Algebraic hyperstructures represent a natural extension of classical algebraic structures. In a classical algebraic structure, the composition of two elements is an element, while in an algebraic hyperstructure, the composition of two elements is a set.
Hypersructure Theory was born in 1934, when Marty at the 8th Congress of Scandinavian Mathematiciens, gave the definition of hypergroup and illustrated some applications and showed its utility in the study of groups, algebraic functions and rational fractions. In the following years, around the 40’s, several others worked on this subject in France (Marty, Krasner, Kuntzman, Croisot), in USA (Dresher and Ore, Prenowitz, Eaton, Griffith, Wall), in Japan (Utumi), in Spain (San Juan), in Russia (Vikhrov), in Uzbekistan (Dietzman), and in Italy (Zappa).
In the 50’s and 60’s they worked on hyperstructures, in Romania (Benado), in Czech Republic (Drbohlav), in France (Koskas, Sureau), in Greece (Mittas, Stratigopoulos), in Italy (Orsatti, Boccioni), in USA (Graetzer, Pickett, McAlister), in Japan (Nakano), and in Yugoslavia (Dacic).
Around the 70’s and 80’s, hyperstructures where cultivated especially in Italy (Corsini, Tallini, Rota, Procesi Ciampi), in Greece (Konguetsof, Vougiouklis), in USA (Prenowitz, Jantoshak, Roth, Comer), in France (Krasner, Sureau, Koskas, Deza), and in Canada (Rosenberg).
Around the 90’s and more recently, many papers appeared, made in:
· Europe: Italy (Udine, Messina, Rome, Teramo, L’Aquila, Brescia, Palermo, Milano), France (Clermont-Ferrand, Lyon), Spain (Malaga), Finland (Oulu), Greece (Thessaloniki, Xanthi, Alexandroupolis, Patras, Athens), Romania (Iasi, Constanta), Czech Republic (Praha, Brno, Olomouc, Vyskov), Montenegro (Podgorica), Slovakia (Bratislava, Kosice).
· Asia: Iran (Babolsar, Yazd, Kerman, Bashan, Tehran, Zahedan, Zanjan, Sari-Branch), Thailand (Bangkok, Samutprakarn, Phitsanulok, Korea (Chinju, Taejon, Chungju), India (Kolkata, Tiruchendur, Tamilnadu), China (Chongqing, Xi’an), Japon (Tokyo, Tagajo), Jordan (Karak), Israel (Ramat Gan),
· America: USA (Charleston, New York, Cleveland, Ohio), Canada (Montreal).
The International Congress on Algebraic Hyperstructures and Applications (AHA) is a meeting of mathematicians working on hyperstructures and in resent years on fuzzy/rough/soft Hyperstructures, which is held once in three years, so it has a very long and fruitful tradition.
The event will be hosted in the Istanbul.