INFORMATION CHANGE THE WORLD

International Journal of Intelligent Systems and Applications(IJISA)

ISSN: 2074-904X (Print), ISSN: 2074-9058 (Online)

Published By: MECS Press

IJISA Vol.7, No.8, Jul. 2017

A Few Applications of Imprecise Matrices

Full Text (PDF, 632KB), PP.9-17


Views:116   Downloads:2

Author(s)

Sahalad Borgoyary

Index Terms

Imprecise Number, Partial Presence, Membership Value, Imprecise Matrix, Reducing Imprecise Matrices, Imprecise Form

Abstract

This article introduces generalized form of extension definition of the Fuzzy set and its complement in the sense of reference function namely in imprecise set and its complement. Discuss Partial presence of element, Membership value of an imprecise number in the normal and subnormal imprecise numbers. Further on the basis of reference function define usual matrix into imprecise form with new notation. And with the help of maximum and minimum operators, obtain some new matrices like reducing imprecise matrices, complement of reducing imprecise matrix etc. Along with discuss some of the classical matrix properties which are hold good in the imprecise matrix also. Further bring out examples of application of the addition of imprecise matrices, subtraction of imprecise matrices etc. in the field of transportation problems.

Cite This Paper

Sahalad Borgoyary,"A Few Applications of Imprecise Matrices", International Journal of Intelligent Systems and Applications(IJISA), vol.7, no.8, pp.9-17, 2015. DOI: 10.5815/ijisa.2015.08.02

Reference

[1]L.A. Zadeh, Fuzzy sets, Inform. And Control, 1965, 8: 338-53

[2]H. K. Baruah, In Search of the Roots of fuzziness: The Measure meaning of Partial Presence, Annals of Fuzzy mathematics and Informatics, 2(1), 2011, 57-68

[3]H. K. Baruah., Theory of fuzzy sets: Beliefs and Realities, I. J. Energy Information and Communications. 2(2), (2011), 1-22

[4]H. K. Baruah., Construction of Membership Function of a Fuzzy Number, ICIC Express Letters 5(2), (2011), 545-549

[5]H. K. Baruah., An introduction Theory of Imprecise Sets: The Mathematics of partial presence, J. Math. Computer Science, 2(2), (2012), 110-124

[6]M. Dhar., Theory of Fuzzy Sets: An Overview, I.J. Information Engineering and Electronic Business, 2013, 3, 22-33

[7]M. Dhar, A Revisit to Probability- Possibility Consistency Principles, I.J. Intelligent Systems and Applications, 2013, 04, 90-99

[8]M. Dhar, A Note on Determinant and Adjoint of Fuzzy Square Matrix, I.J. Intelligent Systems and Applications, 2013, 05, 58-67

[9]M.G. Thomson, Convergence of Powers of a Fuzzy Matrix, J. Math. Anal. Appl., 57, 476-480. Elsevier, 1977

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

[11]M. Z. Ragab and E.G. Emam, The determinant adjoint of a square fuzzy matrix, Fuzzy Sets and Systems, 61 (1994) 297-307 

[12]M. Z. Ragab and E.G. Emam, On the min-max composition of fuzzy matrices, Fuzzy Sets and Systems , 75 (1995) 83-82

[13]L.J. Xin, controllable Fuzzy Matrices, Fuzzy Sets and Systems, 45, 1992, 313-319

[14]L.J. Xin, Convergence of Powers of Controllable Fuzzy Matrices, Fuzzy Sets and Systems, 63, 1994, 83-88

[15]T. J. Neog and D. K. Sut, An Introduction to the Theory of Imprecise soft sets, I.J. Intelligent Systems and Applications, 2012, 11, 75-83

[16]M. Dhar and H.K. Baruah, The Complement of Normal Fuzzy Numbers: An Exposition, I.J. Intelligent Systems and Applications, 2013, 08, 73-82.