Affiliations: [a] School of Science, Xi’an Shiyou University, Xi’an, Shaanxi, China
| [b] Department of Mathematics, Shahid Beheshti University, Tehran, Iran
| [c]
Hatef Higher Education Institute, Zahedan, Iran
Correspondence:
[*]
Corresponding author. Dr. Jun Tao Wang, School of Science, Xi’an Shiyou University, Xi’an 710065, China. Tel.: +08615829065086; E-mails: [email protected]; [email protected].
Abstract: In this paper, we characterize the algebraic structure of hoops via stabilizers. First, we further study left and right stabilizers in hoops and discuss the relationship between them. Then, we characterize some special classes of hoops, for example, Wajsberg hoops, local hoops, Gödel hoops and stabilizer hoops, in terms of stabilizers. Finally, we further determine the relationship between stabilizers and filters in hoops and obtain some improvement results. This results also give answer to open problem, which was proposed in [Stabilizers in MTL-algebras, Journal of Intelligent and Fuzzy Systems, 35 (2018) 717-727]. These results will provide a more general algebraic foundation for consequence connectives in fuzzy logic based on continuous t-norms.
