Affiliations: [a] Department of Mathematics, Golestan University, Gorgan, Iran
| [b] Department of Mechanical Engineering, Australian College of Kuwait, Mishref, Safat 13015, Kuwait and Centre for Infrastructure Engineering, Western Sydney University, Penrith 2751, NSW, Australia
| [c] Department of Materials Science and Engineering, Southern University of Science and Technology, Shenzhen 518055, People’s Republic of China | [d] Department of Statistics, The University of Auckland, Auckland, New Zealand
| [e] Department of Mathematics, Yazd University, Yazd, Iran
Correspondence:
[*]
Corresponding author. A. Amini, Department of Mechanical Engineering, Australian College of Kuwait, Mishref, Safat 13015, Kuwait and Centre for Infrastructure Engineering, Western Sydney University, Penrith 2751, NSW, Australia.
E-mails: a.amini@ack.edu.kw and a.amini@westernsydney.edu.au.
Abstract: Inspired by fuzzy hyperalgebras and fuzzy polynomial function (term function), some homomorphism properties of fundamental relation on fuzzy hyperalgebras are conveyed. The obtained relations of fuzzy hyperalgebra are utilized for certain applications, i.e., biological phenomena and genetics along with some elucidatory examples presenting various aspects of fuzzy hyperalgebras. Then, by considering the definition of identities (weak and strong) as a class of fuzzy polynomial function, the smallest equivalence relation (fundamental relation) is obtained which is an important tool for fuzzy hyperalgebraic systems. Through the characterization of these equivalence relations of a fuzzy hyperalgebra, we assign the smallest equivalence relation
αi1i2∗
on a fuzzy hyperalgebra via identities where the factor hyperalgebra is a universal algebra. We extend and improve the identities on fuzzy hyperalgebras and characterize the smallest equivalence relation
αJ∗
on the set of strong identities.
