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International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 66 | Issue 4 | Year 2020 | Article Id. IJMTT-V66I4P510 | DOI : https://doi.org/10.14445/22315373/IJMTT-V66I4P510

The Partial Orderings of m-Symmetric Fuzzy Matrices


G.Punithavalli
Abstract

In this paper, I introduce the concept of partial orderings on fuzzy matrices using m-symmetric matrix. By using various generalized inverses, we show that the left-star and the right-star partial orderings are identical for certain class of fuzzy matrices. Also I derive the equivalent conditions for the existence of the generalized inverses in fuzzy matrices.

Keywords
Partial order set, m-symmetric matrix, generalized inverse.
References

[1] Ben Israel.A and Greville.T.N.E, Generalized Inverses, Theory and Application, Wiley and Sons, New York, 1974.
[2] Baksalary.J.K and Mitra.S.K, Left-star and right-star partial orderings.Linear Algebra Appl,149:(1991)73-89.
[3] Jian Miao Chen Fuzzy matrix partial orderings and generalized inverses.Fuzzy sets and systems 105(1999)453-458.
[4] Julio Benitez,Xiaoji Liu and Jin Zhong, Some Results on Matrix Partial Orderings and Reverse order Law, Electronic Journal of Linear Algebra,ISSN 1081-3810,V0l.29,254-273,May 2010.
[5] Meenakshi. AR, Fuzzy Matrix, Theory and Applications.
[6] Meenakshi.AR, Range symmetric matrices in Minkowski space, Proc. Nat. Sem. Alg.Appln.Annamalai University(2000)1-4.
[7] Meenakshi.AR and Inbam, The Minus Partial Order in Fuzzy matrices, The Journal of Fuzzy Mathematics, Vol.12, No.3,695-700(2004).
[8] Meenakshi.AR, On Schur complement in an EP matrix, Periodica Math.Hung.16(1985)193-200.
[9] Punithavalli.G, Matrix Partial orderings and the reverse order law for the Minkowski inverse in M , Recent Trends in Pure and Applied Mathematics,AIP Conf.Proc.2177,020073-1-020073-9.

Citation :

G.Punithavalli, "The Partial Orderings of m-Symmetric Fuzzy Matrices," International Journal of Mathematics Trends and Technology (IJMTT), vol. 66, no. 4, pp. 64-70, 2020. Crossref, https://doi.org/10.14445/22315373/IJMTT-V66I4P510

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