Proper Fuzzification of Prime Ideals of a Hemiring
Prime fuzzy ideals, prime fuzzy k-ideals, and prime fuzzy h-ideals are roped in one condition. It is shown that this way better fuzzification is achieved. Other major results of the paper are: every fuzzy ideal (resp., k-ideal, h-ideal) is contained in a prime fuzzy ideal (resp., k-ideal, h-ideal)....
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| Format: | Article |
| Language: | English |
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Wiley
2012-01-01
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| Series: | Advances in Fuzzy Systems |
| Online Access: | http://dx.doi.org/10.1155/2012/801650 |
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| author | H. V. Kumbhojkar |
| author_facet | H. V. Kumbhojkar |
| author_sort | H. V. Kumbhojkar |
| collection | DOAJ |
| description | Prime fuzzy ideals, prime fuzzy k-ideals, and prime fuzzy h-ideals are roped in one condition. It is shown that this way better fuzzification is achieved. Other major results of the paper are: every fuzzy ideal (resp., k-ideal, h-ideal) is contained in a prime fuzzy ideal (resp., k-ideal, h-ideal). Prime radicals and nil radicals of a fuzzy ideal are defined; their relationship is established. The nil radical of a fuzzy k-ideal (resp., an h-ideal) is proved to be a fuzzy k-ideal (resp., h-ideal). The correspondence theorems for different types of fuzzy ideals of hemirings are established. The concept of primary fuzzy ideal is introduced. Minimum imperative for proper fuzzification is suggested and it is shown that the fuzzifications introduced in this paper are proper fuzzifications. |
| format | Article |
| id | doaj-art-fe39a750ee1b4f1cb162d12bfead1c36 |
| institution | Kabale University |
| issn | 1687-7101 1687-711X |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Advances in Fuzzy Systems |
| spelling | doaj-art-fe39a750ee1b4f1cb162d12bfead1c362025-02-03T05:44:07ZengWileyAdvances in Fuzzy Systems1687-71011687-711X2012-01-01201210.1155/2012/801650801650Proper Fuzzification of Prime Ideals of a HemiringH. V. Kumbhojkar0403 Poorvarang Apartments, 13th Lane, Kolhapur 416008, Maharashtra, IndiaPrime fuzzy ideals, prime fuzzy k-ideals, and prime fuzzy h-ideals are roped in one condition. It is shown that this way better fuzzification is achieved. Other major results of the paper are: every fuzzy ideal (resp., k-ideal, h-ideal) is contained in a prime fuzzy ideal (resp., k-ideal, h-ideal). Prime radicals and nil radicals of a fuzzy ideal are defined; their relationship is established. The nil radical of a fuzzy k-ideal (resp., an h-ideal) is proved to be a fuzzy k-ideal (resp., h-ideal). The correspondence theorems for different types of fuzzy ideals of hemirings are established. The concept of primary fuzzy ideal is introduced. Minimum imperative for proper fuzzification is suggested and it is shown that the fuzzifications introduced in this paper are proper fuzzifications.http://dx.doi.org/10.1155/2012/801650 |
| spellingShingle | H. V. Kumbhojkar Proper Fuzzification of Prime Ideals of a Hemiring Advances in Fuzzy Systems |
| title | Proper Fuzzification of Prime Ideals of a Hemiring |
| title_full | Proper Fuzzification of Prime Ideals of a Hemiring |
| title_fullStr | Proper Fuzzification of Prime Ideals of a Hemiring |
| title_full_unstemmed | Proper Fuzzification of Prime Ideals of a Hemiring |
| title_short | Proper Fuzzification of Prime Ideals of a Hemiring |
| title_sort | proper fuzzification of prime ideals of a hemiring |
| url | http://dx.doi.org/10.1155/2012/801650 |
| work_keys_str_mv | AT hvkumbhojkar properfuzzificationofprimeidealsofahemiring |