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International Journal of Pure and Applied Mathematics Volume 114 No. 5 2017, 201-209 ISSN: 1311-8080 (printed version); ISSN: 1314-3395 (on-line version) url: http://www.ijpam.

1 International Journal of Pure and Applied Mathematics Volume 114 No , ISSN: (printed version); ISSN: (on-line version) url: Special Issue Hybrid Evolutionary based Algorithms for Classification of Biomedical Databases S.Poongothai 1,, C.Dharuman 1 and P.Venkatesan 2 1 Department of Mathematics, SRM University, Ramapuram Campus, Chennai, India. 2 Sri Ramachandra University,Chennai, India. Corresponding author:poongothaikannan25@gmail.com February 22, 2017 ijpam.eu Abstract The aim of this paper is to classify the medical data using various hybrid techniques of fuzzy with Evolutionary algorithms. Nowadays Fuzzy classifiers are widely used for efficient classification of data. To improve its efficiency the idea of hybridization has been developed. In this paper fuzzy combines with genetic algorithm, particle swarm optimization (PSO) and ant colony optimisation (ACO) separately to classify the data. Also the results are compared with one another. We have used thoracic surgery data from UCI for classification.the experimental results shows how the fuzzy hybrid techniques performs better than other normal methods. AMS Subject Classification: 03B52, 03E72. Keywords: Fuzzy logic, Evolutionary algorithms, Genetic algorithms, Particle swarm optimization, Ant colony optimization, Hybrid techniques

2 1 Introduction International Journal of Pure and Applied Mathematics Special Issue In the field of artificial intelligence (AI), particularly in machine learning algorithm, any type of problems can be solved using the previous or past experience [1]. It consists of designing and developing algorithms for classifying the data and also used for predicting the classes. One of the most popular hybridization approach is fuzzy systems with evolutionary algorithms. A fuzzy set is distinct from a crisp set which allows its elements to have a degree of membership functions.evolutionary algorithms is a study based on very fundamental principles of Darwin s theory. Genetic Algorithms (GA), Ant Colony Optimisation (ACO) and Particle Swarm Optimisation (PSO) are branches of Evolutionary Algorithms. 2 Description of Datasets The database on Thoracic Surgery data was taken from UCI machine learning repository database. There are 470 cases, out of this 70 cases are in survival category and 400 cases are in death categories. There are seventeen attributes in this data set. The information of attributes are given below 1. DGN: Diagnosis - specific combination of ICD-10 codes for primary and secondary as wellmultiple tumours if any (DGN3,DGN2,DGN4,DGN6,DGN5,DGN8,DGN1) 2. PRE4: Forced vital capacity - FVC (numeric) 3. PRE5: Volume that has been exhaled at the end of the first second of forced expiration - FEV1 (numeric) 4. PRE6: Performance status - Zubrod scale (PRZ2,PRZ1,PRZ0) 5. PRE7: Pain before surgery (T,F) 6. PRE8: Haemoptysis before surgery (T,F) 7. PRE9: Dyspnoea before surgery (T,F) 8. PRE10: Cough before surgery (T,F) 9. PRE11: Weakness before surgery (T,F) 2 202

3 10. International PRE14: Journal T in clinical of PureTNM and Applied - size Mathematics of original tumour, Specialfrom Issue OC11 (smallest) to OC14 (largest) (OC11,OC14,OC12,OC13) 11. PRE17: Type 2 DM - diabetes mellitus (T,F) 12. PRE19: MI up to 6 months (T,F) 13. PRE25: PAD - peripheral arterial diseases (T,F) 14. PRE30: Smoking (T,F) 15. PRE32: Asthma (T,F) 16. AGE: Age at surgery (numeric) 17. Risk1Y: 1 year survival period - T and if died - F 3 Hybrid Evolutionary Algorithms In the world of computational intelligence, hybrid approaches have special attention due to its performance. The most popular approach is the hybridization of Fuzzy Logic and Genetic Algorithms leading to Genetic Fuzzy Systems (GFSs) [2] and Fuzzy Evolutionary Algorithms [3, 4, 5]. Fuzzy sets and fuzzy logic provides smart classification of data. In contrast to crisp classifications, fuzzy classification permits to analyze the data samples in a more accuracy sensitive way [6]. Fuzzy inference system or if-then rules are examples of efficient, excellent and easily interpretable fuzzy classifiers [6, 7]. In the context of machine learning and data mining, the most popular way of expressing the knowledge consists of IF-THEN rules. This is due to the fact that they are comprehensible to a human being [8]. The fuzzy inference system (FIS) follows the technique as If antecedent then consequent [9].In the simple fuzzy partition grid methods, each attribute can be partitioned by various linguistic values [10]. Genetic Algorithm is a search technique used in computing to find true or approximate solutions to optimization and search problems. It is categorized as global search heuristics. It is a particular type of evolutionary algorithms that use techniques inspired by evolutionary biological terms such as inheritance, mutation, selection, and crossover (also called recombination). Genetic Algorithm differs from other search techniques 3 203

