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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

intuitionistic fuzzy soft strong hyper BCK-ideal --- time-varying artificial neuron --- clustering protocols --- 1-hypergroup --- fuzzy multi-Hv-ideal --- multisets --- q-rung picture fuzzy line graphs --- semi-symmetry --- rough set --- quasi-multiautomaton --- height --- transposition hypergroup --- Hv-ring --- m-polar fuzzy hypergraphs --- Hv-structures --- selection operation --- upper approximation --- invertible subhypergroup --- breakable semigroup --- intuitionistic fuzzy soft weak hyper BCK ideal --- functions on multiset --- submultiset --- m-polar fuzzy equivalence relation --- semihypergroup --- granular computing --- q-rung picture fuzzy graphs --- linear differential operator --- perfect edge regular --- Hv-ideal --- lower BCK-semilattice --- square q-rung picture fuzzy graphs --- minimal prime decomposition --- level hypergraphs --- hyperfield --- quasi-automaton --- hyperring --- semi-prime closure operation --- edge regular --- UWSN --- (hyper)homography --- relative annihilator --- hypergroup --- intuitionistic fuzzy soft s-weak hyper BCK-ideal --- fundamental equivalence relation --- intuitionistic fuzzy soft hyper BCK ideal --- hyperideal --- lower approximation --- multiset --- fundamental relation --- ego networks --- application --- minimal prime factor --- single-power cyclic hypergroup --- ordered group --- fuzzy multiset