## I.A. Hodashinsky, M.B. Bardamova, I.V. Kovalev Using shuffled frog-Leaping algorithm for feature selection and fuzzy classifier design

### Abstract.

This article, a new approach to designing fuzzy-rule-based classifier is considered. The fuzzy classifier construction includes the following stages:feature selection, generation of the classifier structure, optimization of the classifier parameters, and choice of the optimal classifier. At the first stage, according to the

principle of "wrappers", binary shuffled frog-leaping algorithm are formed groups of relevant features on the classifiable data set. Since the randomness present in metaheuristics is capable of leading to the selection of various relevant features, several groups of features are formed. At the second stage, on each selected feature group, the structure of the fuzzy classifier is generated on the basis of the extrema of the observation table. The generated structures have the minimum possible number of rules, which is limited by the number of existing classes in the classified data set. The rules bases constructed in this way are simple for understanding and subsequent interpretation of the result obtained. The next step is to optimize the parameters of each classifier using a continuous shuffled frog-leaping algorithm. On a set of constructed classifiers, the optimal classifier is selected with respect to the accuracy and the number of features used, using the statistical Akaike informational criterion. The effectiveness of the proposed ap proach is tested on 15 KEEL data sets. The results obtained are statistically compared with the results of similar algorithms. The new approach to designing fuzzy classifiers proposed in the article allows to reduce the number of rules and attributes, thereby increasing the interpretability of classification results.

### Keywords:

fuzzy classifier, parameters optimization, features selection, shuffled frog-leaping algorithm.

PP. 76-84.

### References

1. Guillaume S. 2001. Designing fuzzy inference systems from data:An interpretability-oriented review. IEEE Transactions on Fuzzy Systems. 9(3):426-443.

2. Ducange P, Lazzerini B, Marcelloni F. 2010. Multi-objective genetic fuzzy classifiers for imbalanced and cost-sensitive datasets. Soft. Comput. 14:713-728.

3. Pota M, Esposito M, Pietro GD. 2017. Designing rule-based fuzzy systems for classification in medicine. Knowl.-Based Syst. 124:105-132.

4. Jamalabadi H, Nasrollahi H, Alizadeh S, Araabi BN, Ahamadabadi MN. 2016, Competitive interaction reasoning:A bioinspired reasoning method for fuzzy rule based classification systems. Information Sciences. 352-353:35-47.

5. Salcedo-Sanz S. 2016. Modern meta-heuristics based on nonlinear physics processes:A review of models and design procedures. Physics Reports. 655:1-70.

6. Melin P, Olivas F., Castillo O., Valdez F., Soria J., Valdez M. 2013. Optimal design of fuzzy classification systems using PSO with dynamic parameter adaptation through fuzzy logic. Expert Systems with Applications. 40(8):3196-3206.

7. Lahsasna A, Seng WC. 2017. An improved genetic-fuzzy system for classification and data analysis. Expert Systems with Applications. 83:49-62.

8. Mekh MA, Hodashinsky IA. 2017. Comparative Analysis of differential evolution methods to optimize parameters of fuzzy classifiers. Journal of Computer and Systems Sciences International. 4(56):65-75.

9. Hodashinsky IA, Mekh MA. 2017. Fuzzy classifier design using harmonic search methods. Programming and computer software. 1(43):54-65.

10. Hodashinsky IA, Gorbunov I.V. & Dudin P.A. 2009. Algoritmy murav'inoi i pchelinoi kolonii dlia obucheniia nechetkikh sistem [Algorithms of ants and bee colony for training a fuzzy system]. Doklady TUSUR [Proceedings of TUSUR], 20(2):157-161.

11. Eusuff MM, Lansey KE. 2003. Optimization of water distribution network design using the shuffled frog leaping algorithm. J. Water Resour. Plann. Manag. 129:210-225.

12. Eusuff MM, Lansey KE, Pasha F. 2006. Shuffled frog-leaping algorithm:a memetic meta heuristic for discrete optimization. Engineering Optimization. 38(2):129-154.

13. Wang L, Gong Y. 2013. Diversity Analysis of Population in Shuffled Frog Leaping Algorithm. ICSI 2013, Part I, LNCS 7928. London. 24-31.

14. Nguyen D-H, Ngo M-D. 2016. Comparing Convergence of PSO and SFLA Optimization Algorithms in Tuning Parameters of Fuzzy Logic Controller. Lecture Notes in Electrical Engineering, 371. London. 457-467.

15. Wu FL, Ding SF, Huang HJ, Zhu ZB. 2014. Mixed kernel twin support vector machines based on the shuffled frog leaping algorithm. J. Comput. 9(4):947-955.

16. Zhang X, Ding S, Sun T. 2016. Multi-class LSTMSVM based on optimal directed acyclic graph and shuffled frog leaping algorithm. Int. J. Mach. Learn. & Cyber. 7:241-251.

17. Zhao Z, Xu Q, Jia M. 2016. Improved shuffled frog leaping algorithm-based BP neural network and its application in bearing early fault diagnosis. Neural Comput. & Applic. 27:375-385.

18. Bolon-Canedo V, Sanchez-Marono N, Alonso-Betanzos A. 2015. Feature Selection for High-Dimensional Data. London: Springer. 142 p.

19. Vakil Baghmisheh MT, Madani K, Navarbaf A. 2011. A discrete shuffled frog optimization algorithm. Artif. Intell. Rev. 36:267-284.

20. Kennedy J, Eberhart RC. 1997. A discrete binary version of the particle swarm algorithm. Proceeding of the IEEE International Conference on System, Man, and Cybernetics. IEEE. 4104-4109.

21. Yen J. 1998. Application of Statistical Information Criteria for Optimal Fuzzy Model Construction. IEEE Transaction on Fuzzy Systems. 6:362-372.

22. Hodashinsky IA. 2014. Postroenie kompaktnyh i tochnyh nechetkih modelej na osnove statisticheskih informacionnyh kriteriev [Design of compact and precise fuzzy models based on statistical information criteria]. Informatika i sistemy upravleniya [Informatics and Control Systems] 1(39):99-107.

23. Fazzolari F. 2014. A multi-objective evolutionary method for learning granularities based on fuzzy discretization to improve the accuracy-complexity trade-off of fuzzy rule-based classification systems:D-MOFARC algorithm. Applied Soft Computing. 24:470-481.