Stabilizers in EQ-algebras
The main goal of this paper is to introduce the notion of stabilizers in EQ-algebras and develop stabilizer theory in EQ-algebras. In the paper, we introduce (fuzzy) left and right stabilizers and investigate some related properties of them. Then, we discuss the relations among (fuzzy) stabilizers,...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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De Gruyter
2019-08-01
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| Series: | Open Mathematics |
| Subjects: | |
| Online Access: | http://www.degruyter.com/view/j/math.2019.17.issue-1/math-2019-0078/math-2019-0078.xml?format=INT |
| _version_ | 1818929365505802240 |
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| author | Cheng Xiao Yun Wang Mei Wang Wei Wang Jun Tao |
| author_facet | Cheng Xiao Yun Wang Mei Wang Wei Wang Jun Tao |
| author_sort | Cheng Xiao Yun |
| collection | DOAJ |
| description | The main goal of this paper is to introduce the notion of stabilizers in EQ-algebras and develop stabilizer theory in EQ-algebras. In the paper, we introduce (fuzzy) left and right stabilizers and investigate some related properties of them. Then, we discuss the relations among (fuzzy) stabilizers, (fuzzy) prefilters (filters) and (fuzzy) co-annihilators. Also, we obtain that the set of all prefilters in a good EQ-algebra forms a relative pseudo-complemented lattice, where Str(F, G) is the relative pseudo-complemented of F with respect to G. These results will provide a solid algebraic foundation for the consequence connectives in higher fuzzy logic. |
| first_indexed | 2024-12-20T03:43:39Z |
| format | Article |
| id | doaj.art-c22b41749bbe4503b5d20521abeab2f4 |
| institution | Directory Open Access Journal |
| issn | 2391-5455 |
| language | English |
| last_indexed | 2024-12-20T03:43:39Z |
| publishDate | 2019-08-01 |
| publisher | De Gruyter |
| record_format | Article |
| series | Open Mathematics |
| spelling | doaj.art-c22b41749bbe4503b5d20521abeab2f42022-12-21T19:54:40ZengDe GruyterOpen Mathematics2391-54552019-08-01171998101310.1515/math-2019-0078math-2019-0078Stabilizers in EQ-algebrasCheng Xiao Yun0Wang Mei1Wang Wei2Wang Jun Tao3School of Science, Xi’an Aeronautical University, Xi’an, 710077, Shaanxi, ChinaSchool of Mathematics and Statistics, Weinan Normal University, WeiNan, 714099, P.R. ChinaDepartment of Basic Courses, Shaanxi Railway institute, WeiNan, 714000, P.R. ChinaSchool of Science, Xi’an Shiyou University, Xi’an, 710065, Shaanxi, ChinaThe main goal of this paper is to introduce the notion of stabilizers in EQ-algebras and develop stabilizer theory in EQ-algebras. In the paper, we introduce (fuzzy) left and right stabilizers and investigate some related properties of them. Then, we discuss the relations among (fuzzy) stabilizers, (fuzzy) prefilters (filters) and (fuzzy) co-annihilators. Also, we obtain that the set of all prefilters in a good EQ-algebra forms a relative pseudo-complemented lattice, where Str(F, G) is the relative pseudo-complemented of F with respect to G. These results will provide a solid algebraic foundation for the consequence connectives in higher fuzzy logic.http://www.degruyter.com/view/j/math.2019.17.issue-1/math-2019-0078/math-2019-0078.xml?format=INTeq-algebra(fuzzy) stabilizer(fuzzy) prefilterfuzzy congruence relation08a7203e72 |
| spellingShingle | Cheng Xiao Yun Wang Mei Wang Wei Wang Jun Tao Stabilizers in EQ-algebras Open Mathematics eq-algebra (fuzzy) stabilizer (fuzzy) prefilter fuzzy congruence relation 08a72 03e72 |
| title | Stabilizers in EQ-algebras |
| title_full | Stabilizers in EQ-algebras |
| title_fullStr | Stabilizers in EQ-algebras |
| title_full_unstemmed | Stabilizers in EQ-algebras |
| title_short | Stabilizers in EQ-algebras |
| title_sort | stabilizers in eq algebras |
| topic | eq-algebra (fuzzy) stabilizer (fuzzy) prefilter fuzzy congruence relation 08a72 03e72 |
| url | http://www.degruyter.com/view/j/math.2019.17.issue-1/math-2019-0078/math-2019-0078.xml?format=INT |
| work_keys_str_mv | AT chengxiaoyun stabilizersineqalgebras AT wangmei stabilizersineqalgebras AT wangwei stabilizersineqalgebras AT wangjuntao stabilizersineqalgebras |