Characterization of Derived Nilpotent (Engel) Lie Ring of Fuzzy Hyperrings by Using Fuzzy Strongly Regular Relations

In this paper, we determined a new characterisation of the derived nilpotent (Engel) Lie ring of fuzzy hyperrings by fuzzy strongly regular relation ( ). Moreover, we proved that for a fuzzy hyperring S, the quotient ( ) was a nilpotent (Engel) Lie ring. Also, we introduced the notion of an ζ-role o...

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Published inFuzzy information and engineering Vol. 14; no. 4; pp. 407 - 424
Main Authors Mohammadzadeh, E., Borzooei, R. A., Mohammadzadeh, F., Ahn, S. S.
Format Journal Article
LanguageEnglish
Published Abingdon Taylor & Francis 02.10.2022
Taylor & Francis Group
Tsinghua University Press
Subjects
(Nilpotent) Lie ring
17B62
20N20
Engel Lie ring
fuzzy hyperring
strongly regular relation
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Abstract In this paper, we determined a new characterisation of the derived nilpotent (Engel) Lie ring of fuzzy hyperrings by fuzzy strongly regular relation ( ). Moreover, we proved that for a fuzzy hyperring S, the quotient ( ) was a nilpotent (Engel) Lie ring. Also, we introduced the notion of an ζ-role of a fuzzy hyperring and investigated its essential properties. Basically, we stated a necessary and sufficient condition for transitivity of ζ. Also, we studied the relationship between the strongly regular relation and ζ-role of a given fuzzy hyperring.
AbstractList In this paper, we determined a new characterisation of the derived nilpotent (Engel) Lie ring of fuzzy hyperrings by fuzzy strongly regular relation [Formula: see text]([Formula: see text]). Moreover, we proved that for a fuzzy hyperring S, the quotient [Formula: see text]([Formula: see text]) was a nilpotent (Engel) Lie ring. Also, we introduced the notion of an ζ-role of a fuzzy hyperring and investigated its essential properties. Basically, we stated a necessary and sufficient condition for transitivity of ζ. Also, we studied the relationship between the strongly regular relation and ζ-role of a given fuzzy hyperring.
In this paper, we determined a new characterisation of the derived nilpotent (Engel) Lie ring of fuzzy hyperrings by fuzzy strongly regular relation (). Moreover, we proved that for a fuzzy hyperring S, the quotient () was a nilpotent (Engel) Lie ring. Also, we introduced the notion of an ζ-role of a fuzzy hyperring and investigated its essential properties. Basically, we stated a necessary and sufficient condition for transitivity of ζ. Also, we studied the relationship between the strongly regular relation and ζ-role of a given fuzzy hyperring.
In this paper, we determined a new characterisation of the derived nilpotent (Engel) Lie ring of fuzzy hyperrings by fuzzy strongly regular relation ( ). Moreover, we proved that for a fuzzy hyperring S, the quotient ( ) was a nilpotent (Engel) Lie ring. Also, we introduced the notion of an ζ-role of a fuzzy hyperring and investigated its essential properties. Basically, we stated a necessary and sufficient condition for transitivity of ζ. Also, we studied the relationship between the strongly regular relation and ζ-role of a given fuzzy hyperring.
Author Mohammadzadeh, F.
Mohammadzadeh, E.
Borzooei, R. A.
Ahn, S. S.
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Cites_doi 10.1016/0022-247X(71)90199-5
10.1142/S1793005717500089
10.3233/JIFS-200211
10.3233/IFS-152045
10.1090/S0002-9939-1985-0781044-9
10.1215/ijm/1255631589
10.3390/math6020027
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10.1007/s00500-007-0257-9
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Copyright 2022 The Authors. Published by Taylor & Francis Group on behalf of the Fuzzy Information and Engineering Branch of the Operations Research Society, Guangdong Province Operations Research Society of China. 2022
2022 The Authors. Published by Taylor & Francis Group on behalf of the Fuzzy Information and Engineering Branch of the Operations Research Society, Guangdong Province Operations Research Society of China. This work is licensed under the Creative Commons Attribution License http://creativecommons.org/licenses/by/4.0/ (the “License”). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License.
Copyright_xml – notice: 2022 The Authors. Published by Taylor & Francis Group on behalf of the Fuzzy Information and Engineering Branch of the Operations Research Society, Guangdong Province Operations Research Society of China. 2022
– notice: 2022 The Authors. Published by Taylor & Francis Group on behalf of the Fuzzy Information and Engineering Branch of the Operations Research Society, Guangdong Province Operations Research Society of China. This work is licensed under the Creative Commons Attribution License http://creativecommons.org/licenses/by/4.0/ (the “License”). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License.
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Snippet In this paper, we determined a new characterisation of the derived nilpotent (Engel) Lie ring of fuzzy hyperrings by fuzzy strongly regular relation ( )....
In this paper, we determined a new characterisation of the derived nilpotent (Engel) Lie ring of fuzzy hyperrings by fuzzy strongly regular relation ()....
In this paper, we determined a new characterisation of the derived nilpotent (Engel) Lie ring of fuzzy hyperrings by fuzzy strongly regular relation [Formula:...
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StartPage 407
SubjectTerms (Nilpotent) Lie ring
17B62
20N20
Engel Lie ring
fuzzy hyperring
strongly regular relation
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Title Characterization of Derived Nilpotent (Engel) Lie Ring of Fuzzy Hyperrings by Using Fuzzy Strongly Regular Relations
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