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## Description

fuzzy particle swarm optimization

A fuzzy particle swarm optimization (FPSO) will be proposed to improve the performance of PSO;
a fuzzy system will be employed to adjust the parameter of PSO, the inertia weight w and learning factors c1 and c2 during the evolution process.
From experience, it is known that:

1. When the best fitness is low at the end of the run in the optimization of a minimum function, low inertia weight and high learning factors are often preferred.

2.When the best fitness is stuck at one value for a long time, number of generations for unchanged best fitness is large. The system is often stuck at a local minimum, so the system should probably concentrate on exploiting rather than exploring. That is, the inertia weight should be increased and learning factors should be decreased. Based on this kind of knowledge, a fuzzy system is developed to adjust the inertia weight, and learning factors with best fitness (BF) and number of generations for unchanged best fitness (NU) as the input variables, and the inertia weight (w) and learning factors (c1 and c2) as output variables.

## Fuzzy Rules of fuzzy particle swarm optimization:

R1 : If NBF is PS and NU is PS then w is PS; c1 is PR and c2 is PR.
R2: If NBF is PM and NU is PS then w is PM; c1 is PB and c2 is PB.
R3: If NBF is PB and NU is PS then w is PB; c1 is PB and c2 is PM.
R4: If NBF is PR and NU is PS then w is PB; c1 is PM and c2 is PM.
R5: If NBF is PS and NU is PM then w is PM; c1 is PB and c2 is PB.
R6: If NBF is PM and NU is PM then w is PM; c1 is PM and c2 is PM.
R7: If NBF is PB and NU is PM then w is PB; c1 is PM and c2 is PM.
R8: If NBF is PR and NU is PM then w is PB; c1 is PM and c2 is PS.
R9: If NBF is PS and NU is PB then w is PB; c1 is PB and c2 is PM.
R10: If NBF is PM and NU is PB then w is PB; c1 is PM and c2 is PS.
R11: If NBF is PB and NU is PB then w is PB; c1 is PS and c2 is PS.
R12: If NBF is PR and NU is PB then w is PR; c1 is PS and c2 is PS.
R13: If NBF is PS and NU is PR then w is PB; c1 is PM and c2 is PM.
R14: If NBF is PM and NU is PR then w is PR; c1 is PS and c2 is PS.
R15: If NBF is PB and NU is PR then w is PR; c1 is PS and c2 is PS.
R16: If NBF is PR and NU is PR then w is PR; c1 is PS and c2 is PS.

This MATLAB code can be used for any type of optimization problem.

You can use this code for any other purpose.

Fuzzy System :

Membership function of the fuzzy system:

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