Some lattices associated with LM-fuzzy topological spaces

Article type: Research Article

Authors: Vivek, S.^{; *} | Mathew, Sunil C.^{; 1}

Affiliations: Department of Mathematics, St. Thomas College, Palai, Arunapuram, Kottayam, Kerala, India

Correspondence: [*] Corresponding author. Sunil C. Mathew, Department of Mathematics, St. Thomas College, Palai, Arunapuram P.O. 686574, Kottayam, Kerala, India. E-mail: [email protected].

Note: [1] +91 9496308382, E-mail: [email protected].

Abstract: This paper studies the closure and interior operators in LM-fuzzy topological spaces. The algebraic structures associated with various collections of closed sets and open sets are identified. Further, certain lattices formed by these algebraic structures are obtained and some lattice theoretic properties of the same are investigated. Corresponding to every element in M, the study associates a lattice of monoids which is determined by various types of closed sets and open sets.

Keywords: LM-fuzzy topology, Closure operator, Lattice, Monoid

Keywords: 54A40

DOI: 10.3233/JIFS-210195

Journal: Journal of Intelligent & Fuzzy Systems, vol. 40, no. 6, pp. 12101-12109, 2021