### Abstract

In this paper, we introduce the notion of an action Yx as a generalization of the notion of a module, and the notion of a norm A: Yx → F, where F is a field and A (xy) A (y^{1}) = A (y) A (xy^{1}) as well as the notion of fuzzy norm, where A: Yx → [0,1] C R, with R the set of all real numbers. A great many standard mappings on algebraic systems can be modeled on norms as shown in the examples and it is seen that Ker A= {y\ A (y) = 0} has many useful properties. Some are explored, especially in the discussion of fuzzy norms as they relate to the complements of subactions Nx of Yx.

Original language | English |
---|---|

Pages (from-to) | 141-147 |

Number of pages | 7 |

Journal | Iranian Journal of Fuzzy Systems |

Volume | 7 |

Issue number | 2 |

State | Published - 2010 Oct 29 |

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### Keywords

- (Fuzzy) norm
- (Sub) action
- Kernel

### Cite this

*Iranian Journal of Fuzzy Systems*,

*7*(2), 141-147.

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*Iranian Journal of Fuzzy Systems*, vol. 7, no. 2, pp. 141-147.

**Actions, norms, subactions and kernels of (fuzzy) norms.** / Han, J. S.; Kim, H. S.; Neggers, J.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Actions, norms, subactions and kernels of (fuzzy) norms

AU - Han, J. S.

AU - Kim, H. S.

AU - Neggers, J.

PY - 2010/10/29

Y1 - 2010/10/29

N2 - In this paper, we introduce the notion of an action Yx as a generalization of the notion of a module, and the notion of a norm A: Yx → F, where F is a field and A (xy) A (y1) = A (y) A (xy1) as well as the notion of fuzzy norm, where A: Yx → [0,1] C R, with R the set of all real numbers. A great many standard mappings on algebraic systems can be modeled on norms as shown in the examples and it is seen that Ker A= {y\ A (y) = 0} has many useful properties. Some are explored, especially in the discussion of fuzzy norms as they relate to the complements of subactions Nx of Yx.

AB - In this paper, we introduce the notion of an action Yx as a generalization of the notion of a module, and the notion of a norm A: Yx → F, where F is a field and A (xy) A (y1) = A (y) A (xy1) as well as the notion of fuzzy norm, where A: Yx → [0,1] C R, with R the set of all real numbers. A great many standard mappings on algebraic systems can be modeled on norms as shown in the examples and it is seen that Ker A= {y\ A (y) = 0} has many useful properties. Some are explored, especially in the discussion of fuzzy norms as they relate to the complements of subactions Nx of Yx.

KW - (Fuzzy) norm

KW - (Sub) action

KW - Kernel

UR - http://www.scopus.com/inward/record.url?scp=77958515768&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:77958515768

VL - 7

SP - 141

EP - 147

JO - Iranian Journal of Fuzzy Systems

JF - Iranian Journal of Fuzzy Systems

SN - 1735-0654

IS - 2

ER -