@article{Wu2022, 
author = {Yaoqiang Wu},
title = {On (fuzzy) pseudo-semi-normed linear spaces},
year = {2022},
journal = {AIMS Mathematics},
volume = {7},
number = {1},
pages = {467-477},
keywords = {pseudo-norm, pseudo-semi-norm, fuzzy pseudo-norm, fuzzy pseudo-semi-norm, fuzzy pseudo-semi-norm linear space},
url = {https://www.sciopen.com/article/10.3934/math.2022030},
doi = {10.3934/math.2022030},
abstract = {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                     a            ~      d                     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.}
}