Connecting Fuzzifying Topologies and Generalized Ideals by Means of Fuzzy Preorders
The present paper investigates the relations between fuzzifying topologies and generalized ideals of fuzzy subsets, as well as constructing generalized ideals and fuzzifying topologies by means of fuzzy preorders. Furthermore, a construction of generalized ideals from preideals, and vice versa, is o...
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| Format: | Article |
| Language: | English |
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Wiley
2009-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/2009/567482 |
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| _version_ | 1832556229114724352 |
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| author | G. Elsalamony |
| author_facet | G. Elsalamony |
| author_sort | G. Elsalamony |
| collection | DOAJ |
| description | The present paper investigates the relations between fuzzifying topologies and generalized ideals of fuzzy subsets, as well as constructing generalized ideals and fuzzifying topologies by means of fuzzy preorders. Furthermore, a construction of generalized ideals from preideals, and vice versa, is obtained. As a particular consequence of the results in this paper, a construction of fuzzifying topology generated by generalized ideals of fuzzy subsets via a given I-topology is given. The notion of σ-generalized ideal is introduced and hence every σ-generalized ideal is shown to be a fuzzifying topology induced by some fuzzy preorder. |
| format | Article |
| id | doaj-art-e540c464158c47c89633da085cf7cabf |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2009-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-e540c464158c47c89633da085cf7cabf2025-02-03T05:45:59ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252009-01-01200910.1155/2009/567482567482Connecting Fuzzifying Topologies and Generalized Ideals by Means of Fuzzy PreordersG. Elsalamony0Department of Mathematics, Faculty of Science, Benha University, Benha, EgyptThe present paper investigates the relations between fuzzifying topologies and generalized ideals of fuzzy subsets, as well as constructing generalized ideals and fuzzifying topologies by means of fuzzy preorders. Furthermore, a construction of generalized ideals from preideals, and vice versa, is obtained. As a particular consequence of the results in this paper, a construction of fuzzifying topology generated by generalized ideals of fuzzy subsets via a given I-topology is given. The notion of σ-generalized ideal is introduced and hence every σ-generalized ideal is shown to be a fuzzifying topology induced by some fuzzy preorder.http://dx.doi.org/10.1155/2009/567482 |
| spellingShingle | G. Elsalamony Connecting Fuzzifying Topologies and Generalized Ideals by Means of Fuzzy Preorders International Journal of Mathematics and Mathematical Sciences |
| title | Connecting Fuzzifying Topologies and Generalized Ideals by Means of Fuzzy Preorders |
| title_full | Connecting Fuzzifying Topologies and Generalized Ideals by Means of Fuzzy Preorders |
| title_fullStr | Connecting Fuzzifying Topologies and Generalized Ideals by Means of Fuzzy Preorders |
| title_full_unstemmed | Connecting Fuzzifying Topologies and Generalized Ideals by Means of Fuzzy Preorders |
| title_short | Connecting Fuzzifying Topologies and Generalized Ideals by Means of Fuzzy Preorders |
| title_sort | connecting fuzzifying topologies and generalized ideals by means of fuzzy preorders |
| url | http://dx.doi.org/10.1155/2009/567482 |
| work_keys_str_mv | AT gelsalamony connectingfuzzifyingtopologiesandgeneralizedidealsbymeansoffuzzypreorders |