Algorithms to Compute The Demonic Transitive Closure of Fuzzy Relations Using Demonic Operators

Abstract

In this paper, we investigate the demonic transitive closure of fuzzy relations in the sense of demonic operators. To address this, we focus on the demonic order refinement of fuzzy relations, which has a special treatment associated with the membership function of fuzzy relations. We look closely at the transitive closure of fuzzy relations with the use of angelic operators (the usual operators ∪, ∩ and ◦) and reform it by applying the demonic operators (˜⊔, ˜⊓ and ˜□ ). In order to carry out this task, we adopt existing algorithms and reformulate them in the means of demonic operators.