<abstract xmlns="http://www.w3.org/1999/xhtml"><p>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.</p></abstract>

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.

Particle Swarm Optimization for Solving a Class of Type-1 and Type-2 Fuzzy Nonlinear Equations

Dept. of Computer and Electrical Engineering

Journal of Artificial Intelligence and Soft Computing Research

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

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...

Particle Swarm Optimization for Solving a Class of Type-1 and Type-2 Fuzzy Nonlinear Equations

Published Online: Nov 01, 2017

Page range: 103 - 110

Received: Jan 30, 2017

Accepted: Mar 31, 2017

DOI: https://doi.org/10.1515/jaiscr-2018-0007

Keywords
type1 and type2 fuzzy sets, polynomial and exponential equations, particle swarm optimization

© 2018 Sheriff Sadiqbatcha et al., published by De Gruyter Open

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Particle Swarm Optimization for Solving a Class of Type-1 and Type-2 Fuzzy Nonlinear Equations

Published Online: Nov 01, 2017

Page range: 103 - 110

Received: Jan 30, 2017

Accepted: Mar 31, 2017

DOI: https://doi.org/10.1515/jaiscr-2018-0007

Keywordstype1 and type2 fuzzy sets, polynomial and exponential equations, particle swarm optimization

© 2018 Sheriff Sadiqbatcha et al., published by De Gruyter Open

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Keywords
type1 and type2 fuzzy sets, polynomial and exponential equations, particle swarm optimization