Extension of HyperGraph to n-SuperHyperGraph and to Plithogenic n-SuperHyperGraph, and Extension of HyperAlgebra to n-ary (Classical-/Neutro-/Anti-)HyperAlgebra

• Main Author: Florentin Smarandache
• Format: Article
• Language: English
• Published: University of New Mexico 2020-05-01
• Series: Neutrosophic Sets and Systems
• Subjects: n-power set of a set; n-superhypergraph (n-shg); n-shg-vertex; n-shg-edge; plithogenic n-superhypergraph; n-ary hyperoperation; n-ary hyperaxiom; n-ary hyperalgebra; n-ary neutrohyperoperation; n-ary neutrohyperaxiom; n-ary neutrohyperalgebra; n-ary antihyperoperation; n-ary antihyperaxiom; n-ary antihyperalgebra
• Online Access: http://fs.unm.edu/NSS/n-SuperHyperGraph-n-HyperAlgebra.pdf

We recall and improve our 2019 concepts of n-Power Set of a Set, n-SuperHyperGraph, Plithogenic n-SuperHyperGraph, and n-ary HyperAlgebra, n-ary NeutroHyperAlgebra, n-ary AntiHyperAlgebra respectively, and we present several properties and examples connected with the real world.