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学者姓名：杨士林
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Abstract ：
The theory of intuitionistic fuzzy sets (IFSs) plays an essential role to deal with uncertainty and ambiguity. However, the IFSs deal only with anticipation, not periodicity. But, complex IFSs (CIFS) can handle both uncertainties and periodicity at a time. Therefore, this paper focuses on a new multi-criteria decision making (MCDM) approach using Maclaurin symmetric mean (MSM) operator in connection with the CIFS setting. Then, we develop some CIF partitioned based MSM (CIFPMSM) operators and their weighted form by considering that all the criteria can be arranged into some groups. The proposed operators not only deal with the interrelationship among criteria but also deal with the partitioned relationship among criteria. We discuss the properties of these proposed operators and investigate their cases. Finally, a decision-making approach for radio frequency identification (RFID) for manufacturing companies is developed based on the proposed operators and compared the results with the existing method to show the application and feasibility of the proposed method.
Keyword ：
CIFWPMSM operator CIFWPMSM operator CIFPMSM operators CIFPMSM operators Complex intuitionistic fuzzy sets (CIFS) Complex intuitionistic fuzzy sets (CIFS) Multi-criteria decision making (MCDM) method Multi-criteria decision making (MCDM) method
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| GB/T 7714 | Azam, Muhammad , Jana, Chiranjibe , Khan, Muhammad Sajjad Ali et al. Multi-criteria Radio Frequency Identification Approach for Manufacturing Company Selection Based on Partitioned Maclaurin Symmetric Mean Operators Under Complex Intuitionistic Fuzzy Set Environment [J]. | INTERNATIONAL JOURNAL OF FUZZY SYSTEMS , 2024 , 26 (5) : 1730-1748 . |
| MLA | Azam, Muhammad et al. "Multi-criteria Radio Frequency Identification Approach for Manufacturing Company Selection Based on Partitioned Maclaurin Symmetric Mean Operators Under Complex Intuitionistic Fuzzy Set Environment" . | INTERNATIONAL JOURNAL OF FUZZY SYSTEMS 26 . 5 (2024) : 1730-1748 . |
| APA | Azam, Muhammad , Jana, Chiranjibe , Khan, Muhammad Sajjad Ali , Pal, Madhumangal , Xin, Qin , Yang, Shilin et al. Multi-criteria Radio Frequency Identification Approach for Manufacturing Company Selection Based on Partitioned Maclaurin Symmetric Mean Operators Under Complex Intuitionistic Fuzzy Set Environment . | INTERNATIONAL JOURNAL OF FUZZY SYSTEMS , 2024 , 26 (5) , 1730-1748 . |
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Abstract ：
Let Aq be the universal Askey-Wilson algebra. If q is not a root of unity, it is shown in the Huang's earlier paper that an (n + 1)-dimensional irreducible Aq-module is a quotient Vn(a, b, c) of a Aq-Verma module with / } Condition A: abc, a-1bc, ab-1c, abc-1<qn-2i+1|1 <i< n . The aim of this paper is to discuss the structures of (n + 1)-dimensional Aq-modules Vn(a, b, c) when the given triples (a, b, c) do not satisfy Condition A.
Keyword ：
Verma module Verma module irreducible module irreducible module universal Askey-Wilson algebra universal Askey-Wilson algebra
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| GB/T 7714 | Wang, Wanxia , Yang, Shilin . On finite-dimensional irreducible modules for the universal Askey-Wilson algebra [J]. | AIMS MATHEMATICS , 2023 , 8 (8) : 18930-18947 . |
| MLA | Wang, Wanxia et al. "On finite-dimensional irreducible modules for the universal Askey-Wilson algebra" . | AIMS MATHEMATICS 8 . 8 (2023) : 18930-18947 . |
| APA | Wang, Wanxia , Yang, Shilin . On finite-dimensional irreducible modules for the universal Askey-Wilson algebra . | AIMS MATHEMATICS , 2023 , 8 (8) , 18930-18947 . |
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Abstract ：
We investigate the representation theory of the positively based algebra A(m,d), which is a generalization of the noncommutative Green algebra of weak Hopf algebra corresponding to the generalized Taft algebra. It turns out that A(m,d) is of finite representative type if d <= 4, of tame type if d = 5, and of wild type if d > 6. In the case when d <= 4, all indecomposable representations of A(m,d) are constructed. Furthermore, their right cell representations as well as left cell representations of A(m,d) are described.
