Document Type: Research Paper

Authors

1 Department of Mathematics, Annamalai University, Annamalainagar-608002, India

2 Department of Mathematics, Government Arts college (Autonomous), Karur, India

3 Mathematics Wing, Directorate of Distance Education, Annamalai University, Annamalainagar-608002, India

Abstract

The aim of this article is to study the concept of unique solvability of max-min fuzzy neutrosophic soft matrix equation and strong regularity of fuzzy neutrosophic soft matrices over Fuzzy Neutrosophic Soft Algebra (FNSA). A Fuzzy Neutrosophic Soft Matrix (FNSM) is said to have Strong, Linear Independent (SLI) column (or, in the case of fuzzy neutrosophic soft square matrices, to be strongly regular) if for some fuzzy neutrosophic soft vector b the system A⊗x = b has a unique solution. A necessary and sufficient condition for linear system of equation over a FNSA to have a unique solution is formulated and the equivalent condition for FNSM to have SLI column and Strong Regular (SR) are presented. Moreover trapezoidal algorithm for testing these properties is reviewed.

Keywords

Main Subjects

[1] I. Arockiarani, I. R. Sumathi, A Fuzzy Neutrosophic Soft Matrix Approach in Decision Making, J. Global Research in Mathematical Archives. 2 (2014), 14-23.

[2] K. Atanassov, Intuitionistic Fuzzy Sets, Fuzzy Sets and System. 20 (1983), 87-96.

[3] P. Butkovic, Strong Regularity of Matrices-a Survey of Results, Discrete Application Mathematics. 48 (1994), 45-68.

[4] P. Butkovic, K. Cechlarova, P. Szabo, Strong Linear Independence in Bottleneck Algebra, Linear Algebra Application 94 (1987), 133-155.

[5] P. Butkovic, F. Hevery, A Condition for the Strong Regularity of Matrices in the Minimax Algebra, Discrete Application Mathematics. 11 (1985), 209-222.

[6] P. Butkovic, P. Szabo, An Algorithm for Checking Strong Regularity of Matrices in the Bottleneck Algebra, Research Report F-1404-1,P. J. Safarik University, Kosice, (1985).

[7] R. A. Cuninghame-Green, Minimax Algebra, Lecture note in Econamic and Mathematics System, 166 Springer, Berlin, (1979).

[8] K. Cechlarova, Strong Regularity of Matrices in a Discrete Bottleneck Algebra, Linear Algebra Application. 128 (1990), 35-50.

[9] F. Smarandache, Neutrosophy, Neutrosophic probability, Set, and Logic, USA, 105 (1998).

[10] S. Z. Guo, P. Z. Wang, A. Di Nola, S. Sesa, Further Contributions to the Study of Finite Fuzzy Relation Equations, Fuzzy Sets and System. 26 (1988), 93-104.

[11] M. Higashi, G. J. Klir, Resolution of Finite Fuzzy Relation Equation, Fuzzy Sets and System. 13 (1984), 65-82.

[12] Li Jian-Xin, The Smallest Solution of Max-min Fuzzy Equations, Fuzzy Sets and System. 41 (1990), 317-327.

[13] K. Cechlarova, Unique Solvability of max-min Fuzzy Equations and Strong Regularity of Matrices over Fuzzy Algebra, Fuzzy Sets and System. 75 (1995), 165-177.

[14] D. Molodtsov, Soft Set Theory First Results, Computer and Mathematics with Application. 37 (1999), 19-31.

[15] P. K. Maji, R. Biswas, A.R.Roy, Fuzzy Soft Set, The Journal of Fuzzy Mathematics. 9 (3) (2001), 589-602.

[16] P. K. Maji, R. Biswas, A. R. Roy, Intuitionistic Fuzzy Soft Sets, The Journal of Fuzzy Mathematics. 12 (2004), 669-683.

[17] P. Rajarajeswari, P. Dhanalakshmi, Intuitionistic Fuzzy Soft Matrix Theory and it Application in Medical Diagnosis, Annals of Fuzzy Mathematics and Informatics. 7 (5) (2014), 765-772.

18] I. R. Sumathi, I. Arockiarani, New Operation on Fuzzy Neutrosophic Soft Matrices, International Journal of Innovative Research and Studies. 13 (3) (2014), 110-124.

[19] E. Sanchez, Resolution of Composite Fuzzy Relations , Information and Control. 30 (1976), 38-48.

[20] F. Smarandache, Neutrosophic Set a Generalization of the Intuitionistic Fuzzy Set, International Journal of Pure Application Mathematics. 24 (2005), 287-297.

[21] R. Uma, P. Murugadas, S. Sriram, Fuzzy Neutrosophic Soft Matrices of Type-I and Type-II, Communicated.

[22] K. Zimmermann, Extremal Algebra, Ekon. Ustav CSAV, Praha, (1976) (in Czech).

[23] L. A. Zadeh, Fuzzy Sets, Information and Control. 8 (1965), 338-353.