Linear fuzzifying uniformities

Article type: Research Article

Authors: Jin, Zhen-Yu | Yan, Cong-Hua^{; *}

Affiliations: Institute of Math., School of Math. Sciences, Nanjing Normal University, Nanjing Jiangsu, People’s Republic of China

Correspondence: [*] Corresponding author. Cong-Hua Yan. Tel.: +8602585481541, Fax: +8602583598493. E-mail: [email protected].

Abstract: The main purpose of this paper is to study Hutton type fuzzifying uniformities on linear spaces. Firstly, we show that if a base of a fuzzifying uniformity defined over a linear space is translation-invariant, balanced and absorbed, then it generates a linear fuzzifying topology. From this linear fuzzifying topology, we can construct a new linear fuzzifying uniformity (i.e., a fuzzifying uniformity compatible with the linear structure) which is equivalent to the original fuzzifying uniformity. Secondly, the Hausdorff separation and complete boundedness in linear fuzzifying uniformities are investigated. In addition, as an example, the linear fuzzifying uniformity induced by a fuzzy norm is also discussed.

Keywords: Linear fuzzifying uniformity, linear fuzzifying topology, complete boundedness, Hausdorff separation axiom, fuzzy norm

DOI: 10.3233/JIFS-200702

Journal: Journal of Intelligent & Fuzzy Systems, vol. 40, no. 6, pp. 10453-10464, 2021