Keyword ：
cell module cell module indecomposable module indecomposable module positively based algebra positively based algebra
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| GB/T 7714 | Lin, Shiyu , Yang, Shilin . Representations of a class of positively based algebras [J]. | CZECHOSLOVAK MATHEMATICAL JOURNAL , 2023 , 73 (3) : 811-838 . |
| MLA | Lin, Shiyu et al. "Representations of a class of positively based algebras" . | CZECHOSLOVAK MATHEMATICAL JOURNAL 73 . 3 (2023) : 811-838 . |
| APA | Lin, Shiyu , Yang, Shilin . Representations of a class of positively based algebras . | CZECHOSLOVAK MATHEMATICAL JOURNAL , 2023 , 73 (3) , 811-838 . |
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Abstract ：
In this paper, we study the structure of F-q-linear skewcyclic codes over F-q2. Some good F-q-linear skew cyclic codes over F-q2 are constructed. Moreover, as an application, some good quantum codes are obtained by F-q-linear skew cyclic codes over F-q2.
Keyword ：
F-q-Linear skew cyclic codes over F-q2 F-q-Linear skew cyclic codes over F-q2 Trace-alternating form Trace-alternating form Quantum codes Quantum codes
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| GB/T 7714 | Gao, Yun , Gao, Jian , Yang, Shilin et al. F-q-Linear skew cyclic codes over F-q2 and their applications of quantum codes construction [J]. | JOURNAL OF APPLIED MATHEMATICS AND COMPUTING , 2021 . |
| MLA | Gao, Yun et al. "F-q-Linear skew cyclic codes over F-q2 and their applications of quantum codes construction" . | JOURNAL OF APPLIED MATHEMATICS AND COMPUTING (2021) . |
| APA | Gao, Yun , Gao, Jian , Yang, Shilin , Fu, Fang-Wei . F-q-Linear skew cyclic codes over F-q2 and their applications of quantum codes construction . | JOURNAL OF APPLIED MATHEMATICS AND COMPUTING , 2021 . |
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Abstract ：
Let F-qt be a finite field of cardinality q(t), where q is a power of a prime number p and t >= 1 is a positive integer. Firstly, a family of cyclic F-q-linear F-qt-codes of length n is given, where n is a positive integer coprime to q. Then according to the structure of this kind of codes, we construct 60 optimal cyclic Fq-linear F-q2-codes which have the same parameters as the MDS codes over F-q2.
Keyword ：
Cyclic F-q-linear F(q)t-codes Cyclic F-q-linear F(q)t-codes optimal codes optimal codes MDS codes MDS codes
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| GB/T 7714 | Gao, Yun , Yang, Shilin , Fu, Fang-Wei . SOME OPTIMAL CYCLIC F-q-LINEAR F-qt-CODES [J]. | ADVANCES IN MATHEMATICS OF COMMUNICATIONS , 2021 , 15 (3) : 387-396 . |
| MLA | Gao, Yun et al. "SOME OPTIMAL CYCLIC F-q-LINEAR F-qt-CODES" . | ADVANCES IN MATHEMATICS OF COMMUNICATIONS 15 . 3 (2021) : 387-396 . |
| APA | Gao, Yun , Yang, Shilin , Fu, Fang-Wei . SOME OPTIMAL CYCLIC F-q-LINEAR F-qt-CODES . | ADVANCES IN MATHEMATICS OF COMMUNICATIONS , 2021 , 15 (3) , 387-396 . |
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Abstract ：
In this paper, we construct all the indecomposable modules of a class of non-pointed Hopf algebras, which are quotient Hopf algebras of a class of prime Hopf algebras of GK-dimension one. Then the decomposition formulas of the tensor product of any two indecomposable modules are established. Based on these results, the representation ring of the Hopf algebras is characterized by generators and some relations.
Keyword ：
Hopf algebra Hopf algebra representation ring representation ring tensor product tensor product indecomposable module indecomposable module representation type representation type
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| GB/T 7714 | Yang, Ruifang , Yang, Shilin . Representations of a non-pointed Hopf algebra [J]. | AIMS MATHEMATICS , 2021 , 6 (10) : 10523-10539 . |
| MLA | Yang, Ruifang et al. "Representations of a non-pointed Hopf algebra" . | AIMS MATHEMATICS 6 . 10 (2021) : 10523-10539 . |
| APA | Yang, Ruifang , Yang, Shilin . Representations of a non-pointed Hopf algebra . | AIMS MATHEMATICS , 2021 , 6 (10) , 10523-10539 . |
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Abstract ：
We construct the Grothendieck rings of a class of 2n(2) dimensional semisimple Hopf Algebras H-2n2; which can be viewed as a generalization of the 8 dimensional Kac-Paljutkin Hopf algebra H-8. All irreducible H-2n2-modules are classified. Furthermore, we describe the Grothendieck rings r(H-2n2) by generators and relations explicitly.
