Fuzzy complete lattices, Alexandrov L-topologies and fuzzy rough sets

Article type: Research Article

Authors: Ko, Jung Mi | Kim, Yong Chan^{; *}

Affiliations: Department of Mathematics, Gangneung-Wonju NationalUniversity, Gangneung, Gangwondo, Korea

Correspondence: [*] Corresponding author. Yong Chan Kim, Department of Mathematics, Gangneung-Wonju National University, Gangneung, Gangwondo 25457, Korea. E-mail: [email protected].

Abstract:  We introduce the concepts of fuzzy join complete lattices and Alexandrov L-pretopologies in complete residuated lattices. We show that fuzzy join complete lattices, Alexandrov L-pretopologies, fuzzy meet complete lattices and Alexandrov L-precotopologies are equivalent. Moreover, we define L-preinterior operators (resp. L-preclosure operators) as a viewpoint of fuzzy joins (resp. fuzzy meet) and fuzzy rough sets. Furthermore their properties and examples are investigated.

Keywords: Complete residuated lattices, fuzzy join(meet)-complete lattices Alexandrov L-pre(co)topologies, fuzzy rough sets

DOI: 10.3233/JIFS-191344

Journal: Journal of Intelligent & Fuzzy Systems, vol. 38, no. 3, pp. 3253-3266, 2020