The purpose of this paper is to study matroids on intuitionistic fuzzy sets, so as to generalize G - V fuzzy matroids.The ranking, union and intersection between two intuitionistic fuzzy sets are firstly defined by using the similarity function h and the accuracy function H of the intuitionistic fuzzy value. Then a G - V intuitionistic fuzzy matroid which can be regarded as an extension of G - V fuzzy matroids is proposed. Particularly, the induced matroid sequence and the rank function of a G - V intuitionistic fuzzy matroid and their properties are studied.
WhitneyH., On the abstract properties of linear dependence, American Journal of Mathematics57(3) (1935)509–533.
2.
GaleD., Optimal assignments in an ordered set: An application of matroid theory, Journal of Combinatorial Theory4(2) (1968)176–180.
3.
KasperskiA. and ZielinskiP., On combinatorial optimization problems on matroids with uncertain weights, European Journal of Operational Research177(2) (2007)851–864.
4.
OkadaS., Fuzzy shortest path problems incorporating interactivity among paths, Fuzzy Sets and Systems142(3) (2004)335–357.
5.
ShiF.-G., A new approach to the fuzzification of matroids, Journal of Intelligent & Fuzzy Systems34(1) (2018)221–231.
6.
ShiF.-G., (L, M)-fuzzy matroids, Fuzzy Sets and Systems160(16) (2009)2387–2400.
7.
ShiF.-G., L-fuzzy relation and L-fuzzy subgroup, Journal of Fuzzy Mathematics8(2) (2000)491–499.
8.
HuangC.-E. and ShiF.-G., Bases of [0,1]-matroids, Hacettepe Journal of Mathematics and Statistics39(2) (2010)233–240.
9.
YaoW. and ShiF.-G., Bases axioms and circuits axioms for fuzzifying matroids, Fuzzy Sets and Systems161(24) (2010)3155–3165.
10.
XinX. and ShiF.-G., Rank functions for closed and perfect [0,1]-matroids, Hacettepe Journal of Mathematics and Statistics39(1) (2010)31–39.
11.
BinP., Degrees of separation properties in stratified Lgeneralized convergence spaces using residual implication, Filomat31(20) (2017)6293–6305.
XiuZhen-Yu and Pang*B., M-fuzzifying cotopological spaces and M-fuzzifying convex spaces as M-fuzzifying closure spaces, Journal of Intelligent and Fuzzy Systems33(1) (2017)613–620.
14.
XiuZhen-Yu and Pang*B., A degree approach to special mappings between L-fuzzifying convex spaces, Journal of Intelligent and Fuzzy Systems35(1) (2018)705–716.
15.
XiuZ.-Y. and Pang*B., Base axioms and subbase axioms in Mfuzzifying convex structures, Iranian Journal of Fuzzy Systems15(2) (2018)75–87.
16.
HsuehI.-C., On fuzzification of matroids, Fuzzy Sets and Systems53(3) (1993)319–327.
GoetschelR. and VoxmanW., Fuzzy matroids, Fuzzy Sets and Systems27(3) (1988)291–302.
20.
GoetschelR. and VoxmanW., Bases of fuzzy matroids, Fuzzy Sets and Systems31(2) (1989)253–261.
21.
GoetschelR. and VoxmanW., Fuzzy matroids and a greedy algorithm, Fuzzy Sets and Systems37(2) (1990)201–213.
22.
GoetschelR. and VoxmanW., Fuzzy rank functions, Fuzzy Sets and Systems42(2) (1991)245–258.
23.
LiY.-L., ZhangG.-J. and LuL.-X., Axioms for bases of closed regular fuzzy matroids, Fuzzy Sets and Systems161(12) (2010)1711–1725.
24.
LiX.-N., LiuS.-y. and LiS.-G, Connectedness of refined Goetschel-Voxman fuzzy matroids, Fuzzy Sets and Systems161(20) (2010)2709–2723.
25.
AtanassovK., Intuitionistic fuzzy sets, Fuzzy Sets and Systems20(1) (1986)87–96.
26.
AtanassovK., Remark on the intuitionistic fuzzy sets-III, Fuzzy Sets and Systems75(3), 401–402.
27.
ZadehL.A., Fuzzy sets, Inform and Control8(3) (1965)338–353.
28.
XuZ.-S. and YagerR.-R., Some geometric aggregation operators based on intuitionistic fuzzy sets, International Journal of General Systems35(3) (2006)417–433.
29.
YagerR.-R., Some aspects of intuitionistic fuzzy sets fuzzy, Optim Decis Making8(1) (2009)67–90.
30.
YagerR.-R., OWA aggregation of intuitionistic fuzzy sets, International Journal of General Systems38(6) (2009)617–641.
31.
HongD.-H. and ChoiC.-H., Multicriteria fuzzy decision making problems based on vague set theory, Fuzzy Sets and Systems114(1) (2000)103–113.
32.
SzmidtE. and KacprzykJ., Distances between intuitionistic fuzzy sets, Fuzzy Sets and Systems114(3) (2000)505–518.
33.
ZhangX.-M. and XuZ.-S., A new method for ranking intuitionistic fuzzy values and its application in multi-attribute decision making, Fuzzy Optim Decis Making11(2) (2012)135–146.
34.
LiX. and YiH., Intuitionistic fuzzy matroids, Journal of Intelligent and Fuzzy Systems33(6) (2017)3653–3663.
