Filtering Algorithm for Real Eigenvalue Bounds of Interval and Fuzzy Generalized Eigenvalue Problems

Abstract

This paper deals with an interval and fuzzy generalized eigenvalue problem involving uncertain parameters. Based on a sufficient regularity condition for intervals, an interval filtering eigenvalue procedure for generalized eigenvalue problems with interval parameters is proposed, which iteratively eliminates the parts that do not contain an eigenvalue and thus reduces the initial eigenvalue bound to a precise bound. The same iterative procedure has been proposed for generalized fuzzy eigenvalue problems. In general, the solution of dynamic problems of structures using the finite element method (FEM) leads to a generalized eigenvalue problem. Based on the proposed procedures, various structural examples with an interval and fuzzy parameter such as triangular fuzzy number (TFN) are investigated to show the efficiency of the algorithms stated. Finally, fuzzy filtered eigenvalue bounds are depicted by fuzzy plots using the α-cut.

Nonlinear interval eigenvalue problems for damped spring-mass system

“…The filtering procedure presented by Hladík et al (2011) has been further extended by Mahato and Chakraverty (2016a) for fuzzy eigenvalue bounds of standard eigenvalue problems. Further, the procedure of Hladík et al (2011) has been extended for generalized interval and fuzzy filtered eigenvalue bounds by Mahato and Chakraverty (2016b). The literature studies mentioned above discuss interval linear eigenvalue problems, and literature studies related to solving nonlinear interval eigenvalue problems (NIEPs) are scarce.…”