Generalized inverse of fuzzy neutrosophic soft matrix

الموضوعات :

R. Uma ¹ (Department of Mathematics, Annamalai University, Annamalainagar-608002, India)
P. Murugadas ² (Department of Mathematics, Annamalai University, Annamalainagar-608002. India)
S. Sriram ³ (Mathematics Wing, Directorate of Distance Education, Annamalai University, Annamalainagar-608002, India)

تاريخ الإرسال : 02 الأربعاء , جمادى الثانية, 1438 تاريخ التأكيد : 03 الجمعة , ذو الحجة, 1438 تاريخ الإصدار : 04 السبت , رجب, 1438

الکلمات المفتاحية: Fuzzy Neutrosophic Soft Set (FNSS), Fuzzy Neutrosophic Soft Matrix (FNSM), g-inverse,

ملخص المقالة :

Neutrosophy is a new branch of philosophy that studies the origin, nature, and scope of neutralities, as well as their interactions with different ideational spectra. Aim of this article is to find the maximum and minimum solution of the fuzzy neutrosophic soft relational equations xA=b and Ax=b, where x and b are fuzzy neutrosophic soft vector and A is a fuzzy neutrosophic soft matrix. Whenever A is singular we can not find A^{-1}. In that case we can use g-inverse to get the solution of the above relational equations. Further, using this concept maximum and minimum g-inverse of fuzzy neutrosophic soft matrix are obtained.

المصادر:

[1] I. Arockiarani, I. R. Sumathi, J. Martina Jency, Fuzzy Neutrosophic soft topological spaces, Int. J. Math. Archive. 4 (10) (2013), 225-238.

[2] I. Arockiarani, I. R. Sumathi, A fuzzy neutrosophic soft Matrix approach in decision making, J. Global Research Math. Archives. 2 (2) (2014), 14-23.

[3] K. Atanassov, Intuitionistic fuzzy sets, Fuzzy sets and systems. 20 (1986), 87-96.

[4] H. H. Cho, Fuzzy Matrices and Fuzzy Equation, Fuzzy sets and system. 105 (1999), 445-451.

[5] F. Smarandache, Neutrosophy, Neutrosophic Probability, Set, and Logic, Pn USA, 1998.

[6] I. Deli, Npn-soft sets theory and their applications, viXra: 1508.0402.

[7] K. Cechlarova, Unique solvability of Max-min fuzzy equations and strong regularity of matrices over fuzzy algebra, Fuzzy sets and systems. 75 (1975), 165-177.

[8] J. X. Li, The smallest solution of max-min fuzzy equations, Fuzzy sets and system. 41 (1990), 317-327.

[9] P. K. Maji, R. Biswas, A. R. Roy, Fuzzy Soft set, The journal of fuzzy mathematics. 9 (3) (2001), 589-602.

[10] P. K. Maji, R. Biswas, A. R. Roy, Intuitionistic Fuzzy Soft sets, journal of fuzzy mathematics. 12 (2004), 669-683.

[11] D. Molodtsov, Soft set theory first results, Computer and mathematics with applications, 37 (1999), 19-31.

[12] P. Murugadas, Contribution to a study on Generalized Fuzzy Matrices, P.hD., Thesis, Department of Mathematics, Annamalai University, 2011.

[13] P. K. Maji, Neutrosophic soft set, Annals of Fuzzy Mathematics and Informatics. 5 (2013), 157-168.

[14] W. Pedrycz, Fuzzy relational equations with generalized connectives and their application, Fuzzy sets and system. 10 (1983), 185-201.

[15] S. Broumi, R. Sahin, F. Smarandache, Generalized interval Neutrosophic soft set and its Decision Making Problem, Journal of New Results in Science. 7 (2014), 29-47.

[16] F. Smarandache, Neutrosophic set, a generalisation of the intuitionistic fuzzy set, Int. J. Pure Appl. Math. 24 (2005), 287-297.

[17] T. M. Basu, Sh. K. Mondal Neutrosophic Soft Matrix and its application in solving Group Decision making Problems from Medical Science, Computer Communication and Collaboration. 3 (1) (2015), 1-31.

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