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Membership Value, Reference Function, Boolean Matrices
The main intention of this article is to represent fuzzy matrices with the help of reference function.Thereafter addition and multiplication of fuzzy matrices are defined keeping in pace with the newly represented fuzzy matrices. Here we study the determinant theory as well as the adjoint theory of square fuzzy matrices. The contribution of this article is to put forward a new way of expanding the determinant of fuzzy matrices and this process has led the foundation for defining the adjoint of square fuzzy matrices in a quite different way. In the process some properties of determinant as well as adjoint of fuzzy matrices are considered which are found to be almost analogus with the properties in crisp cases.
Mamoni Dhar, "A Note on Determinant and Adjoint of Fuzzy Square Matrix", International Journal of Intelligent Systems and Applications(IJISA), vol.5, no.5, pp.58-67, 2013. DOI:10.5815/ijisa.2013.05.07
S.V Ovehinnikov, Structure of fuzzy relations, Fuzzy Sets and Systems, 6(1981), 169-195.
M.G Thomson, Convergence of powers of a fuzzy matrix, J. Math. Anal. Appl. 57, 476-480, Elsevier, 1977.
H Hasimato, Convergence of powers of fuzzy transitive matrix, Fuzzy Sets and Systems, 9(1983), 153-160
A Kandel, Fuzy Mathematical Techniques with Applications, Addition Wisley, Tokyo, 1996.
W Kolodziejezyk, Convergence of s-transitive fuzzy matrices, Fuzzy Sets and System, 26(1988), 127-130.
J.B Kim, A. Baartmans Determinant Theory for Fuzzy Matrices, Fuzzy Sets and Systems, 29(1989), 349-356.
J.B Kim, Determinant theory for Fuzzy and Boolean Matices, Congressus Numerantium Utilitus Mathematica Pub (1978), 273-276.
J.B Kim, Idempotents and Inverses in Fuzzy Matrices, Malayasian Math 6(2)1988, Management Science.
J.B Kim, Inverses of Boolean Matrices, Bull.Inst. Math. Acod, Science 12(2)(1984), 125-128
Baruah H K, Fuzzy Membership with respect to a Reference Function, Journal of the Assam Science Society, 1999, 40(.3):65-73.
Baruah H K, Towards Forming A Field of Fuzzy Sets, International Journal of Energy Information and Communications, 2011, 2(1): 16 – 20.
Baruah H K, Theory of Fuzzy sets Beliefs and Realities, International Journal of Energy, Information and Communications, 2011, 2(2): 1-22.
Dhar M, On Hwang and Yang’s definition of Entropy of Fuzzy sets, International Journal of Latest Trend Computing, 2011, 2(4): 496-497.
Dhar M, A Note on existing Definition of Fuzzy Entropy, International Journal of Energy Information and Communications, 2012, 3( 1): 17-21.
Dhar M, On Separation Index of Fuzzy Sets, International Journal of Mathematical Archives, 2012, .3(3): 932-934.
Dhar M, On Geometrical Representation of Fuzzy Numbers, International Journal of Energy Information and Communications, 2012, 3(2): 29-34.
Dhar M, On Fuzzy Measures of Symmetry Breaking of Conditions, Similarity and Comparisons: Non Statistical Information for the Single Patient., Accepted for publication in International Journal of Mathematical Archives, 2012.
Dhar M, A Note on Subsethood measure of fuzzy sets, accepted for publication in International Journal of Energy, Information and Communications, 2012.