Automated Generation of EQ-Algebras through Genetic Algorithms

• Published in: Mathematics (Basel) 2021-04, Vol.9 (8), p.861
• Main Authors: Habiballa, Hashim, Volna, Eva, Kotyrba, Martin
• Format: Article
• Language: English
• Subjects: Algebra; Automation; Axioms; Chromosomes; Complexity; Computing time; Efficiency; EQ-algebra; finite algebra; Fuzzy logic; genetic algorithm; Genetic algorithms; Mathematics; Mutation; Operators (mathematics); Optimization; Population; Statistical analysis; superexponential problem
• ISSN: 2227-7390; 2227-7390
• DOI: 10.3390/math9080861

This article introduces an approach to the automated generation of special algebras through genetic algorithms. These algorithms can be also used for a broader variety of applications in mathematics. We describe the results of research aiming at automated production of such algebras with the help of evolutionary techniques. Standard approach is not relevant due to the time complexity of the task, which is superexponential. Our research concerning the usage of genetic algorithms enabled the problem to be solvable in reasonable time and we were able to produce finite algebras with special properties called EQ-algebras. EQ-algebras form an alternate truth–value structure for new fuzzy logics. We present the algorithms and special versions of genetic operators suitable for this task. Then we performed experiments with application EQ-Creator are discussed with proper statistical analysis through ANOVA. The genetic approach enables to automatically generate algebras of sufficient extent without superexponential complexity. Our main results include: that elitism is necessary at least for several parent members, a high mutation ratio must be set, optional axioms fulfilment increases computing time significantly, optional properties negatively affect convergence, and colorfulness was defined to prevent trivial solutions (evolution tends to the simplest way of achieving results).