Redundancy of fuzzy soft topological spaces

Article type: Research Article

Authors: Shi, Fu-Gui | Pang, Bin

Affiliations: School of Mathematics and Statistics, Beijing Institute of Technology, Beijing, P.R. China

Note: [] Corresponding author. F.-G. Shi, School of Mathematics and Statistics, Beijing Institute of Technology, Beijing 100081, China. +86 1068918069; E-mails: fuguishi@bit.edu.cn (F.-G. Shi), pangbin1205@163.com (B. Pang).

Abstract: In this paper, it is shown that there is a complement preserving isomorphism (preserving arbitrary union and arbitrary intersection) between the lattice ($\mathcal{FS}(X,E),\sqsubseteq$) of all fuzzy soft sets on X and the I-powerset lattice (IX × E,≤) of all fuzzy subsets of X × E. It therefore follows that fuzzy soft topologies are redundant and unnecessarily complicated in theoretical sense.

Keywords: Fuzzy set, soft set, fuzzy soft set, fuzzy soft topology

DOI: 10.3233/IFS-141141

Journal: Journal of Intelligent & Fuzzy Systems, vol. 27, no. 4, pp. 1757-1760, 2014