Mamoni Dhar

A Note on Determinant of Square Fuzzy Matrix

Full Text (PDF, 282KB), PP.26-32

Views: 0 Downloads: 0

Author(s)

Mamoni Dhar ^1,*

1. Department of Mathematics, Science College, Kokrajhar, Assam, India

* Corresponding author.

DOI: https://doi.org/10.5815/ijieeb.2013.01.03

Received: 2 Feb. 2013 / Revised: 5 Mar. 2013 / Accepted: 1 Apr. 2013 / Published: 8 May 2013

Index Terms

Reference function, membership value, convergence of powers of fuzzy matrices, complement of a fuzzy set

Abstract

In this article, we would like to study the determinant theory of fuzzy matrices. The purpose of this article is to present a new way of expanding the determinant of fuzzy matrices and thereafter some properties of determinant are considered. Most of the properties are found to be analogus to the properties of determinant of matrices in crisp cases.

Cite This Paper

Mamoni Dhar, "A Note on Determinant of Square Fuzzy Matrix", International Journal of Information Engineering and Electronic Business(IJIEEB), vol.5, no.1, pp.26-32, 2013. DOI:10.5815/ijieeb.2013.01.03

Reference

[1]Zadeh L A, Fuzzy Sets, Inform. and Control, 1965,8: 338-353.

[2]S.V Ovehinnikov, Structure of fuzzy relations , Fuzzy Sets and Systems, 6(1981), 169-195.

[3]M.G Thomson, Convergence of powers of a fuzzy matrix, J. Math. Anal. Appl. 57, 476-480, Elsevier, 1977.

[4]H Hasimato, Convergence of powers of fuzzy transitive matrix, Fuzzy Sets and Systems, 9(1983), 153-160

[5]A Kandel, Fuzy Mathematical Techniques with Applications, Addition Wisley, Tokyo, 1996.

[6]W Kolodziejezyk, Convergence of s-transitive fuzzy matrices, Fuzzy Sets and System, 26(1988), 127-130.

[7]J.B Kim, A. Baartmans Determinant Theory for Fuzzy Matrices, Fuzzy Sets and Systems, 29(1989), 349-356.

[8]J.B Kim, Idempotents and Inverses in Fuzzy Matrices, Malayasian Math 6(2)1988, Management Science.

[9]J.B Kim, Inverses of Boolean Matrices, Bull.Inst. Math. Acod, Science 12(2)(1984), 125-128

[10]J.B Kim, Determinant theory for Fuzzy and Boolean Matices, Congressus Numerantium Utilitus Mathematica Pub(1978),273-276.

[11]Dhar. M, Representation of fuzzy matrices Based on Reference Function, I.J. Intelligence Systems and Applications, 2013, 5(2), 84-90.

[12]Dhar. M, A Note on Determinant and Adjoint of Fuzzy Square Matrix ,accepted for publication in IJISA Baruah H K, Fuzzy Membership with respect to a Reference Function, Journal of the Assam Science Society, 1999, 40(.3):65-73.

[13]Baruah H K, Towards Forming A Field of Fuzzy Sets, International Journal of Energy Information and Communications, 2011, 2(1): 16 – 20.

[14]Baruah H K, Theory of Fuzzy sets Beliefs and Realities, International Journal of Energy, Information and Communications, 2011, 2(2): 1-22.

[15]Dhar M, On Hwang and Yang’s definition of Entropy of Fuzzy sets, International Journal of Latest Trend Computing, 2011, 2(4): 496-497.

[16]Dhar M, A Note on existing Definition of Fuzzy Entropy, International Journal of Energy Information and Communications, 2012, 3( 1): 17-21.

[17]Dhar M, On Separation Index of Fuzzy Sets, International Journal of Mathematical Archives, 2012, .3(3): 932-934.

[18]Dhar M, On Geometrical Representation of Fuzzy Numbers, International Journal of Energy Information and Communications, 2012, 3(2): 29-34.

[19]Dhar M, On Fuzzy Measures of Symmetry Breaking of Conditions, Similarity and Comparisons: Non Statistical Information for the Single Patient., IJMA, 2516-2519, 3(7), 2012.

[20]Dhar M, A Note on Subsethood measure of fuzzy sets, IJEIC, Korea.,55-61, 3(3).

International Journal of Information Engineering and Electronic Business (IJIEEB)