Hypergroups and Fuzzy Sets Associated modulo a Subgroup
نویسنده
چکیده
This paper is the results of the ideas suggested by P. Corsini in his paper [10]. Our investigations take in account the paper [13] of I. Cristea. We study the hypergroup generated by the cosets modulo a subgroup (normal subgroup). We prove that (G/H, ◦4) is a complete hypergroup. We take many particular examples to illustrate some known results on hypergroups. Keyword: fuzzy sets, hypergroups, complete hypergroup, hyperoperation.
منابع مشابه
FUZZY GRADE OF THE COMPLETE HYPERGROUPS
This paper continues the study of the connection between hyper- groups and fuzzy sets, investigating the length of the sequence of join spaces associated with a hypergroup. The classes of complete hypergroups and of 1-hypergroups are considered and analyzed in this context. Finally, we give a method to construct a nite hypergroup with the strong fuzzy grade equal to a given natural number
متن کاملFUZZY GRADE OF I.P.S. HYPERGROUPS OF ORDER 7
i.p.s. hypergroups are canonical hypergroups such that$[forall(a,x),a+xni x]Longrightarrow[a+x=x].$i.p.s. hypergroups were investigated in [1], [2], [3], [4] and it was proved thatif the order is less than 9, they are strongly canonical (see [13]). In this paperwe obtain the sequences of fuzzy sets and of join spaces determined (see [8])by all i.p.s. hypergroups of order seven. For the meaning ...
متن کامل(Intuitionistic) Fuzzy Grade of a Hypergroupoid: A Survey of Some Recent Researches
This paper aims to present a short survey on two numerical functions determined by a hypergroupoid, called the fuzzy grade and the intuitionistic fuzzy grade of a hypergroupoid. It starts with the main construction of the sequences of join spaces and (intuitionistic) fuzzy sets associated with a hypergroupoid. After some computations of the above grades, we discuss some similarities and differe...
متن کاملHX-hypergroups associated with the direct products of some ${bf Z}/n {bf Z}$
One studies the $HX$-hypergroups, corresponding to the Chinese hypergroups associated with the direct products of some ${bf Z}/n {bf Z},$ calculating their fuzzy grades.
متن کاملATANASSOV'S INTUITIONISTIC FUZZY GRADE OF I.P.S. HYPERGROUPS OF ORDER LESS THAN OR EQUAL TO 6
In this paper we determine the sequences of join spaces and Atanassov's intuitionistic fuzzy sets associated with all i.p.s. hypergroups of order less than or equal to 6, focusing on the calculation of their lengths.
متن کامل