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Symmetry in Classical and Fuzzy Algebraic Hypercompositional Structures
Irina Cristea
2020
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This book is a collection of 12 innovative research papers in the field of hypercompositional algebra, 7 of them being more theoretically oriented, with the other 5 presenting strong applicative aspects in engineering, control theory, artificial intelligence, and graph theory. Hypercompositional algebra is now a well-established branch of abstract algebra dealing with structures endowed with multi-valued operations, also called hyperoperations, having a set as the result of the interrelation between two elements of the support set. The theoretical papers in this book are principally related to three main topics: (semi)hypergroups, hyperfields, and BCK-algebra. Heidari and Cristea present a natural generalization of breakable semigroups, defining the breakable semihypergroups where every non-empty subset is a subsemihypergroup. Using the fundamental relation ? on a hypergroup, some new properties of the
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Keywords
- (hyper)homography
- 1-hypergroup
- application
- breakable semigroup
- clustering protocols
- edge regular
- ego networks
- functions on multiset
- fundamental equivalence relation
- fundamental relation
- fuzzy multi-Hv-ideal
- fuzzy multiset
- Granular computing
- height
- Hv-ideal
- Hv-ring
- Hv-structures
- hyperfield
- hypergroup
- hyperideal
- hyperring
- intuitionistic fuzzy soft hyper BCK ideal
- intuitionistic fuzzy soft s-weak hyper BCK-ideal
- intuitionistic fuzzy soft strong hyper BCK-ideal
- intuitionistic fuzzy soft weak hyper BCK ideal
- invertible subhypergroup
- level hypergraphs
- linear differential operator
- lower approximation
- lower BCK-semilattice
- m-polar fuzzy equivalence relation
- m-polar fuzzy hypergraphs
- minimal prime decomposition
- minimal prime factor
- multiset
- multisets
- ordered group
- perfect edge regular
- q-rung picture fuzzy graphs
- q-rung picture fuzzy line graphs
- quasi-automaton
- quasi-multiautomaton
- relative annihilator
- rough set
- selection operation
- semi-prime closure operation
- semi-symmetry
- semihypergroup
- single-power cyclic hypergroup
- square q-rung picture fuzzy graphs
- submultiset
- time-varying artificial neuron
- transposition hypergroup
- upper approximation
- UWSN
Links
DOI: 10.3390/books978-3-03928-709-3Editions
