# Actions, norms, subactions and kernels of (fuzzy) norms

J. S. Han, H. S. Kim, J. Neggers

Research output: Contribution to journalArticle

2 Citations (Scopus)

### 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 (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.

Original language English 141-147 7 Iranian Journal of Fuzzy Systems 7 2 Published - 2010 Oct 29

Fuzzy Norm
kernel
Norm
Complement
Module
Kernel

• (Fuzzy) norm
• (Sub) action
• Kernel

### Cite this

Han, J. S. ; Kim, H. S. ; Neggers, J. / Actions, norms, subactions and kernels of (fuzzy) norms. In: Iranian Journal of Fuzzy Systems. 2010 ; Vol. 7, No. 2. pp. 141-147.
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Actions, norms, subactions and kernels of (fuzzy) norms. / Han, J. S.; Kim, H. S.; Neggers, J.

In: Iranian Journal of Fuzzy Systems, Vol. 7, No. 2, 29.10.2010, p. 141-147.

Research output: Contribution to journalArticle

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