×

Finding fuzzy inverse matrix using Wu’s method. (English) Zbl 1499.15113

MSC:

15B15 Fuzzy matrices
15A09 Theory of matrix inversion and generalized inverses
Full Text: DOI

References:

[1] Basaran, M.A., Calculating fuzzy inverse matrix using fuzzy linear equation system, Applied Soft Computing, Vol. 12, (2012), 1810-1813.
[2] Basiri, B., Faug‘ere, J.-C., Changing the ordering of Grbner bases with LLL: case of two variables, In: Proceedings of ISSAC, ACM Press, New York, (2003), 23-29. · Zbl 1072.68645
[3] Becker, T., Weispfenning, V., Gr¨obner Bases, Springer-Varlag, New York, 1993.
[4] Buchberger, B., Gr¨obner bases : an algorithmic method in polynomial ideal theory. R. P. Company, Ed. Bose, 1985. · Zbl 0587.13009
[5] Buckley, J.J., Qu, Y., Solving systems of linear fuzzy equations, Fuzzy sets and systems, Vol. 43, (1991), 33-43. · Zbl 0741.65023
[6] Cen, J., Fuzzy matrix partial orderings and generalized inverses, Fuzzy Systems and Mathematics, Vol. 105, (1999), 453-458. · Zbl 0933.15042
[7] Cen, J., On Moore-Penrose Inverses of Fuzzy Matrices, Fuzzy Systems and Mathematics, Vol. 19, (2005), 66-70. · Zbl 1332.15062
[8] Chou, S., Gao, X., McPhee, N., A Combination of Ritt-Wu’s Method and Collins’ Method, Technical report, Austin, Texax, USA, 1989. · Zbl 1433.68547
[9] Cho, H.H., Regular fuzzy matrices and fuzzy equations, Fuzzy sets and systems, Vol. 105, (1999), 445-451. · Zbl 0942.15012
[10] Cox, D., J. Little, J., O’Shea, D., Ideal, Varieties, and Algorithms: An introduction to computational algebra geometry and commutative algebra, third edition, Springer-Varlag, New York, 2007. · Zbl 1118.13001
[11] Dehghan, M., Hashemi, B., Ghatee, M., Computational methods for solving fully fuzzy linear systems, Applied Mathematics and Computation, Vol. 179, (2006), 328-343. · Zbl 1101.65040
[12] Dubois, D., Prade, H., Systems of linear fuzzy constrains, International Journal of Systems Science, Vol. 9, (1978), 613-626. · Zbl 0383.94045
[13] Dubois, D., Prade, H., Fuzzy Sets and Systems: Theory and Applications, Academic Press, New York, 1980. · Zbl 0444.94049
[14] Ebadi, M. J., Suleiman, M., Ismail, F. B., Ahmadian, A., Shahryari, M. R., Salahshour, S., A new distance measure for trapezoidal fuzzy numbers, Mathematical Problems in Engineering, 2013:424186. · Zbl 1296.03029
[15] Elias, J., Automated geometric theorem proving:Wu’s method, The Montana Mathematics Enthusiast, Vol. 3, (2006), 3-50.
[16] Farahani, H., Ebadi, M. J., Jafari, Hossein Finding inverse of a fuzzy matrix using eigenvalue method, International Journal of Innovative Technology & Exploring Engineering, Vol. 9, No. 2, (2019), 30303037.
[17] Farahani, H., Mishmast Nehi, H., Paripour, M., Solving fuzzy complex system of linear equations using eigenvalue method, Journal of Intelligent & Fuzzy Systems, Vol. 31, (2016), 1689-1699. · Zbl 1367.65039
[18] Faug‘ere, J.-C., A new efficient algorithm for computing Gr¨obner bases (F4), Journal of Pure and Applied Algebra, Vol. 139, (1999), 61-88. · Zbl 0930.68174
[19] Faug‘ere, J.-C., A new efficient algorithm for computing Gr¨obner bases without reduction to zero ( F5), Proceedings of ISSACS, T. Mora, Ed., ACM Press, 2002. · Zbl 1072.68664
[20] Gao, X., Hou, X., Tang, J., Cheng, H., Complete solution classification for the perspective-three-point problem, IEEE Trans. Pattern Anal. Mach. Intell., Vol. 25, (2003), 930-943.
