On Comparison of Crisp, Fuzzy, Intuitionistic Fuzzy Unconstrained Optimization Problems Using Newton’s Method
DOI:
https://doi.org/10.26713/cma.v13i4.2187Keywords:
Complex interval-valued Pythagorean fuzzy set, Fuzzy numbers, Intuitionistic set, Unconstrained optimizationAbstract
This paper is focused on arithmetic operations on fuzzy and intuitionistic fuzzy numbers to solve the fuzzy unconstrained optimization problems with triangular and trapezoidal, fuzzy number coefficients. The optimal solution is obtained by fuzzy Newton’s method, and the MATLAB outputs are also provided with illustrative examples. The method proposed in this research work has been compared with the existing Newton’s method.
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F. B. Aicha, F. Bouani and M. Ksouri, A multivariable multiobjective predictive controller, International Journal of Applied Mathematics and Computer Science 23(1) (2013), 35 – 45, DOI: 10.2478/amcs-2013-0004.
K. T. Atanassov, Intuitionistic fuzzy sets, Fuzzy Sets and Systems 20(1) (1986), 87 – 96, DOI: 10.1016/S0165-0114(86)80034-3.
R. E. Bellman and L. A. Zadeh, Decision-making in a fuzzy environment, Management Science 17(4) (1970), B141 – B164, DOI: 10.1287/mnsc.17.4.B141.
Y. Chalco-Cano, G. N. Silva and A. Rufián-Lizanac, On the newton method for solving fuzzy unconstrained optimization problems, Fuzzy Sets and Systems 272 (2015), 60 – 69, DOI: 10.1016/j.fss.2015.02.001.
T. C. E. Cheng and M. Y. Kovalyov, An unconstrained optimization problem is NP-hard given an oracle representation of its objective function: A technical note, Computer & Operations Research 29(14) (2002), 2087 – 2091, DOI: 10.1016/S0305-0548(02)00065-5.
R. D˛ebski, An adaptive multi-spline refinement algorithm in simulation based sailboat trajectory optimization using onboard multi-core computer systems, International Journal of Applied Mathematics and Computer Science 26(2) (2016), 351 – 360, DOI: 10.1515/amcs-2016-0025.
J. E. Dennis, Jr. and R. B. Shanabel, Numerical Methods for Unconstrained Optimization and Nonlinear Equations, Prentice-Hall, Inc., Englewood Cliffs, NJ (1983), URL: https://bayanbox.ir/view/1159218030012565111/Numerical-Method-for-uncostrained-optimization-J.-E.-Dennis-Robert-B.-Schnabel.pdf.
A. N. Gani and S. N. M. Assarudeen, A new operation on triangular fuzzy number for solving fuzzy linear programming problem, Applied Mathematics and Sciences 6(11) (2012), 525 – 532.
R. I. Hepzibah and N. Gani, An Algorithmic Approach to Fuzzy Linear and Complementarity Problems, Lambert Academic Publishing, Germany (2021).
R. I. Hepzibah and Vidhya, Modified new operation for triangular intuitionistic fuzzy numbers (TIFNS), Malaya Journal of Matematik 2(3) (2014), 301 – 307, URL: https://www.malayajournal.org/articles/MJM097.pdf.
G. S. Mahapatra and T. K. Roy, Intuitionistic fuzzy number and its arithmetic operation with application on system failure, Journal of Uncertain Systems 7(2) (2013), 92 – 107.
R. S. Porchelvi and S. Sathya, A Newton’s method for nonlinear unconstrained optimization problems with two variables, International Journal of Science and Research 2(1) (2013), 726 – 728.
L. R. Ronald, Optimization in Operations Research, Pearson Education, Inc., (1998), URL: https://industri.fatek.unpatti.ac.id/wp-content/uploads/2019/03/173-Optimization-in-Operations-Research-Ronald-L.-Rardin-Edisi-2-2015.pdf.
Z.-J. Shi, Convergence of line search methods for unconstrained optimization, Applied Mathematics and Computation 157(2) (2004), 393 – 405, DOI: 10.1016/j.amc.2003.08.058.
J. R. Timothy, Fuzzy Logic With Engineering Applications, 3rd edition, Wiley, New York, NY (2010).
P. Umamaheshwari and K. Ganesan, A solution approach to fuzzy nonlinear programming problems, International Journal of Pure and Applied Mathematics 113(13) (2017), 291 – 300.
R. Vidhya and R. I. Hepzibah, A comparative study on interval arithmetic operations with intuitionistic fuzzy numbers for solving an intuitionistic fuzzy multi-objective linear programming problems, International Journal of Applied Mathematics and Computer Science 27(3) (2017), 563 – 573, DOI: 10.1515/amcs-2017-0040.
L. A. Zadeh, Fuzzy sets, Information and Control 8 (1965), 338 – 353, DOI: 10.1016/S0019-9958(65)90241-X.
L. A. Zadeh, The concept of a linguistic variable and its application to approximate reasoning–I, Information Sciences 8 (1975), 199 – 249, DOI: 10.1016/0020-0255(75)90036-5.
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