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Particle swarm optimization for solving a class of type-1 and type-2 fuzzy nonlinear equations

Sadiqbatcha S., Jafarzadeh S., Ampatzidis Y.

Journal of Artificial Intelligence and Soft Computing Research

2018

Vol. 8, No. 2

103--110

This paper proposes a modified particle swarm optimization (PSO) algorithm that can be used to solve a variety of fuzzy nonlinear equations, i.e. fuzzy polynomials and exponential equations. Fuzzy nonlinear equations are reduced to a number of interval nonlinear equations using alpha cuts. These equations are then sequentially solved using the proposed methodology. Finally, the membership functions of the fuzzy solutions are constructed using the interval results at each alpha cut. Unlike existing methods, the proposed algorithm does not impose any restriction on the fuzzy variables in the problem. It is designed to work for equations containing both positive and negative fuzzy sets and even for the cases when the support of the fuzzy sets extends across 0, which is a particularly problematic case.