[21] Gao, S., Guan, Y., Volny IV, F., A new incremental algorithm for computing Gr¨obner bases, Proceedings of the 2010 International Symposium on Symbolic and Algebraic Computation, ISSAC’10, ACM, (2010), 13-19. · Zbl 1321.68531
[22] Gao, S., Volny IV, F., Wang, M., A new framework for computing Gr¨obner bases), Mathematics of Computation, Vol. 85, (2016), 449-465. · Zbl 1331.13018
[23] Hashimoto, H., Subinverses of fuzzy matrices, Fuzzy sets and systems, Vol. 12, (1984), 155-168. · Zbl 0551.15011
[24] Ismail, H.N., Morsi, N.N., Fuzzy rank of a fuzzy matrix, Fuzzy sets and systems, Vol. 41, (1991), 243-249. · Zbl 0729.15005
[25] Jafari, H., Malinowski, M.T., Ebadi, M.J., Fuzzy stochastic differential equations driven by fractional Brownian motion, Advances in Difference Equations, 2021, 16 (2021). · Zbl 1485.60054
[26] Jafari, H., Ebadi, M.J., Malliavin calculus in statistical inference: Cramer-Rao lower bound for fuzzy random variables, Journal of Decisions and Operations Research , Vol. 5, No. 2, (2020), 124-132,
[27] Jamali, N., Sadegheih, A., Lotfi, M.M., Wood, Lincoln C., Ebadi, M.J., Estimating the Depth of Anesthesia During the Induction by a Novel Adaptive Neuro-Fuzzy Inference System: A Case Study, Neural Processing Letters, Vol. 53, (2020), 131-175.
[28] Jin, M., Li, X., Wang, D., A new algorithmic scheme for computing characteristic sets, Journal of Symbolic Computation, Vol. 50, (2013), 431-449. · Zbl 1255.13001
[29] Kim, K.H., Roush, F.W., Generalized Fuzzy matrices, Fuzzy sets and systems, Vol. 4, (1980), 293-315. · Zbl 0451.20055
[30] Mosleh, M, Otadi, M., A discussion on “Calculating fuzzy inverse matrix using fuzzy linear equation system”, Applied Soft Computing, Vol. 28, (2015), 511-513.
[31] Pang, C.T., Simultaneously controllable fuzzy matrices, Computers and Mathematics with Applications, Vol. 50, (2005), 1647-1658. · Zbl 1100.15008
[32] Thomasan, M.G., Convergence of powers of fuzzy matrix, Journal of Mathematical Analysis and Applications, Vol. 57, (1977), 476-480. · Zbl 0345.15007
[33] Zadeh, L.A., Fuzzy sets as a basis of possibility theory, Fuzzy Sets and Systems, Vol. 1, (1978), 3-28. · Zbl 0377.04002
[34] Wen-Tsun, W., Basic principles of mechanical theorem proving in geometrics, Journal of Systems Sciences and Mathematical Sciences, Vol. 4, (1984), 207-235.
[35] Wen-Tsun, W. On the decision problem and the mechanization of theorem-proving in elementary geometry, Contemporary Mathematics, Vol. 29, (1984), 213-234. · Zbl 0578.68078
[36] Wen-Tsun, W. Mathematics Mechanization: Mechanical Geometry Theorem-Proving, Mechanical Geometry Problem-Solving and Polynomial Equations-Solving, Mathematics and Its Applications, Beijing b Science Press, London, 2001. · Zbl 0987.68074
[37] Wen-Tsun, W., Gao, X. Automated reasoning and equation solving with the characteristic set method., Journal of Computer Science and Technology, Vol. 21, No. 5, (2006), 756-764.
[38] Wen-Tsun, W., Gao, X. Mathematics mechanization and applications after thirty years, Frontiers of Computer Science in China, Vol. 1, No. 1, (2007), 1-8.
[39] Zuzeng, P., Yunyu, S., Fuzzy Mathematics and Its Applications. . Wuhan University Press, Wuhan · Zbl 0811.04007
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.