Normal parameter reduction algorithm in soft set based on hybrid binary particle swarm and biogeography optimizer


Existing classification techniques that are proposed previously for eliminating data inconsistency could not achieve an efficient parameter reduction in soft set theory, which effects on the obtained decisions. Meanwhile, the computational cost made during combination generation process of soft sets could cause machine infinite state, which is known as nondeterministic polynomial time. The contributions of this study are mainly focused on minimizing choices costs through adjusting the original classifications by decision partition order and enhancing the probability of searching domain space using a developed Markov chain model. Furthermore, this study introduces an efficient soft set reduction-based binary particle swarm optimized by biogeography-based optimizer (SSR-BPSO-BBO) algorithm that generates an accurate decision for optimal and sub-optimal choices. The results show that the decision partition order technique is performing better in parameter reduction up to 50%, while other algorithms could not obtain high reduction rates in some scenarios. In terms of accuracy, the proposed SSR-BPSO-BBO algorithm outperforms the other optimization algorithms in achieving high accuracy percentage of a given soft dataset. On the other hand, the proposed Markov chain model could significantly represent the robustness of our parameter reduction technique in obtaining the optimal decision and minimizing the search domain.

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  1. 1.

    Min H, Eom SB (1994). An integrated decision support system for global logistics. Int J Phys Distrib Logistics Manage 24(1):29–39

    Google Scholar 

  2. 2.

    Fulmer CA (2011) Developing information storage and retrieval systems on the internet a knowledge management approach. Naval Postgraduate School, Monterey

    Google Scholar 

  3. 3.

    Gottschalk P (2007) Knowledge management systems in law enforcement: technologies and techniques. IGI Global, Hershey

    Google Scholar 

  4. 4.

    Maier R (2007) Knowledge management systems: information and communication technologies for knowledge management. Springer, Berlin

    Google Scholar 

  5. 5.

    Osei-Bryson K-M, Mansingh G, Rao L (2014) knowledge management for development: domains, strategies and technologies for developing countries. Springer, Berlin

    Google Scholar 

  6. 6.

    Dalkir K (2013) Knowledge management in theory and practice. Routledge, Abingdon

    Google Scholar 

  7. 7.

    Yu H, Huang X, Hu X, Wan C (2009) Knowledge management in E-commerce: a data mining perspective. Paper presented at the international conference on management of e-Commerce and e-Government, 2009. ICMECG’09

  8. 8.

    Castillo O, Muhuri PK (2019) Special issue on “Type-2 fuzzy systems and granular computing. Granul Comput 4(2):143–143

    Google Scholar 

  9. 9.

    Chang M-Y, Hung Y-C, Yen DC, Tseng PT (2009) The research on the critical success factors of knowledge management and classification framework project in the Executive Yuan of Taiwan Government. Expert Syst Appl 36(3):5376–5386

    Google Scholar 

  10. 10.

    Ji M, Han J, Danilevsky M (2011) Ranking-based classification of heterogeneous information networks. Paper presented at the Proceedings of the 17th ACM SIGKDD international conference on Knowledge discovery and data mining

  11. 11.

    King WR (2009) Knowledge management and organizational learning. Annals of information systems, 4th edn, LLC

  12. 12.

    Batrouni M, Bertaux A, Nicolle C (2018) Scenario analysis, from BigData to black swan. Comput Sci Rev 28:131–139.

    Article  Google Scholar 

  13. 13.

    Merminod V, Rowe F (2012) How does PLM technology support knowledge transfer and translation in new product development? Transparency and boundary spanners in an international context. Inf Organ 22(4):295–322

    Google Scholar 

  14. 14.

    Sadiq AS, Faris H, Ala’M A-Z, Mirjalili S, Ghafoor KZ (2019) Fraud detection model based on multi-verse features extraction approach for smart city applications. In: Rawat DB, Ghafoor KZ (eds) Smart cities cybersecurity and privacy. Elsevier, Amsterdam, pp 241–251

    Google Scholar 

  15. 15.

