AZERBAIJAN NATIONAL ACADEMY OF SCIENCES
APPROXIMATION TASK FOR GIVEN CLASSES OF MEMBERSHIP FUNCTIONS (rus.)
Nigar T. Ismayilova

Approximation task for triangular, trapezoidal, Gaussian, Bell and class of smooth membership functions was solved. Analytical formulas for gradients of target function for different classes of membership functions were recieved. Results of the minimization of target function and graphics of membership functions were demonstrated. (pp. 70-78) 

Keywords: membership function, fuzzy sets, target function, approximation task
References
  • Mandal S.N., Choudhury J.P., Chaudhuri B.S.R. Role of membership functions in fuzzy logic for prediction of shoot length of mustard plant based on residual analysis // World Academy of Science Engineering and Technology, 2008, no 38, pp. 378–384.
  • Himmelblau D.M. Applied nonlinear programming. – McGraw-Hill, 1972, 498 p.
  • Aida-zade K.R., Aliyeva N.T. Study of one class of membership functions of fuzzy sets // Automatic Control and Computer Sciences, 2011, vol. 45, no 3, pp. 142–152.
  • Hill F., Murray W., Wright M. Practical optimization, Academic Press, 1981, 511 p.
  • Aida-zade K.R., Aliyeva N.T. On a class of smooth membership functions // Journal of Automation and Information Sciences, 2012, vol. 44, no 3, pp. 57–71.
  • Rutkowski L. Flexible neuro-fuzzy systems: structures, learning, and performance evaluation, Kluwer Academic Publishers, 2004, 277 p.