Abstract
In this article, after describing some examples to explain the concept of fuzzy multiplicative (m, n)-hyperrings (F(m,n)-hyperrings), we will offer some related properties. Also, by defining F-hyperideals and regular relations, we will study the quotient of multiplicative F(m,n)-hyperrings. Finally, we will generalize the classical isomorphism theorems of groups to multiplicative F(m,n)-hyperrings.
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References
1.
Corsini
P.
,
Davvaz
B.
and
Leoreanu-Fotea
V.
, Atanassov’s intuitionistic (s, t)-fuzzy n -ary subhypergroups and their properties , Inform Sci 179 (5 ) (2009 ), 654 –666 .
2.
Davvaz
B.
, Fuzzy krasner (m, n)-hyperrings , Comput Math Appl 59 (12 ) (2010 ), 3879 –3891 .
3.
Davvaz
B.
, Isomorphism theorems on hyperrings , Indian J Pure Appl Math 35 (3 ) (2004 ), 321 –331 .
4.
Davvaz
B.
and
Corsini
P.
, Fuzzy n -ary hypergroups , J Intell Fuzzy Systems 18 (4 ) (2007 ), 377 –382 .
5.
Davvaz
B.
and
Leoreanu-Fotea
V.
, Binary relations on ternary semihypergroups , Comm Algebra 38 (10 ) (2010 ), 3621 –3636 .
6.
Davvaz
B.
and
Leoreanu-Fotea
V.
, Hyperring Theory and Applications , International Academic Press , Palm Harbor, USA , 2007 .
7.
Davvaz
B.
and
Mirvakili
S.
, Relations on krasner (m, n)- hyperrings , European J Combin 31 (2010 ), 790 –802 .
8.
Davvaz
B.
and
Vougiouklis
T.
, n -ary hypergroups , Iran J Sci Technol Trans A 30 (2 ) (2006 ), 165 –174 .
9.
Farshi
M.
and
Davvaz
B.
, Krasner F(m;n)-Hyperrings , Iran J Fuzzy Systems 11 (6 ) (2014 ), 67 –88 .
10.
Farshi
M.
and
Davvaz
B.
, On isomorphism theorems ofFn-polygroups , J Sci I R Iran 24 (3 ) (2013 ), 259 –267 .
11.
Kazancı
O.
and
Davvaz
B.
, Fuzzy n -ary polygroups related to fuzzy points , Comput Math Appl 58 (7 ) (2009 ), 1466 –1474 .
12.
Leoreanu-Fotea
V.
and
Davvaz
B.
, Fuzzy hyperrings , Fuzzy Sets and Systems 160 (16 ) (2009 ), 2366 –2378 .
13.
Leoreanu-Fotea
V.
and
Davvaz
B.
, Join n-spaces and lattices , J Mult-Valued Logic Soft Comput 15 (5-6 ) (2009 ), 421 –432 .
14.
Leoreanu-Fotea
V.
and
Davvaz
B.
, n -hypergroups and binary relations , European J Combin 29 (5 ) (2008 ), 1207 –1218 .
15.
Leoreanu-Fotea
V.
,
Zhan
J.
and
Leoreanu
L.
, FuzzyΓ -hyperrings and fuzzy Γ -hypermodules , J Intell Fuzzy Systems 24 (3 ) (2013 ), 647 –655 .
16.
Nakassis
A.
, Expository and survey article recent results in hyperring and hyperfield theory , Internat J Math Math Sci 11 (1988 ), 209 –220 .
17.
Rota
R.
, Sugli iperanelli moltiplicativi,(4) , Rend Di Mat 7 (2 ) (1982 ), 711 –724 .
18.
Waphare
B.N.
and
Ghadiri
M.
, n-ary polygroups , Iran J Sci Technol Trans A 33 (2 ) (2009 ), 145 –158 .
19.
Yamak
S.
,
Kazancı
O.
and
Davvaz
B.
, On n -ary hypergroups and fuzzy n -ary homomorphism , Iran J Fuzzy Syst 8 (1 ) (2011 ), 65 –76 .
20.
Zadeh
L.A.
, Fuzzy sets , Inform and Control 8 (1065 ), 338 –353 .
21.
Zahedi
M.
and
Hasankhani
A.
, F -polygroups. I , J Fuzzy Math 4 (3 ) (1996 ), 533 –548 .
22.
Zahedi
M.
and
Hasankhani
A.
, F -polygroups. II , Inform Sci 89 (3-4 ) (1996 ), 225 –243 .
23.
Zhan
J.
, Fuzzy soft Γ -hyperrings , Iran J Sci Technol Trans A Sci 36 (2 ) (2012 ), 125 –135 .
24.
Zhan
J.
and
Davvaz
B.
, Fuzzy isomorphism theorems of soft Γ -hyperrings , An Stiint Univ Al I Cuza Iasi Mat (N.S.) 60 (2 ) (2014 ), 279 –292 .
