We introduce the notion of fuzzy soft hypealgebras as an extension of the notion of soft hyperalgebras as well as soft algebras. Also, some basic properties of fuzzy soft sets and homomorphisms between fuzzy soft hypealgebras are presented and discussed. Finally, we study the image and inverse image of a fuzzy soft hypealgebra under a fuzzy soft hyperalgebra homomorphism.
G.E.Hansoul, A simultaneous characterization of subalgebras and conditional subal-gebras of multialgebra, Bull Soc Roy Science Liege50 (1981), 16–19.
13.
S.Hoskova and A.Maturo, Decision-making process using hyperstructures and fuzzy structures in social sciences, soft computing applications for group decision-making and consensus modeling, Studies in Fuzziness and Soft Computing (2017), 103–111.
14.
S.Hoskova and A.Maturo, Fuzzy sets and algebraic hyperoperations to model interpersonal relations, recent trends in social systems: Quantitative theories and quantitative models, Studies in Systems, decision and Control (2016), 211–221.
15.
S.Hoskova and A.Maturo, On some applications of fuzzy sets for the management of teaching and relationships in schools, models and theories in social systems, Studies in system, Decision and Control (2018), 343–353.
16.
H.Jiang, J.Zhan and D.Chen, Covering based variable precision (I,T)-fuzzy rough sets with applications to multi-attribute decision-making, IEEE Transactions on Fuzzy Systems. DOI 10.1109/TFUZZ.2018.2883023
17.
V.Leoreanu, B.Davvaz, F.Feng and C.Chiper, Join spaces, soft join spaces and lattices, An Sţ Univ Ovidius Constantą, VERSITA22(1) (2014), 155–167.
18.
V.Leoreanu, F.Feng and J.Zhan, Fuzzy soft hypergroups, International Journal of Computer Mathematics89(8) (2012), 963–974.
19.
F.Marty, Surnue generaliz-ation de la notion de group, 8iem course, Math Scandinaves Stockholm (1934), 45–49.
20.
D.Molodtsov, Soft set theory- first results, Comput Math Appl37(4-5) (1999), 19–31.
21.
J.N.Mordeson and M.S.Malik, Fuzzy commutative algebra, Word Publ, 1998.
22.
C.Pelea, On the direct limit of a direct system of multialgebras, Discrete Mathematics306 (2006), 2916–2930.
23.
H.E.Pikett, Subdirect representations of relational systems, Fund Math56 (1964), 223–240.
24.
H.E.Pikett, Homomorphisms and subalgebras of multialgebras, Pacific J of Math21 (1967), 327–343.
25.
R.Rosenfeld, Fuzzy groups, J Math Anal Appl35 (1971), 512–517.
26.
D.Schweigert, Congruence relations of multialgebras, Discrete Mathematics53 (1985), 249–253.
27.
G.Selvachandran and A.R.Salleh, Soft hypergroups and soft hypergroup homomorphism, Proceeding of the 20th National Symp Math Scie, AIP Conf2013, 821–827.
28.
J.Šlapal, On Exponentiations of universal hyperalgebras, Algebra Universalis44 (2000), 187–193.
29.
T.Vougiuklis, Hyperstructures and their representations, Hardonic, Press, Inc, 1994.
30.
I.Wang, M.Yin and W.Gu, Soft polygroups, Comput Math Appl62 (2011), 3529–3537.
31.
S.Yamaka, O.Kazanci and B.Davvaz, Soft hyperstructures, Comput Math Appl62 (2011), 797–803.
32.
L.A.Zadeh, Fuzzy sets, Inform and Control8 (1965), 338–353.
33.
J.Zhan, V.Leoreanu and T.Vougiouklis, Fuzzy soft -hypermodule, UPB Sci Bull, Series A73(3) (2011), 13–28.
34.
J.Zhan, B.Sun and J.C.R.Alcantud, Covering based multigranulation (I,T)-fuzzy rough set models and applications in multi-attribute group decision-making, Information Sciences476 (2019), 290–318.
35.
L.Zhang, J.Zhan and Z.X.Xu, Covering-based generalized IF rough sets with applications to multi-attribute decision-making, Information Sciences478 (2019), 275–302.
36.
K.Zhang, J.Zhan, W.Z.Wu and J.C.R.Alcantud, Fuzzy-covering based (I, T)-fuzzy rough set models and applications to multi-attribute decision-making, Computers Industrial Engineering128 (2019), 605–621.