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AIMS Mathematics

2022, Volume 7, Issue 1: 467-477. doi: 10.3934/math.2022030
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Research article

On (fuzzy) pseudo-semi-normed linear spaces

  • School of Mathematics and Arts, Suqian University, Suqian, 223800, Jiangsu, China
  • Received: 25 July 2021 Accepted: 09 October 2021 Published: 13 October 2021

  • MSC : 47A30, 54A21, 54A40

  • In this paper, we introduce the notion of pseudo-semi-normed linear spaces, following the concept of pseudo-norm which was presented by Schaefer and Wolff, and illustrate their relationship. On the other hand, we introduce the concept of fuzzy pseudo-semi-norm, which is weaker than the notion of fuzzy pseudo-norm initiated by N$ \tilde{\rm{a}} $d$ \tilde{\rm{a}} $ban. Moreover, we give some examples which are according to the commonly used $ t $-norms. Finally, we establish norm structures of fuzzy pseudo-semi-normed spaces and provide (fuzzy) topological spaces induced by (fuzzy) pseudo-semi-norms, and prove that the (fuzzy) topological spaces are (fuzzy) Hausdorff.

    Citation: Yaoqiang Wu. On (fuzzy) pseudo-semi-normed linear spaces[J]. AIMS Mathematics, 2022, 7(1): 467-477. doi: 10.3934/math.2022030

    Related Papers:

  • In this paper, we introduce the notion of pseudo-semi-normed linear spaces, following the concept of pseudo-norm which was presented by Schaefer and Wolff, and illustrate their relationship. On the other hand, we introduce the concept of fuzzy pseudo-semi-norm, which is weaker than the notion of fuzzy pseudo-norm initiated by N$ \tilde{\rm{a}} $d$ \tilde{\rm{a}} $ban. Moreover, we give some examples which are according to the commonly used $ t $-norms. Finally, we establish norm structures of fuzzy pseudo-semi-normed spaces and provide (fuzzy) topological spaces induced by (fuzzy) pseudo-semi-norms, and prove that the (fuzzy) topological spaces are (fuzzy) Hausdorff.


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