4 byinternational four ways [11, Journal 12, of13]. PureThey and Applied are (i) Mathematics work with a coding Special of Issue the parameter set, not the parameter themselves. (ii) Search from a population of points, not a single point. (iii) Use objective function information, not derivatives or other auxiliary knowledge. (iv) Use probabilistic transition rules, not deterministic rules. 3.1 Particle Swarm Optimisation (PSO) PSO is a robust stochastic optimization evolutionary computing technique based on the movement and intelligence of swarms. It applies the concept of social interaction to solve the problem.in 1995, it was developed by James Kennedy and Russell Eberhart. It uses a number of particles that constitute a swarm moving around to find the best solution in the search space.each particle is considered as a point in a n-dimensional space which adjusts its flyingby its own experience as well as the experience of other particles. In the solution space each and every particle keeps track of its coordinates which are associated with the better solution,say fitness,that has achieved so far by the corresponding particle. This value is considered as personal best, pbest.another best value that is tracked by the PSO obtained so far by any particle in the neighborhood of that particle is called gbest. The basic idea behind PSO is accelerating each particle towards its pbest and the gbest positions, with acceleration having random weighted at each time. Each particle tries to modify its position using (i) the current velocities,(ii) the current positions, (iii) the distance between the current position and the pbest and (iv) the distance between the current position and the gbest. The modification of position of the particles can be mathematically modeled according to the following equation V k+1 i = wvi k +c 1 rand 1 ( ) (pbest i s k i )+c 2 rand 2 ( ) (gbest s k i ) (1) is velocity of agent i at iteration k, w is weighting func- where, vi k tion, c j is weighting factor, rand is uniformly distributed random number between 0 and 1, s k i is current position of agent i at iteration k, pbest i is pbest of agent i, gbest : gbest of the group. Thefollowing weighting function is usually utilized in (1) w = wmax [(wmax wmin) iter]/maxiter (2) 4 204

5 where International wmax= Journal initialof weight, Pure and wmin Applied = final Mathematics weight, maxiter Special = maximum number of iterations, iter = current iteration number. Issue Selection operation is not employed in PSO.All particles in PSO are treated as individuals of the population through the course of the run. There is no crossover operation in PSO. Recently, PSO has proving as a best algorithm in solving various optimization problems in the field of science and engineering [14]. 3.2 Ant Colony Optimization (ACO) ACO was inspired from the behavior of real ant colonies, and it is used to solve discrete optimization problems. ACO system was first developed by Marco Dorigo in his Ph.D. thesis [15] and was called the ant system (AS). It is also a type of Evolutionary Computations. Initially travelling salesman problem was solved by AS [16] and then to other hard problems. The behavior of ants that deposits their pheromone on the ground to make a desired path so that other members of the colony should follow. Their ultimate aim is to find the shortest path between a food source and the nest. Theoretically, if the quantity of pheromone remains the same over time on all edges, no route is chosen. However, a slight variation on an edge allows the edge to be chosen. The algorithm moves from an unstable state in which no edge is stronger than another, to a stable state in which the route having the strongest edges. Ant colony optimization has a wide application domain; for example, Liu et al. [17] applied ACO for continuous domains. 4 Results In this paper three types of evolutionary algorithms are used for feature selection namely Genetic Algorithms, Particle Swarm Optimisation and Ant Colony Optimisation. Then reduced features acts as input for Fuzzy systems for classification. Using simple fuzzy grid system, the data is classified by WEKA tool. Figure 1 shows feature selection by GA. It reduces 16 attributes to 7 numbered 2,3,8,9,11,12 and13, Figure 2 shows feature selection by PSO which reduces to 5 attributes from 16 attributes numbered 1,7,10,11 and 14, Figure 3 shows the feature selection by ACO. It reduces to 4 attributes numbered 2,3,9,

International Journal of Pure and Applied Mathematics Special Issue Figure 1: Feature selection by

Table 1 shows the classification results and mean absolute error of the Fuzzy and hybrid of FGA,

Figure 4 shows the classification rate of Fuzzy and its hybrid fuzzy evolutionary algorithms (FEA).

