The generalized inverse is an important result in matrix theory. In this paper, a necessary and sufficient condition for the regularity of a given intuitionistic fuzzy matrix is provided. For regular intuitionistic fuzzy matrices, how to solve the problem of finding all generalized inverses is discussed.
PalM., KhanS. and ShyamalA.K., Intuitionistic fuzzy matrices, Notes on Intuitionistic Fuzzy Sets8(2) (2002), 51–62.
7.
PalM., KhanS. and ShyamalA.K., Distance between fuzzy matrices and its applications-I, Journal of Natural and Physical Sciences19(1) (2005), 39–58.
8.
SriramS. and MurugadasP., On semiring of intuitionistic fuzzy matrices, Applied Mathematical Science4(23) (2010), 1099–1105.
9.
PradhanR. and PalM., Intuitionistic fuzzy linear transformations, Annals of Pure and Applied Mathematics1(1) (2012), 57–68.
10.
PradhanR. and PalM., Convergence of maxarithmetic mean-minarithmetic mean powers of intuitionistic fuzzy matrices, International Journal of Fuzzy Mathematical Archive2 (2013), 58–69.
11.
PradhanR. and PalM., Convergence of maxgeneralized mean-mingeneralized mean powers of intuitionistic fuzzy matrices, The Journal of Fuzzy Mathematics22(2) (2014), 477–492.
12.
KhanS.K. and PalM., Interval-valued intuitionistic fuzzy matrices, Notes on Intuitionistic Fuzzy Sets11(1) (2005), 16–27.
13.
ShyamalA.K. and PalM., Interval-valued fuzzy matrices, of Fuzzy Mathematics, Journal14(3) (2006), 583–604.
14.
BhowmikM. and PalM., Some results on intuitionistic fuzzy matrices and circulant intuitionistic fuzzy matrices, International Journal of Mathematical Sciences7(1-2) (2008), 81–96.
15.
BhowmikM. and PalM., Generalized intuitionistic fuzzy matrices, Far East Journal of Mathematical Sciences29(3) (2008), 533–554.
16.
AdakA.K., BhowmikM. and PalM., Intuitionistic fuzzy block matrix and its some properties, Annals of Pure and Applied Mathematics1(1) (2012), 13–31.
17.
AdakA.K., PalM. and BhowmikM., Distributive lattice over intuitionistic fuzzy matrices, The Journal of Fuzzy Mathematics21(2) (2013), 401–416.
18.
MondalS. and PalM., Similarity relations, invertibility and eigenvalues of intuitoinistic fuzzy matrix, Fuzzy Information and Engineering4 (2013), 431–443.
19.
MondalS. and PalM., Intuitionistic fuzzy incline matrix and determinant, Annals of Fuzzy Mathematics and Informatics8(1) (2014), 19–32.
20.
FredholmI., Sur une classe d’equation fonctionelles, Acta Mathematica27 (1903), 365–390.
21.
BapatR.B. and RobinsonD.W., The Moore-Penrose inverse over a commutative ring, Linear Algebra and its Applications177 (1992), 51–69.
22.
PuystjensR. and HartwigR.E., The group inverse of a companion matrix, Linear and Multilinear Algebra43 (1997), 137–150.
23.
PatricioP., The Moore-Penrose inverse of von Neumann regular matrices over a ring, Linear Algebra and its Applications332 (2001), 469–483.
24.
PuystjensR. and GouveiaM.C., Drazin invertibility for matrices over an arbitrary ring, Linear Algebra and its Applications385 (2004), 105–116.
25.
PatiS., Moore-Penrose inverse of matrices on idempotent semirings, SIAM Journal on Matrix Analysis and Applications22(2) (2000), 617–626.
26.
KhanS.K. and PalA., The generalized inverse of intuitionistic fuzzy matrices, Journal of Physical Sciences11 (2007), 62–67.
27.
PradhanR. and PalM., Generalized inverse of block intuitionistic fuzzy matrices, International Journal of Applications of Fuzzy Sets and Artificial Intelligence3 (2013), 23–38.
28.
PradhanR. and PalM., Some results on generalized inverse of intuitionistic fuzzy matrices, Fuzzy Information and Engineering6 (2014), 133–145.
