Characterizations of Ordered Semigroups by New Type of Interval Valued Fuzzy Quasi-Ideals
The concept of non-k-quasi-coincidence of an interval valued ordered fuzzy point with an interval valued fuzzy set is considered. In fact, this concept is a generalized concept of the non-k-quasi-coincidence of a fuzzy point with a fuzzy set. By using this new concept, we introduce the notion of int...
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2014/867459 |
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| author | Jian Tang Xiangyun Xie Yanfeng Luo |
| author_facet | Jian Tang Xiangyun Xie Yanfeng Luo |
| author_sort | Jian Tang |
| collection | DOAJ |
| description | The concept of non-k-quasi-coincidence of an interval valued ordered fuzzy point with an interval valued fuzzy set is considered. In fact, this concept is a generalized concept of the non-k-quasi-coincidence of a fuzzy point with a fuzzy set. By using this new concept, we introduce the notion of interval valued (∈¯,∈¯∨qk~¯)-fuzzy quasi-ideals of ordered semigroups and study their related properties. In addition, we also introduce the concepts of prime and completely semiprime interval valued (∈¯,∈¯∨qk~¯)-fuzzy quasi-ideals of ordered semigroups and characterize bi-regular ordered semigroups in terms of completely semiprime interval valued (∈¯,∈¯∨qk~¯)-fuzzy quasi-ideals. Furthermore, some new characterizations of regular and intra-regular ordered semigroups by the properties of interval valued (∈¯,∈¯∨qk~¯)-fuzzy quasi-ideals are given. |
| format | Article |
| id | doaj-art-c5896adcdba545688066f308690481c7 |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-c5896adcdba545688066f308690481c72025-02-03T01:02:57ZengWileyJournal of Applied Mathematics1110-757X1687-00422014-01-01201410.1155/2014/867459867459Characterizations of Ordered Semigroups by New Type of Interval Valued Fuzzy Quasi-IdealsJian Tang0Xiangyun Xie1Yanfeng Luo2School of Mathematics and Statistics, Lanzhou University, Lanzhou, Gansu 730000, ChinaSchool of Mathematics and Computational Science, Wuyi University, Jiangmen, Guangdong 529020, ChinaSchool of Mathematics and Statistics, Lanzhou University, Lanzhou, Gansu 730000, ChinaThe concept of non-k-quasi-coincidence of an interval valued ordered fuzzy point with an interval valued fuzzy set is considered. In fact, this concept is a generalized concept of the non-k-quasi-coincidence of a fuzzy point with a fuzzy set. By using this new concept, we introduce the notion of interval valued (∈¯,∈¯∨qk~¯)-fuzzy quasi-ideals of ordered semigroups and study their related properties. In addition, we also introduce the concepts of prime and completely semiprime interval valued (∈¯,∈¯∨qk~¯)-fuzzy quasi-ideals of ordered semigroups and characterize bi-regular ordered semigroups in terms of completely semiprime interval valued (∈¯,∈¯∨qk~¯)-fuzzy quasi-ideals. Furthermore, some new characterizations of regular and intra-regular ordered semigroups by the properties of interval valued (∈¯,∈¯∨qk~¯)-fuzzy quasi-ideals are given.http://dx.doi.org/10.1155/2014/867459 |
| spellingShingle | Jian Tang Xiangyun Xie Yanfeng Luo Characterizations of Ordered Semigroups by New Type of Interval Valued Fuzzy Quasi-Ideals Journal of Applied Mathematics |
| title | Characterizations of Ordered Semigroups by New Type of Interval Valued Fuzzy Quasi-Ideals |
| title_full | Characterizations of Ordered Semigroups by New Type of Interval Valued Fuzzy Quasi-Ideals |
| title_fullStr | Characterizations of Ordered Semigroups by New Type of Interval Valued Fuzzy Quasi-Ideals |
| title_full_unstemmed | Characterizations of Ordered Semigroups by New Type of Interval Valued Fuzzy Quasi-Ideals |
| title_short | Characterizations of Ordered Semigroups by New Type of Interval Valued Fuzzy Quasi-Ideals |
| title_sort | characterizations of ordered semigroups by new type of interval valued fuzzy quasi ideals |
| url | http://dx.doi.org/10.1155/2014/867459 |
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