A textural view of soft fuzzy rough sets

Article type: Research Article

Authors: Dost, Şenol^*

Affiliations: Department of Secondary Science and Mathematics Education, Hacettepe University, Beytepe, Ankara, Turkey

Correspondence: [*] Corresponding author. Şenol Dost, Department of Secondary Science and Mathematics Education, Hacettepe University, Beytepe, Ankara, Turkey. Tel.: +90 312 2976104; Fax: +90 312 2978600; E-mail: [email protected].

Abstract: This paper aims to give a new insight for soft fuzzy sets. Firstly, using textural soft fuzzy direlations on a soft fuzzy lattice, we obtain a soft fuzzy rough set algebra where the inverse soft fuzzy relation and inverse soft fuzzy corelation are the upper approximation and lower approximation, respectively. On the other hand, we consider Alexandroff soft fuzzy topology and we prove that there exists a one-to-one correspondence between the Alexandroff topologies and the reflexive and transitive direlations on a texture space.

Keywords: Texture space, direlation, soft fuzzy set, rough set, approximation operator

DOI: 10.3233/IFS-151531

Journal: Journal of Intelligent & Fuzzy Systems, vol. 28, no. 6, pp. 2519-2535, 2015