    Văduva I (2012) On solving some types of multiple attribute decision making problems. Romanian J Econ Forecast 15(1):41–61

    Google Scholar 

  16. 16.

    Laudon K, Laudon J (2009) Management information systems: international edition, 11/E. Pearson Higher Education

  17. 17.

    Ayyub BM, Klir GJ (2010) Uncertainty modeling and analysis in engineering and the sciences. CRC Press, Boca Raton

    MATH  Google Scholar 

  18. 18.

    Akerkar R, Sajja P (2010) Knowledge-based systems. Jones & Bartlett Publishers, Burlington

    Google Scholar 

  19. 19.

    Del Junco JG, Zaballa RDR, de Perea JGÁ (2010) Evidence-based administration for decision making in the framework of knowledge strategic management. Learn Organ 17(4):343–363

    Google Scholar 

  20. 20.

    Sadiq AS, Alkazemi B, Mirjalili S, Ahmed N, Khan S, Ali I, Pathan A-SK, Ghafoor KZ (2018) An efficient ids using hybrid magnetic swarm optimization in wanets. IEEE Access 6:29041–29053

    Google Scholar 

  21. 21.

    Asemi A, Safari A, Zavareh AA (2011) The role of management information system (MIS) and Decision support system (DSS) for manager’s decision making process. Int J Bus Manag 6(7):p164

    Google Scholar 

  22. 22.

    Babitha K, Sunil J (2010) Soft set relations and functions. Comput Math Appl 60(7):1840–1849

    MathSciNet  MATH  Google Scholar 

  23. 23.

    Chen Y-C, Shang R-A, Kao C-Y (2009) The effects of information overload on consumers’ subjective state towards buying decision in the internet shopping environment. Electron Commer Res Appl 8(1):48–58

    Google Scholar 

  24. 24.

    Herawan T (2014) Recent advances on soft computing and data mining: proceedings of the first international conference on soft computing and data mining (Scdm-2014) Universiti Tun Hussein Onn Malaysia, Johor, Malaysiajune 16Th–18Th. Springer

  25. 25.

    Mirjalili S, Dong JS, Sadiq AS, Faris H (2020) Genetic algorithm: theory, literature review, and application in image reconstruction, nature-inspired optimizers. Springer, Berlin, pp 69–85

    Google Scholar 

  26. 26.

    Mirjalili S, Dong JS, Lewis A, Sadiq AS (2020) particle swarm optimization: theory, literature review, and application in airfoil design, nature-inspired optimizers. Springer, Berlin, pp 167–184

    Google Scholar 

  27. 27.

    Herawan T, Deris MM (2009) A direct proof of every rough set is a soft set. In 2009 Third Asia International Conference on Modelling & Simulation, IEEE. pp 119–124

  28. 28.

    Herawan T, Deris MM (2009) A soft set approach for association rules mining. Knowl Based Syst 24(1):186–195

    MATH  Google Scholar 

  29. 29.

    Rose ANM, Awang MI, Hassan H, Zakaria AH, Herawan T, Deris MM (2011) Hybrid reduction in soft set decision making. In: International Conference on Intelligent Computing, Springer, Berlin, Heidelberg, pp 108–115

  30. 30.

    Zhao Y, Luo F, Wong SM, Yao Y (2007) A general definition of an attribute reduct. In: International Conference on Rough Sets and Knowledge Technology, Springer, Berlin, Heidelberg, pp 101–108

  31. 31.

    Mohammed MAT, Sadiq AS, Arshah RA, Ernawan F, Mirjalili S (2017) Soft set decision/forecasting system based on hybrid parameter reduction algorithm. J Telecommun Electron Comput Eng (JTEC) 9(2–7):143–148

    Google Scholar 

  32. 32.

    Chen D, Tsang E, Yeung DS, Wang X (2005) The parameterization reduction of soft sets and its applications. Comput Math Appl 49(5):757–763

    MathSciNet  MATH  Google Scholar 

  33. 33.

