Extension of HyperAlgebra to SuperHyperAlgebra and Neutrosophic SuperHyperAlgebra (Revisited)

Smarandache, Florentín

doi:10.1007/978-3-031-16684-6_36

Cited by 5 publications

(6 citation statements)

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“…The relation between the n-closed graphs of subspace graph topology and the ambient graph topological space can be verified. Some significant works in a similar area can be found in [8,9]. All these facts highlights the wide scope for further investigation in the area concerned.…”

Section: Discussionmentioning

confidence: 64%

Subspace graph topological space of graphs

Aniyan

Naduvath

2023

Proyecciones (Antofagasta)

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A graph topology defined on a graph G is a collection 𝒯 of subgraphs of G which satisfies the properties such as K0, G ∈ 𝒯 and 𝒯 is closed under arbitrary union and finite intersection. Let (X, T) be a topological space and Y ⊆ X then, TY = {U ∩ Y : U ∈ T} is a topological space called a subspace topology or relative topology defined by T on Y. In this P1 we discusses the subspace or the relative graph topology defined by the graph topology 𝒯 on a subgraph H of G. We also study the properties of subspace graph topologies, open graphs, d-closed graphs and nbd-closed graphs of subspace graph topologies.

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Section: Discussionmentioning

confidence: 64%

Subspace graph topological space of graphs

Aniyan

Naduvath

2023

Proyecciones (Antofagasta)

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“…means to split C into three parts (two parts opposite to each other, and another part which is the neutral / indeterminacy between the opposites), as pertinent to neutrosophy {(< A >, < neutA >, < antiA >), or with other notation (T, I, F )}, meaning cases where C is partially true (T ), partially indeterminate (I), and partially false (F ). While anti-sophication of C means to totally deny C (meaning that C is made false on its whole domain) (for detail see Smarandache [21,22,24,25]). Neutro-sophication of an axiom on a given set X, means to split the set X into three regions such that: on one region the axiom is true (we say degree of truth T of the axiom), on another region the axiom is indeterminate (we say degree of indeterminacy I of the axiom), and on the third region the axiom is false (we say degree of falsehood F of the axiom), such that the union of the regions covers the whole set, while the regions may or may not be disjoint, where (T, I, F ) is different from (1, 0, 0) and from (0, 0, 1).…”

Section: Preliminariesmentioning

confidence: 99%

“…Smarandache in [23] revisited the notions of neutroalgebras and antialgebras, where he studied partial algebras, Universal algebras, Effect algebras and Boole ′ s partial algebras, and showed that neutroalgebras are generalization of partial algebras. Further, he extended the classical hyperalgebra to n-ary hyperalgebra and its alternatives n-ary neutrohyperalgebra and n-ary antihyperalgebra [25].…”

Section: Introductionmentioning

confidence: 99%

On Neutro-LA-semihypergroups and Neutro-Hv-LA-semigroups

Mirvakili

Rezaei

Al-Shanqiti

et al. 2023

Preprint

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In this paper, we extend the notion of LA-semihypergroups (resp. Hv-LA-semigroups) to neutro-LA-semihypergroups (respectively, neutro-Hv-LA-semigroups). Anti-LA-semihypergroups (respectively, anti-Hv-LA-semigroups) are studied and investigated some of their properties. We show that these new concepts are di fferent from classical concepts by several examples. These are particular cases of the classical algebraic structures generalized to neutroalgebraic structures and antialgebraic structures (Smarandache, 2019). 2000 Mathematics subject classification: 20N20, 20N99.

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“…• On the Figure (13), the neutrosophic SuperHyperNotion, namely, neutrosophic 1-failed SuperHyperForcing, is up. There's neither empty neutrosophic SuperHyperEdge nor loop neutrosophic SuperHyperEdge.…”

Section: T a (X) = Min[t A (V I )T A (V J )] Vivj ∈ X I A (X) = Min[i...mentioning

confidence: 99%

Untitled

2023

J Math Techniques Comput Math

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In this research, new setting is introduced for new SuperHyperNotion, namely, Neutrosophic 1-failed SuperHyperForcing. Two different types of SuperHyperDefinitions are debut for them but the research goes further and the SuperHyper-Notion, SuperHyperUniform, and SuperHyperClass based on that are well-defined and well-reviewed. The literature review is implemented in the whole of this research. For shining the elegancy and the significancy of this research, the comparison between this SuperHyperNotion with other SuperHyperNotions and fundamental SuperHyperNumbers are featured. The definitions are followed by the examples and the instances thus the clarifications are driven with different tools. The applications are figured out to make sense about the theoretical aspect of this ongoing research. The "Cancer's Neutrosophic Recognition" are the under research to figure out the challenges make sense about ongoing and upcoming research. The special case is up. The cells are viewed in the deemed ways. There are different types of them. Some of them are individuals and some of them are well-modeled by the group of cells. These types are all officially called "SuperHyperVertex" but the relations amid them all officially called "SuperHyperEdge". The frameworks "Su-perHyperGraph" and "neutrosophic SuperHyperGraph" are chosen and elected to research about "Cancer's Neutrosophic Recognition". Thus these complex and dense SuperHyperModels open up some avenues to research on theoretical segments and "Cancer's Neutrosophic Recognition". Some avenues are posed to pursue this research. It's also officially collected in the form of some questions and some problems. Assume a SuperHyperGraph. Then a "1-failed SuperHyperForcing" Z(NSHG) for a neutrosophic SuperHyperGraph is the maximum cardinality of a SuperHyperSet S of black SuperHyperVertices (whereas SuperHyperVertices in V (G) \ S are colored white) such that V (G) isn't turned black after finitely many applications of "the color-change rule": a white SuperHyperVertex is converted to a black SuperHyperVertex if it is the only white SuperHyperNeighbor of a black SuperHyperVertex. The additional condition is referred by "1-" about the usage of any black SuperHyperVertex only once to act on white SuperHyperVertex to be black SuperHyperVertex; a "neutrosophic 1-failed SuperHyperForcing" Z n (NSHG) for a neutrosophic SuperHyperGraph is the maximum neutrosophic cardinality of a SuperHyperSet S of black SuperHyperVertices (whereas SuperHyperVertices in V (G) \ S are colored white) such that V (G) isn't turned black after finitely many applications of "the color-change rule":a white SuperHyperVertex is converted to a black SuperHyperVertex if it is the only white SuperHyperNeighbor of a black SuperHyperVertex. The additional condition is referred by "1-" about the usage of any black SuperHyperVertex only once to act on white SuperHyperVertex to be black SuperHyperVertex. Assume a SuperHyperGraph. Then an "δ−1-failed SuperHyperForcing" is a maximal 1-failed SuperHyperForcing of SuperHyper...

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Extension of HyperAlgebra to SuperHyperAlgebra and Neutrosophic SuperHyperAlgebra (Revisited)

Cited by 5 publications

References 5 publications

Subspace graph topological space of graphs

Subspace graph topological space of graphs

On Neutro-LA-semihypergroups and Neutro-Hv-LA-semigroups

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