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In this paper we extend the SuperHyperAlgebra, SuperHyperGraph, SuperHyperTopology, SuperHyperSoft Set, endowed with SuperHyperOperations, SuperHyperAxioms, and SuperHyperFunctions, to the most general form of structure, from our real world, called SuperHyperStructure in any field of knowledge. A practical application of the SuperHyperStructure is presented at the end. The prefix “Hyper” [Marty, 1934] stand for the codomain of the functions and operations to be P(H), or the powerset of the set H. While the prefix “Super” [Smarandache, 2016] stands for using the Pn (H), n ≥ 2, or the n-th PowerSet of the Set H {because the set (or system) 𝐻 (that may be a set of items, a company, institution, country, region, etc.) is organized in sub-systems, which in their turn are organized in sub-sub-systems, and so on} in the domain and/or codomain of the functions and operations.

The theory of superhyperalgebras is a new concept in the study of all branches of algebra structures. In this paper, we introduce a novel concept of (m, n)-superhyper G-algebra and present several results from the study of certain properties of (m, n)-superhyper G-algebras. The purpose of this paper is the study an extension of G-algebras to (m, n)-superhyper G-algebras, as a generalization of a logic algebra. The main motivation of this work was obtained based on an extension of G-algebra to superhyper G-algebra based on the n th-power set of a set.

The aim of this paper is to extend the concept of hyperideals to the SuperHyperAlgebras. In this paper, we introduce the concept of 2-SuperHyperLeftAlmostSemihypergroups which is a generalization of LA-semihypergroups. Furthermore, we define and study 2-SuperHyper-LA-subsemihypergroups, SuperHyperLeft(Right)HyperIdeals and SuperHyperHyperIdeals of 2-SuperHyperLeftAlmostSemihypergroups, and related properties are investigated. We give an example to show that in general these two notions are different. Finally, we show that every SuperHyperRightHyperIdeal of 2-SuperHyper-LA-semihypergroup S with pure left identity is SuperHyperHyperIdeal.

In this paper, one recalls the general definition of the SuperHyperAlgebra with its SuperHyperOperations and SuperHyperAxioms [2, 6]. Then one introduces for the first time the SuperHyperTopology and especially the SuperHyperFunction and Neutrosophic SuperHyperFunction. One gives a numerical example of a Neutro-SuperHyperGroup.