdealsFaiz Muhammad Khan0Nie Yufeng1Hidayat Ullah Khan2Bakht Muhammad Khan3Department of Applied Mathematics, School of Natural and Applied Sciences, Northwestern Polytechnical University, Xi’an, Shaanxi, ChinaDepartment of Applied Mathematics, School of Natural and Applied Sciences, Northwestern Polytechnical University, Xi’an, Shaanxi, ChinaDepartment of Mathematics, University of Malakand, Chakdara, KP, PakistanSchool of Electronics and Information, Northwestern Polytechnical University, Xi’an, Shaanxi, ChinaA new trend of using fuzzy algebraic structures in various applied sciences is becoming a central focus due to the accuracy and nondecoding nature. The aim of the present paper is to develop a new type of fuzzy subsystem of an ordered semigroup S. This new type of fuzzy subsystem will overcome the difficulties faced in fuzzy ideal theory of an ordered semigroup up to some extent. More precisely, we introduce ∈,∈∨qkδ-fuzzy left (resp., right, quasi-) ideals of S. These concepts are elaborated through appropriate examples. Further, we are bridging ordinary ideals and ∈,∈∨qkδ-fuzzy ideals of an ordered semigroup S through level subset and characteristic function. Finally, we characterize regular ordered semigroups in terms of ∈,∈∨qkδ-fuzzy left (resp., right, quasi-) ideals.http://dx.doi.org/10.1155/2018/5304514 |
| spellingShingle | Faiz Muhammad Khan Nie Yufeng Hidayat Ullah Khan Bakht Muhammad Khan Ordered Semigroups Based on ∈,∈∨qkδ-Fuzzy Ideals Advances in Fuzzy Systems |
| title | Ordered Semigroups Based on ∈,∈∨qkδ-Fuzzy Ideals |
| title_full | Ordered Semigroups Based on ∈,∈∨qkδ-Fuzzy Ideals |
| title_fullStr | Ordered Semigroups Based on ∈,∈∨qkδ-Fuzzy Ideals |
| title_full_unstemmed | Ordered Semigroups Based on ∈,∈∨qkδ-Fuzzy Ideals |
| title_short | Ordered Semigroups Based on ∈,∈∨qkδ-Fuzzy Ideals |
| title_sort | ordered semigroups based on ∈ ∈∨qkδ fuzzy ideals |
| url | http://dx.doi.org/10.1155/2018/5304514 |
| work_keys_str_mv | AT faizmuhammadkhan orderedsemigroupsbasedonqkdfuzzyideals AT nieyufeng orderedsemigroupsbasedonqkdfuzzyideals AT hidayatullahkhan orderedsemigroupsbasedonqkdfuzzyideals AT bakhtmuhammadkhan orderedsemigroupsbasedonqkdfuzzyideals |