6 International Journal of Pure and Applied Mathematics Special Issue Figure 1: Feature selection by GA. Figure 2: Feature selection by PSO. Figure 3: Feature selection by ACO. Table 1 shows the classification results and mean absolute error of the Fuzzy and hybrid of FGA, FPSO, FACO. Figure 4 shows the classification rate of Fuzzy and its hybrid fuzzy evolutionary algorithms (FEA). From the figure, we are able to see thatfuzzy combined Evolutionary Algorithms gives better classification than fuzzy alone. In particular, hybrid of Fuzzy with ACO performs good with less number of attributes 6 206

7 International Journal of Pure and Applied Mathematics Special Issue Table 1: Classification rate and mean absolute error of Fuzzy and its hybrid FEA Algorithms Classification rate (%) Mean Absolute Error Fuzzy FGA FPSO FACO Classifica on Rate (%) Classifica on Rate (%) Fuzzy FGA FPSO FACO Figure 4: Classification rates by Fuzzy and hybrid Fuzzy Evolutionary Algorithms. 5 Discussions and conclusions The evolution of classification in data mining by fuzzy systems is ongoing project.the hybrid based methods provides better classification of data even if it is noisy. The classification is done by simple fuzzy grid system which gives the promising classification performance. This paper shows the comparative study of hybrid techniques of fuzzy and fuzzy with various types of evolutionary algorithms and we can conclude that hybridization of Fuzzy with Evolutionary Algorithms gives better classification and also fuzzy system performs well with ACO. In future, more experiments with other various data sets are going to be studied by applying Fuzzy- Rough set with advanced version of evolutionary computations with hope that gives better classification results

8 References International Journal of Pure and Applied Mathematics Special Issue [1] T. Mitchell (1997), Machine Learning McGraw Hill, ISBN [2] O. Cordon, F. Herrera, F. Hoffmann and L.Magdalena, Genetic fuzzy systems. In: Evolutionary tuning and learning of fuzzy knowledge bases, World Scientific, Singapore (2001). [3] F. Herrera, M. Lozano and J.L. Verdegay, Tackling fuzzy genetic algorithms. In: Genetic Algorithms in Engineering and Computer Science,JohnWiley, New York. (1995), [4] W. Pedrycz, Fuzzy evolutionary computing. Soft Computing 2, (1998), [5] A. Tettamanziand M. Tomassini, Fuzzy evolutionary algorithms. In: Soft Computing: Integrating Evolutionary, Neural, and Fuzzy Systems, Springer, Heidelberg. (2001), [6] J. C. Bezdek, J. Keller, R. Krisnapuram, and N. R. Pal, Fuzzy Modelsand Algorithms for Pattern Recognition and Image Processing (TheHandbooks of Fuzzy Sets). Secaucus, NJ, USA: Springer- Verlag NewYork, Inc., [7] A. Verikas, J. Guzaitis, A. Gelzinis, and M. Bacauskiene, A generalframework for designing a fuzzy rule-based classifier, Knowledge andinformation Systems, (2010), [8] U.M. Fayyad, G. Piatetsky-Shapiro and P. Smyth. From data mining to knowledge discovery: an overview. In: U.M. Fayyad et al. (Eds.) Advances in Knowledge Discovery and Data Mining, AAAI/MIT, (1996), [9] T.Hong,MCMC algorithm, integrated four-dimensional seismic reservoir characterization and uncertainty analysis in a bayesian framework, ProQuest LLC, (2008) p. 31. [10] S.Poongothai, C.Dharuman and P.Venkatesan, Fuzzy Evolutionary Computing in Biological Data Mining, Global Journal of Pure and Applied Mathematics (GJPAM) ISSN , 12, No. 1(2016), [11] David E. Goldberg, Genetic Algorithms in Search Optimization and Machine Learning, Addison Wesley, (1989)

9 [12] International Hansen, V.James, Journal of Pure Benjamin and Applied Lowry, Mathematics Paul, Meservy, Special Rayman, Issue McDonald and Dan, Genetic programming for prevention of cyberterrorism through dynamic and evolving intrusion detection, Decision Support Systems. 43 (4)(2007) doi: /j.dss [13] John R. Koza. 36 Human-Competitive Results Produced by Genetic Programming, retrieved [14] K.-B. Lee, and J.-H. Kim, Multiobjective particle swarm optimization with preference- based sort and its application to path following footstep optimization for humanoid robots, IEEE Transactions on Evolutionary Computation 17 No.6 (2013) doi: /tevc [15] M. Dorigo, Optimization, learning and natural algorithms [Ph. D. thesis], Politecnico di Milano, Milan, Italy, (1992). [16] M. Dorigo, V. Maniezzo, and A. Colorni, Ant system: optimization by a colony of cooperating agents, IEEE Transactions on Systems, Man, and Cybernetics B: Cybernetics, 26, No. 1,(1996) [17] L. Liu, Y. Dai, and J. Gao, Ant colony optimization algorithm for continuous domains based on position distribution model of ant colony foraging, The Scientific World Journal, (2014), Article ID , 9 pages

CT79 SOFT COMPUTING ALCCS-FEB 2014

CT79 SOFT COMPUTING ALCCS-FEB 2014 Q.1 a. Define Union, Intersection and complement operations of Fuzzy sets. For fuzzy sets A and B Figure Fuzzy sets A & B The union of two fuzzy sets A and B is a fuzzy set C, written as C=AUB or C=A OR