Crossing Cubic Structures Applied to Hoop Algebras

Anas Al-Masarwah1,∗, Fawziah Alharthi2, Noor Bani Abd Al-Rahman1

1Department of Mathematics, Faculty of Science, Ajloun National University, P.O. Box 43, Ajloun 26810,

Jordan

2Department of Mathematics, College of Science, Qassim University, Buraydah, Saudi Arabia

Emails: almasarwah85@gmail.com; f.alharthi@qu.edu.sa; noorbaniabdalrahman@gmail.com

Abstract

Recent years have witnessed remarkable developments in fuzzy logic, with interval-valued fuzziness and neg-

ative structures emerging as powerful tools for modeling inaccurate phenomena. The crossing cubic struc-

tures (CCs), as a generalization of the bipolar fuzziness structures, represent a comprehensive mathematical

framework capable of dealing with a wide range of fuzziness and contradictory data, thus expanding research

prospects in this area. This paper has made a new contribution to some algebraic structures by investigating

the concept of CCs on algebraic substructures in a hoop algebra. The concepts of crossing cubic sub-hoops

(CC − SHs) and crossing cubic filters (CCFs) are introduced, and a deeper understanding is sought to ana-

lyze their characteristics. The effect on the relationship between CC − SHs and CCFs is revealed, and the

characterizations of CC − SHs and CCFs are analyzed.

Keywords: Hoop algebras; Sub-Hoops; Filters; Crossing cubic structures; Crossing cubic sub-hoops; Cross-

ing cubic filters