Solving Fully Fuzzy Nonlinear Eigenvalue Problems using a Novel Fuzzy-affine Arithmetic of Damped Spring-mass Structural Systems

  • SAUDAMINI ROUT, SR National Institute of Technology Rourkela
  • Snehashish Chakraverty, SC National Institute of Technology Rourkela
Keywords: Fuzzy nonlinear eigenvalue problem, fuzzy set theory, affine arithmetic, interval overestimation problem, triangular fuzzy number, trapezoidal fuzzy number, fuzzy-affine arithmetic.


This article proposes an efficient fuzzy-affine arithmetic (FAA) to solve fully fuzzy nonlinear eigenvalue problems (FNEPs) where involved parameters are fuzzy numbers. Based on parametric form fuzzy numbers have been transformed into standard intervals. Further due to the presence of interval overestimation problem in standard interval arithmetic (IA), affine arithmetic (AA) based approach has been implemented to treat each fuzzy numbers as crisp values. Then nonlinear eigenvalue problem (NEP) has been linearized and converted into generalized eigenvalue problem (GEP). In general, the dynamic analysis of damped structural system by using finite element method leads to NEP [particularly, quadratic eigenvalue problem (QEP)]. On the basis of proposed procedure, several application problems of structures and also general QEP with fuzzy parameters are investigated. Here both triangular fuzzy number (TFN) and trapezoidal fuzzy number (TrFN) are used to handle uncertainties. Lastly, fuzzy eigenvalue bounds are illustrated with fuzzy plots with respect to its membership function.       


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