Abstract
In this paper, we give a new characterization of M-fuzzifying span mappings defined by M-fuzzifying rank functions. Then we research the relations between M-fuzzifying span mappings and other M-fuzzifying mappings on M-fuzzifying matroid, and characterize the M-fuzzifying coindependent, nonspan and hyperplane mappings. Based on these characterizations, we put forward one class of special fuzzifying matroids.
Keywords
Get full access to this article
View all access options for this article.
References
1.
Gale
D.
, Optimal assignments in an ordered set: An application of matroid theory , J Combinatoral Theory 4 (1968 ), 176 –180 .
2.
Lai
H.-J.
, Matroid Theory , Higher Education Press , Beijing , 2002 .(in Chinese)
3.
Li
E.-Q.
and
Shi
F.-G.
, Minors of M-fuzzifying matroids , Journal of Intelligent and Fuzzy Systems 28 (2015 ), 1213 –1224 .
4.
Li
E.-Q.
and
Shi
F.-G.
, The free product of M-fuzzifying matroids , Journal of Intelligent and Fuzzy Systems 30 (2016 ), 679 –690 .
5.
Lian
H.
and
Xin
X.
, The nullities for M-fuzzifying matroids , Applied Mathematics Letters 25 (2012 ), 279 –286 .
6.
Shi
F.-G.
, A new approach to the fuzzification of matroids , Fuzzy Sets and Systems 160 (2009 ), 696 –705 .
7.
Shi
F.-G.
, (L;M)-fuzzy matroids , Fuzzy Sets and Systems 160 (2009 ), 2387 –2400 .
8.
Shi
F.-G.
and
Wang
L.
, Characterizations and applications of Mfuzzifying matroids , Journal of Intelligent and Fuzzy Systems 25 (2013 ), 919 –930 .
9.
Sun
S.-B.
,
Li
L.-Q.
and
Hu
K.
, M-fuzzifying family of spanning sets , Fuzzy Systems and Mathematics 28 (2014 ), 148 –152 .(in Chinese)
10.
Sun
S.-B.
,
Xiu
Z.-Y.
and
Li
L.-Q.
, On fuzzifying matroids: Dual matroids and spanning , Journal of Intelligent and Fuzzy Systems 28 (2015 ), 1435 –1440 .
11.
Sun
S.-B.
,
Li
L.-Q.
,
Meng
G.-W.
and
Xu
L.-L.
, M-fuzzifying family of nonspanning sets , Fuzzy Systems and Mathematics 29 (2015 ), 103 –107 . (in Chinese)
12.
Wang
L.
and
Wei
Y.-P.
, M-fuzzifying P-closure operators , Advances in Intelligent and Soft Computing 62 (2009 ), 547 –554 .
13.
White
N.
, Theory of matroids(2rd Edition) , Cambridge University Press , Cambridge , 2008 .
14.
Whitney
H.
, On the abstract properties of linear dependence , American Journal of Mathematics 57 (1935 ), 509 –533 .
15.
Xin
X.
and
Lian
H.
, M-fuzzifying matroids induced by M-fuzzy families of circuits , Journal of Intelligent and Fuzzy Systems 34 (2018 ), 2223 –2234 .
16.
Xin
X.
and
Shi
F.-G.
, M-fuzzifying bases , Proyecciones Revista De Matemática 28 (2009), 271 –283 .
17.
Xin
X.
,
Shi
F.-G.
and
Li
S.-G.
, M-fuzzifying derived operators and difference derived operators , Iranian Journal of Fuzzy Systems 7 (2 ) (2010 ), 71 –81 .
18.
Xin
X.
and
Yang
S.-J.
, M-fuzzifying matroids induced by M-fuzzifying closure operators , Iranian Journal of Fuzzy Systems 14 (3 ) (2017 ), 139 –149 .
19.
Xiu
Z.-Y.
and
Shi
F.-G.
, M-fuzzifying submodular functions , Journal of Intelligent and Fuzzy Systems 27 (2014 ), 1243 –1255 .
20.
Yang
S.-J.
and
Shi
F.-G.
, Bases and circuits of fuzzifying matroids , Iranian Journal of Fuzzy Systems 15 (2 ) (2018 ), 41 –52 .
21.
Yao
W.
and
Shi
F.-G.
, Bases axioms and circuits axioms for fuzzifying matroids , Fuzzy Sets and Systems 161 (2010 ), 3155 –3165 .