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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

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This book is intended as an introduction to fuzzy algebraic hyperstructures. As the first in its genre, it includes a number of topics, most of which reflect the authors’ past research and thus provides a starting point for future research directions. The book is organized in five chapters. The first chapter introduces readers to the basic notions of algebraic structures and hyperstructures. The second covers fuzzy sets, fuzzy groups and fuzzy polygroups. The following two chapters are concerned with the theory of fuzzy Hv-structures: while the third chapter presents the concept of fuzzy Hv-subgroup of Hv-groups, the fourth covers the theory of fuzzy Hv-ideals of Hv-rings. The final chapter discusses several connections between hypergroups and fuzzy sets, and includes a study on the association between hypergroupoids and fuzzy sets endowed with two membership functions. In addition to providing a reference guide to researchers, the book is also intended as textbook for undergraduate and graduate students.

Engineering. --- Computational Intelligence. --- General Algebraic Systems. --- Symbolic and Algebraic Manipulation. --- Algebra --- Algebra. --- Ingénierie --- Algèbre --- Data processing. --- Informatique --- Engineering & Applied Sciences --- Computer Science --- Computer science --- Computational intelligence. --- Mathematics. --- Intelligence, Computational --- Artificial intelligence --- Soft computing --- Mathematics --- Mathematical analysis --- Computer mathematics --- Discrete mathematics --- Electronic data processing --- Construction --- Industrial arts --- Technology --- Computer science—Mathematics. --- Fuzzy sets. --- Sets, Fuzzy --- Fuzzy mathematics --- Set theory