Hypergroup and join space induced by a fuzzy subset

Abstract

Zadeh in 1965 [17] introduced the notion of a fuzzy subset of a nonemptyset X as a function from Xto interval [0;1]. Rosenfeld [15] de ned the conceptof fuzzy group. Since then several researchers have studied in this eld, forexample see [1-4,7,12,14].The concept of a hypergroups introduced by F.Marty in 1934 [13]. Hy-pergroups are the largest class of multivalued systems that satisfy the axiomssimilar to groups.Now in this note by considering a fuzzy subset of a group Gand thefuzzy left (right) cosets of in G, we de ne the hyperoperation o

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