Authors: S.P. Tiwari; Shambhu Sharan; Bijan Davvaz
Addresses: Department of Applied Mathematics, Indian School of Mines, Dhanbad-826004, India ' Department of Applied Mathematics, Indian School of Mines, Dhanbad-826004, India ' Department of Mathematics, Yazd University, P.O. Box 89195-741, Yazd, Iran
Abstract: The study is to show a nice interplay among ℓ-valued approximation operator (ℓ is a complete orthomodular lattice) on an ℓ-valued approximation space, ℓ-valued topology and ℓ-valued automaton. We begin by noting that each ℓ-valued approximation space is associated with an ℓ-valued approximation operator, which turns out to be Kuratowski saturated ℓ-valued closure operator on X, if the ℓ-valued relation associated with ℓ-valued approximation space is ℓ-valued reflexive and ℓ-valued transitive. The ℓ-valued approximation operator gives rise to a saturated ℓ-valued topology on X. It is shown that the existence of dual ℓ-valued topology depends on the distributivity of associated lattice. The observations made so far are applied to ℓ-valued automata.
Keywords: ℓ-valued automata; ℓ-valued approximation space; ℓ-valued successor; ℓ-valued source; ℓ-valued topology; orthomodular lattice.
International Journal of Granular Computing, Rough Sets and Intelligent Systems, 2013 Vol.3 No.1, pp.85 - 94
Accepted: 11 Feb 2013
Published online: 23 May 2013 *