Nodal filters in hoop algebras

• Published in: Soft computing (Berlin, Germany) Vol. 22; no. 21; pp. 7119 - 7128
• Main Authors: Namdar, A., Borzooei, R. A.
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.11.2018; Springer Nature B.V
• Subjects: Algebra; Artificial Intelligence; Computational Intelligence; Control; Engineering; Foundations; Hoops; Mathematical Logic and Foundations; Mechatronics; Monoids; Robotics; Heyting algebra; Node; Hertz algebra; Hilbert algebra; BCK-algebra; Kleene algebra; Semi-De Morgan algebra; Hoop; Nodal filter

Hoop algebras or hoops are naturally ordered commutative residuated integral monoids, introduced by Bosbach (Fundam Math 64:257–287, 1969 , Fundam Math 69:1–14, 1970 ). In this paper, we introduce the notions of node and nodal filter in hoops and study some properties of them. First, we prove that t...