Keyword ：
irreducible module irreducible module Grothendieck ring Grothendieck ring Hopf algebra Hopf algebra
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| GB/T 7714 | Chen, Jialei , Yang, Shilin , Wang, Dingguo . Grothendieck rings of a class of Hopf algebras of Kac-Paljutkin type [J]. | FRONTIERS OF MATHEMATICS IN CHINA , 2021 , 16 (1) : 29-47 . |
| MLA | Chen, Jialei et al. "Grothendieck rings of a class of Hopf algebras of Kac-Paljutkin type" . | FRONTIERS OF MATHEMATICS IN CHINA 16 . 1 (2021) : 29-47 . |
| APA | Chen, Jialei , Yang, Shilin , Wang, Dingguo . Grothendieck rings of a class of Hopf algebras of Kac-Paljutkin type . | FRONTIERS OF MATHEMATICS IN CHINA , 2021 , 16 (1) , 29-47 . |
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Abstract ：
The aim of this paper is to classify all Hopf algebra structures on the quotient of Ore extensions H-4[z;sigma]of automorphism type for the Sweedler ' s 4-dimensional Hopf algebra H-4. Firstly, we calculate all equivalent classes of twisted homomorphisms (sigma,J) for H-4. Then we give the classification of all bialgebra (Hopf algebra) structures on the quotients of H-4[z;sigma] up to isomorphism.
Keyword ：
Hopf algebra Hopf algebra Drinfeld twist Drinfeld twist twisted homomorphism twisted homomorphism Ore extension Ore extension
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| GB/T 7714 | Yang, Shilin , Zhang, Yongfeng . Ore Extensions for the Sweedler's Hopf Algebra H-4 [J]. | MATHEMATICS , 2020 , 8 (8) . |
| MLA | Yang, Shilin et al. "Ore Extensions for the Sweedler's Hopf Algebra H-4" . | MATHEMATICS 8 . 8 (2020) . |
| APA | Yang, Shilin , Zhang, Yongfeng . Ore Extensions for the Sweedler's Hopf Algebra H-4 . | MATHEMATICS , 2020 , 8 (8) . |
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Abstract ：
The aim of this paper is to study bialgebras(Hopf algebras) on the skew polynomial algebras R[ z; s] of automorphism type, which comultiplication defined on the variable z is extended by a Drinfeld twist J for a Hopf algebra R. Firstly, we establish some necessary and sufficient conditions that are of Hopf algebra structures on the localization of skew polynomial ring R[z; s] and on the quotients of R[ z; s]/I, for a certain Hopf ideal I of R[ z; s]. Then, we give some examples for these results. Specially, the non-semisimple and non-pointed 16 dimension self-dual Hopf algebra is also constructed by the Ore extensions of automorphism type.
Keyword ：
Twisted homomorphism Twisted homomorphism Ore extension Ore extension Drinfeld twist Drinfeld twist Hopf algebra Hopf algebra
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| GB/T 7714 | Yang, Shilin , Zhang, Yongfeng . Ore Extensions of Automorphism Type for Hopf Algebras [J]. | BULLETIN OF THE IRANIAN MATHEMATICAL SOCIETY , 2020 , 46 (2) : 487-501 . |
| MLA | Yang, Shilin et al. "Ore Extensions of Automorphism Type for Hopf Algebras" . | BULLETIN OF THE IRANIAN MATHEMATICAL SOCIETY 46 . 2 (2020) : 487-501 . |
| APA | Yang, Shilin , Zhang, Yongfeng . Ore Extensions of Automorphism Type for Hopf Algebras . | BULLETIN OF THE IRANIAN MATHEMATICAL SOCIETY , 2020 , 46 (2) , 487-501 . |
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Abstract ：
Wu-Liu-Ding algebras, that is D(m, d, xi), are a class of non-pointed affine prime regular Hopf algebras of GK-dimension one. In this paper, we mainly study a class of quotient algebras of D(m, d, xi), denoted by D'(m, d, xi), which are 2m(2)d-dimensional non-pointed semisimple Hopf algebras. For a better understanding of the structure of the Hopf algebra D'(m, d, xi), we have considered the Grothendieck rings of D'(m, d, xi) and their Casimir numbers when d is odd in our previous paper. In this paper we continue dealing with the more complex case when d is even. It turns out that the Grothendieck rings of D'(m, d, xi) are generated by four elements subject to some relations. Then we give the Casimir numbers of the Grothendieck rings of D'(1, d, xi) and D'(2, d, xi).
Keyword ：
Frobenius algebra Frobenius algebra Casimir number Casimir number Grothendieck ring Grothendieck ring
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| GB/T 7714 | Yang, Ruifang , Yang, Shilin . The Grothendieck rings of Wu-Liu-Ding algebras and their Casimir numbers (II) [J]. | COMMUNICATIONS IN ALGEBRA , 2020 , 49 (5) : 2041-2073 . |
| MLA | Yang, Ruifang et al. "The Grothendieck rings of Wu-Liu-Ding algebras and their Casimir numbers (II)" . | COMMUNICATIONS IN ALGEBRA 49 . 5 (2020) : 2041-2073 . |
| APA | Yang, Ruifang , Yang, Shilin . The Grothendieck rings of Wu-Liu-Ding algebras and their Casimir numbers (II) . | COMMUNICATIONS IN ALGEBRA , 2020 , 49 (5) , 2041-2073 . |
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