On Bipolar Anti Fuzzy h-ideals in Hemi-rings
In this work, we present notions of bipolar anti fuzzy h-ideals and bipolar anti fuzzy interior h-ideals in hemi-rings. Investigating some of their properties, we characterize hemi-rings by means of positive anti β-cut and negative anti α-cut. Meanwhile, some results of homomorphisms, anti images an...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Tsinghua University Press
2017-03-01
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| Series: | Fuzzy Information and Engineering |
| Subjects: | |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S1616865817300729 |
| _version_ | 1797757006238449664 |
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| author | Khizar Hayat Tahir Mahmood Bing-Yuan Cao |
| author_facet | Khizar Hayat Tahir Mahmood Bing-Yuan Cao |
| author_sort | Khizar Hayat |
| collection | DOAJ |
| description | In this work, we present notions of bipolar anti fuzzy h-ideals and bipolar anti fuzzy interior h-ideals in hemi-rings. Investigating some of their properties, we characterize hemi-rings by means of positive anti β-cut and negative anti α-cut. Meanwhile, some results of homomorphisms, anti images and anti pre-images are given to show the rationality of the definitions introduced in the present paper. Also, we define an equivalence relation on bipolar anti fuzzy h-ideals. In particular, we investigate translations, extensions and multiplications of bipolar anti fuzzy h-ideals. Finally, we present characterizations of h-hemi-regular and h-semi-simple hemi-rings in terms of bipolar anti fuzzy h-ideals. |
| first_indexed | 2024-03-12T18:08:48Z |
| format | Article |
| id | doaj.art-e3ad8c81013447f9a7663416f70c46cf |
| institution | Directory Open Access Journal |
| issn | 1616-8658 |
| language | English |
| last_indexed | 2024-03-12T18:08:48Z |
| publishDate | 2017-03-01 |
| publisher | Tsinghua University Press |
| record_format | Article |
| series | Fuzzy Information and Engineering |
| spelling | doaj.art-e3ad8c81013447f9a7663416f70c46cf2023-08-02T09:18:44ZengTsinghua University PressFuzzy Information and Engineering1616-86582017-03-019111910.1016/j.fiae.2017.03.001On Bipolar Anti Fuzzy h-ideals in Hemi-ringsKhizar Hayat0Tahir Mahmood1Bing-Yuan Cao2School of Mathematics and Information Sciences, Guangzhou University, Guangzhou, 510006, ChinaDepartment of Mathematics and Statistics, International Islamic University Islamabad, 44000, PakistanSchool of Mathematics and Information Science, Guangzhou University, Guangzhou, 510006, ChinaIn this work, we present notions of bipolar anti fuzzy h-ideals and bipolar anti fuzzy interior h-ideals in hemi-rings. Investigating some of their properties, we characterize hemi-rings by means of positive anti β-cut and negative anti α-cut. Meanwhile, some results of homomorphisms, anti images and anti pre-images are given to show the rationality of the definitions introduced in the present paper. Also, we define an equivalence relation on bipolar anti fuzzy h-ideals. In particular, we investigate translations, extensions and multiplications of bipolar anti fuzzy h-ideals. Finally, we present characterizations of h-hemi-regular and h-semi-simple hemi-rings in terms of bipolar anti fuzzy h-ideals.http://www.sciencedirect.com/science/article/pii/S1616865817300729BAF h-idealsHemi-ringsPositive anti β-cutsNegative anti α-cutsAnti images and anti pre-images |
| spellingShingle | Khizar Hayat Tahir Mahmood Bing-Yuan Cao On Bipolar Anti Fuzzy h-ideals in Hemi-rings Fuzzy Information and Engineering BAF h-ideals Hemi-rings Positive anti β-cuts Negative anti α-cuts Anti images and anti pre-images |
| title | On Bipolar Anti Fuzzy h-ideals in Hemi-rings |
| title_full | On Bipolar Anti Fuzzy h-ideals in Hemi-rings |
| title_fullStr | On Bipolar Anti Fuzzy h-ideals in Hemi-rings |
| title_full_unstemmed | On Bipolar Anti Fuzzy h-ideals in Hemi-rings |
| title_short | On Bipolar Anti Fuzzy h-ideals in Hemi-rings |
| title_sort | on bipolar anti fuzzy h ideals in hemi rings |
| topic | BAF h-ideals Hemi-rings Positive anti β-cuts Negative anti α-cuts Anti images and anti pre-images |
| url | http://www.sciencedirect.com/science/article/pii/S1616865817300729 |
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