Solution of fuzzy relation equations by genetic algorithms

Rok, strany: 1999, 225 - 234

General fuzzy relation equations are solved by genetic algorithms. Genetic algorithms represent powerful stochastic optimization methods that are able to look for global minima of complex multimodal objective functions. A modification of genetic algorithms for purposes of finding solution of general fuzzy relations is proposed. Basic concept of genetic algorithms is a population of chromosomes, which is for the considered fuzzy relation equations composed of matrices that correspond to solutions of problem. An objective function assigns to each chromosome a value that is vanishing if the chromosome corresponds to a correct solution. In the opposite case, if the chromosome is not a solution, then the function value is positive. This means that the solution of fuzzy relation can be transformed onto an equivalent minimization problem with the above specified objective function. A crossover operation between two chromosomes — matrices is determined, such that there is selected randomly (vertical) crossover line, and then matrix parts that are behind (below) the crossover line are mutually exchanged. A mutation operation goes through all chromosome elements, to which a small random number $r(O,σ)$ is added, where $r(O,σ)$ is a random number with a normal distribution, zero mean and a dispersion $σ$. Simple illustrative examples are discussed.

ISO 690:

Boor, Š., Kvasnička, V., Pospíchal, J. 1999. Solution of fuzzy relation equations by genetic algorithms. In Tatra Mountains Mathematical Publications, vol. 16, no.2, pp. 225-234. 1210-3195.

APA:

Boor, Š., Kvasnička, V., Pospíchal, J. (1999). Solution of fuzzy relation equations by genetic algorithms. Tatra Mountains Mathematical Publications, 16(2), 225-234. 1210-3195.