In this paper, we introduce the concepts of fuzzy congruence relation and fuzzy coset relation on vector spaces and find some their properties. We define some operations on fuzzy coset relations and show that the set of all fuzzy coset relations on a vector space is a vector space, too. We study the union of two fuzzy congruence relations and investigate some its properties. Finally, by using the concepts of a generated subspace of a set and a congruence relation on a vector space, we introduce the notion of a fuzzy congruence relation generated by a fuzzy relation in a vector space.
DasP., Fuzzy vector spaces under triangular norms, Fuzzy Sets and Systems25 (1988), 73–85.
2.
GoguenJ., L-fuzzy sets, J Math Anal Appl18 (1967), 145–174.
3.
KatsarasA.K. and LiuD.B., Fuzzy vector spaces and fuzzy topological vector spaces, J Math Anal Appl58 (1977), 135–146.
4.
KumarR., Fuzzy vector spaces and fuzzy cosets, Fuzzy Sets and Systems45 (1992), 109–116.
5.
MaX., LiuQ. and ZhanJ., A survey of decision making methods based on certain hybrid soft set models, Artificial Intelligence Review47 (2017), 507–530.
6.
MoradianaR., Khosravi ShoarS. and RadfarA., Rough sets induced by fuzzy ideals in BCK-Algebras, Journal of Intelligent and Fuzzy Systems30 (2016), 2397–2404.
7.
MukherjeeN.P., Fuzzy normal subgroups and fuzzy cosets, Information Sciences34 (1984), 225–239.
8.
MuraliV., Fuzzy equivalence relations, Fuzzy Sets and Systems30(2) (1989), 155–163.
9.
MuraliV., Fuzzy congruences, Fuzzy Sets and Systems41(3) (1991), 359–369.
10.
SamhanM., Fuzzy congruence in semigroups, Information Sciences74 (1993), 165–175.
11.
TanY., Fuzzy congruences on a regular semigroup, Fuzzy Sets and Systems117(3) (2001), 399–408.
12.
ZadehL.A., Fuzzy sets, Information and Control8 (1965), 338–353.
13.
ZhanJ., Irfan AliM. and MehmoodN., On a novel uncertain soft set model: Z-soft fuzzy rough set model and corresponding decision making methods, Applied Soft Computing56 (2017), 446–457.
14.
ZhanJ., LiuQ. and HerawanT., A novel soft rough set: Soft rough hemirings and its multicriteria group decision making, Applied Soft Computing54 (2017), 393–402.
15.
ZhanJ., YuB. and FoteaV.E., Characterizations of two kinds of hemirings based on probability spaces, Soft Computing20 (2016), 637–648.
16.
ZhanJ. and ZhuK., A novel soft rough fuzzy set: Z-soft rough fuzzy ideals of hemirings and corresponding decision making, Soft Computing21 (2017), 1923–1936.
