Affiliations: [a] Department of Mathematics, Payame Noor University, Tehran, Iran
| [b] Department of Mathematics and Science, University of New Mexico, Gallup, NM, USA
Correspondence:
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Corresponding author. Akbar Rezaei, Department of Mathematics, Payame Noor University, P.O. Box. 19395-3697, Tehran, Iran. Tel.: +98 9131405381; E-mail: rezaei@pnu.ac.ir
Abstract: In this paper, we extend the notion of Hv-semigroups to neutro-Hv-semigroups and anti-Hv-semigroups and investigate many of their properties. We show that these new concepts are different from the classical concept of Hv-semigroups by presenting several examples. In general, the neutro-algebras and anti-algebras are generalizations and alternatives of classical algebras. The goal and benefits of our proposed extension of this study is to explore not only the hyperoperations and axioms that are totally true as in previous algebraic hyperstructures, but also the cases when they have degrees of truth, indeterminacy and falsehood. Therefore, we enlarge the field of research.
