Rough Fuzzy Ideals Induced by Set-Valued Homomorphism in Ternary Semigroups
The main objective of this paper is to characterize rough approximations of fuzzy ideals in ternary semigroups. Rough fuzzy ideals are used to deal with vague and incomplete information in decision-making problems. In this research, approximations for fuzzy prime ideals in ternary semigroups are stu...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2022-01-01
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| Series: | Journal of Function Spaces |
| Online Access: | http://dx.doi.org/10.1155/2022/6247354 |
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| _version_ | 1832565478843744256 |
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| author | Shahida Bashir Muhammad Aslam Rabia Mazhar Junaid Asghar |
| author_facet | Shahida Bashir Muhammad Aslam Rabia Mazhar Junaid Asghar |
| author_sort | Shahida Bashir |
| collection | DOAJ |
| description | The main objective of this paper is to characterize rough approximations of fuzzy ideals in ternary semigroups. Rough fuzzy ideals are used to deal with vague and incomplete information in decision-making problems. In this research, approximations for fuzzy prime ideals in ternary semigroups are studied. It is proved that generalized lower approximations and generalized upper approximations of ∈,∈∨q-fuzzy prime (resp., semiprime) ideals of ternary semigroups are ∈,∈∨q-fuzzy prime (resp., semiprime) ideals. For this, the concept of SSVH (strong set-valued homomorphism) and SVH (set-valued homomorphism) is used. Also, it is shown by examples that the lower approximations of fuzzy subsemigroups and fuzzy ideals are not fuzzy subsemigroups and fuzzy ideals, respectively, for SVH. |
| format | Article |
| id | doaj-art-e814d8ba6458431bbb5ca37e57905364 |
| institution | Kabale University |
| issn | 2314-8888 |
| language | English |
| publishDate | 2022-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Function Spaces |
| spelling | doaj-art-e814d8ba6458431bbb5ca37e579053642025-02-03T01:07:37ZengWileyJournal of Function Spaces2314-88882022-01-01202210.1155/2022/6247354Rough Fuzzy Ideals Induced by Set-Valued Homomorphism in Ternary SemigroupsShahida Bashir0Muhammad Aslam1Rabia Mazhar2Junaid Asghar3Department of MathematicsDepartment of MathematicsDepartment of MathematicsDepartment of MathematicsThe main objective of this paper is to characterize rough approximations of fuzzy ideals in ternary semigroups. Rough fuzzy ideals are used to deal with vague and incomplete information in decision-making problems. In this research, approximations for fuzzy prime ideals in ternary semigroups are studied. It is proved that generalized lower approximations and generalized upper approximations of ∈,∈∨q-fuzzy prime (resp., semiprime) ideals of ternary semigroups are ∈,∈∨q-fuzzy prime (resp., semiprime) ideals. For this, the concept of SSVH (strong set-valued homomorphism) and SVH (set-valued homomorphism) is used. Also, it is shown by examples that the lower approximations of fuzzy subsemigroups and fuzzy ideals are not fuzzy subsemigroups and fuzzy ideals, respectively, for SVH.http://dx.doi.org/10.1155/2022/6247354 |
| spellingShingle | Shahida Bashir Muhammad Aslam Rabia Mazhar Junaid Asghar Rough Fuzzy Ideals Induced by Set-Valued Homomorphism in Ternary Semigroups Journal of Function Spaces |
| title | Rough Fuzzy Ideals Induced by Set-Valued Homomorphism in Ternary Semigroups |
| title_full | Rough Fuzzy Ideals Induced by Set-Valued Homomorphism in Ternary Semigroups |
| title_fullStr | Rough Fuzzy Ideals Induced by Set-Valued Homomorphism in Ternary Semigroups |
| title_full_unstemmed | Rough Fuzzy Ideals Induced by Set-Valued Homomorphism in Ternary Semigroups |
| title_short | Rough Fuzzy Ideals Induced by Set-Valued Homomorphism in Ternary Semigroups |
| title_sort | rough fuzzy ideals induced by set valued homomorphism in ternary semigroups |
| url | http://dx.doi.org/10.1155/2022/6247354 |
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