On the powers of fuzzy neutrosophic soft matrices

Subject Areas : History and biography

M. Kavitha ¹ , P. Murugadas ² , S. Sriram ³

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

Received: 2018-03-12 Accepted : 2018-04-20 Published : 2018-06-01

Keywords: Fuzzy neutrosophic soft set‎, ‎fuzzy neutrosophic soft matrix, ‎fuzzy neutrosophic soft vector, ‎fuzzy neutrosophic soft eigenvectors‎, ‎circulant fuzzy neutrosophic soft matrix,

Abstract :

In this paper, ‎The powers of fuzzy neutrosophic soft square matrices (FNSSMs) under the operations $\oplus(=max)$ and $\otimes(=min)$ are studied‎. ‎We show that the powers of a given FNSM stabilize if and only if its orbits stabilize for each starting fuzzy neutrosophic soft vector (FNSV) and prove a necessary and sufficient condition for this property using the associated graphs of the FNSM‎. ‎Applications of the obtained results to several spacial classes of FNSMs (including circulants) are given‎.

References:

[1] I. Arockiarani, I. R. Sumathi, A fuzzy neutrosophic soft matrix approach in decision making, JGRMA. 2 (2) (2014), 14-23.

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

[3] K. Atanassov, More on intuitionistic fuzzy sets, Fuzzy Sets System. 33 (1989), 37-46.

[4] S. Broumi, F. Smarandache, Intuitionistic neutrosophic soft set, J. Inform. Computer. Sci. 8 (2) (2013), 130-140.

[5] K. Cechlarova, Eigenvectors in bottleneck algebra. Linear Algebra Appl. 179 (1992), 63-73.

[6] K. Cechlarova, On the powers of matrices in bottleneck /fuzzy Algebra, Linear. Algebra. Appl. 246 (1996), 97-111.

[7] R. A. Cuninghame-Green, Minimax algebra, Lecture notes in economics and mathematics systems, Springer-Verlag, Berlin, 1979.

[8] S. Das, S. Kumar, S. Kar, T. Pal, Group decision making using neutrosophic soft matrix, an algorithmic approach, J. of King Saud University-Comput. Inform. Sci. (2017), In press.

[9] Y. Guo, A. Sengur, A novel image segmentation algorithm based on neutrosophic similarity clustering application soft computing, 25 (2014), 391-398.

[10] R. Hemasinha, N. R. Pal, J. C. Bezdek, Iterates of fuzzy circulant matrices, Preprint, 1993.

[11] L. Jian-Xin, An upper bound on indices of finite fuzzy relation, Fuzzy sets and systems. 49 (1992), 317-321.

[12] L. Jian-Xin, Periodicity of powers of fuzzy matrices (finite fuzzy relations), Fuzzy Sets and Systems. 48 (1992), 365-369.

[13] C. F. Liu, Y. S. Luo, Power aggregation operators of simplified neutrosophic sets and their use in multiattribute group decision making, IEEE/CAA J. Automatica. Sinica. (2017), 1-10.

[14] M. Kavitha, P. Murugadas, S. Sriram, Minimal solution of fuzzy neutrosophic soft matrix, J. Linear. Topological. Algebra. 6 (2017), 171-189.

[15] M. Kavitha, P. Murugadas, S. Sriram, On the λ-robustness of fuzzy neutrosophic soft matrix, Inter. J. Fuzzy Math. Archive. 2 (2017), 267-287.

[16] P. K. Maji, A neutrosophic soft set approach to a decision making problem, Annauls Fuzzy Math. Information. 3 (2) (2012), 313-319.

[17] D. A. Molodtsov, Soft set theory-first result, Comput. Math. Appl. 37 (1999), 19-31.

[18] P. Rajarajeswari, P. Dhanalakshmi, Intuitionistic fuzzy soft matrix theory and it application in medical diagnosis, Annauls of Fuzzy Math. Informatics. 7 (5) (2014), 765-772.

[19] F. Smarandache, Neutrosophic set a generalization of the intuitionistic fuzzy set, Inter. J. pure. Appl. Math. 24 (2005), 287-297.

[20] I. R. Sumathi, I. Arockiarani, New operation on fuzzy neutrosophic soft matrices, Inter. J. Innovative Research. Studies. 13 (3) (2014), 110-124.

[21] M. G. Thomasson, Convergence of powers of a fuzzy matrix, J. Math. Annauls Appl. 57 (1977), 476-480.

[22] I. B. Turksen, Interval valued fuzzy Sets based on normal forms, Fuzzy Sets and System. 20 (1986), 191-210.

[23] R. Uma, P. Murugadas, S. Sriram, Fuzzy neutrosophic soft matrices of type-I and type-II, Communicated.

[24] L. A. Zadeh, Fuzzy sets, Information and control. 8 (1965), 338-353.

[25] U. Zimmermann, Linear and combinatorial optimization in ordered algebraic structure, Annauls Discrete Mathematics 10, North Holland, Amsterdam, 1981.