Approximated Solutions for Fuzzy Polynomials

Suriana Lasaraiya; Suzelawati Zenian.

Transactions on Science and Technology, 8(3-3), 539 - 544.

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ABSTRACT
Polynomials plays a major role in various fields such as mathematics, statistics, engineering and social science. By using the properties of triangular membership functions, we apply the learning algorithm of fuzzy neural network to solve the fuzzy polynomial equation. The learning algorithm is including the fuzzy coefficient Ai where i=1,2,3 and fuzzy output of Ao. In this paper, we are interested in finding solutions for polynomial like A1x + A2x2 + A3x3=A0 for x∈R where A0, A1, A2 and A3 are fuzzy numbers.

KEYWORDS: fuzzy, polynomials, triangular, fuzzy number, membership function




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REFERENCES
  1. Abbasbandy, S. & Otadi, M. 2006. Numerical Solution of Fuzzy Polynomials by Fuzzy Neural Network. Applied Mathematics and Computation, 181, 1084-1089.
  2. Buckley, J.J. & Eslami, E. 1997. Neural net solutions to fuzzy problems: The quadratic equation. Fuzzy Set Systems, 86, 289-298.
  3. Behera, D. & Chakraverty, S. 2013. Solution to Fuzzy System of Linear Equations with Crisp Coeeficients. Fuzzy nformation and Engineering, 2, 205-219.
  4. Hayashi, Y., Buckley, J.J. & Czogala, E. 1993. Fuzzy neural network with fuzzy signals and weights. International Journal of Intelligent System, 8, 527-537
  5. Ishibuchi, H., Kwon, K. & Tanaka, H. 1995. A learning algorithmn of fuzzy neural networks with triangular fuzzy weights. Fuzzy Sets and Systems, 71, 277-293.
  6. Jafarian, A. & Jafari, R. 2013. New Iterative Approach for Solving Fully Fuzzy Polynomials. International Journal of Fuzzy Mathematics and Systems, 3(1), 75-83.
  7. Nurhakimah, A. R., Lazim, A. & Ahmad Termimi, A. G. 2018. Learning Algorithm of Fuzzy Neural Network for Solving Trapezoidal Fuzzy Polynomial Equation. Discovering Mathematics, 40(1), 1-10.
  8. Zadeh, L.A. 1975. The Concept of a Linguistic Variable and its application to approximate reasoning: Part 1-3. Informatics Science, 9(1), 43-80.