    Kong Z, Gao L, Wang L, Li S (2008) The normal parameter reduction of soft sets and its algorithm. Comput Math Appl 56(12):3029–3037

    MathSciNet  MATH  Google Scholar 

  34. 34.

    Kumar DA, Rengasamy R (2013) Parameterization reduction using soft set theory for better decision making. Paper presented at the 2013 international conference pattern recognition, informatics and mobile engineering (PRIME)

  35. 35.

    Maji P, Roy AR, Biswas R (2002) An application of soft sets in a decision making problem. Comput Math Appl 44(8):1077–1083

    MathSciNet  MATH  Google Scholar 

  36. 36.

    Mamat R, Herawan T, Deris MM (2011) Super attribute representative for decision attribute selection. In: International Conference on Software Engineering and Computer Systems, Springer, Berlin, Heidelberg, pp 137–147

  37. 37.

    Rose ANM, Herawan T, Deris MM (2010) A framework of decision making based on maximal supported sets. In: Advances in Neural Networks-ISNN 2010. Springer, pp 473–482

  38. 38.

    Miller BM, Rubinovich EY (2012) Impulsive control in continuous and discrete-continuous systems. Springer, Berlin

    MATH  Google Scholar 

  39. 39.

    Wolsey LA, Nemhauser GL (2014) Integer and combinatorial optimization. Wiley, London

    MATH  Google Scholar 

  40. 40.

    Huang Z-H, Ni T (2010) Smoothing algorithms for complementarity problems over symmetric cones. Comput Optim Appl 45(3):557–579

    MathSciNet  MATH  Google Scholar 

  41. 41.

    Bertekas DP (2014) Constrained optimization and Lagrange multiplier methods. Academic Press, Cambridge

    Google Scholar 

  42. 42.

    Horst R, Tuy H (2013) Global optimization: deterministic approaches. Springer, Berlin

    MATH  Google Scholar 

  43. 43.

    Streiner DL, Norman GR, Cairney J (2014) Health measurement scales: a practical guide to their development and use. Oxford University Press, Oxford

    Google Scholar 

  44. 44.

    Nemhauser G, Bienstock D (2005) Integer programming and combinatorial optimization. Springer, Berlin

    Google Scholar 

  45. 45.

    Xu H, Caramanis C, Mannor S (2012) sparse algorithms are not stable: a no-free-lunch theorem. IEEE Trans Pattern Anal Mach Intell 34(1):187–193

    Google Scholar 

  46. 46.

    Goldberg DE, Holland JH (1988) Genetic algorithms and machine learning. Mach Learn 3(2):95–99

    Google Scholar 

  47. 47.

    Holland JH (1992) Genetic algorithms. Sci Am 267(1):66–73

    Google Scholar 

  48. 48.

    Kennedy, J. (2010). Particle swarm optimization. Encyclopedia of machine learning, pp 760–766.

  49. 49.

    Yang X-S (2010a) A new metaheuristic bat-inspired algorithm. In: Nature inspired cooperative strategies for optimization (NICSO 2010). Springer, pp 65–74

  50. 50.

    Yang XS (2010) Firefly algorithm, stochastic test functions and design optimisation. Int J Bio-Inspired Comput 2(2):78–84

    Google Scholar 

  51. 51.

    Mohapatra P, Chakravarty S, Dash PK (2015) An improved cuckoo search based extreme learning machine for medical data classification. Swarm Evolut Comput 24:25–49

    Google Scholar 

  52. 52.

    Mirjalili S, Mirjalili SM, Lewis A (2014) Grey wolf optimizer. Adv Eng Softw 69:46–61

    Google Scholar 

  53. 53.

    Yang X-S (2012) Swarm-based metaheuristic algorithms and no-free-lunch theorems. In: Theory and new applications of swarm intelligence

  54. 54.

    Cortes C, Vapnik V (1995) Support-vector networks. Mach Learn 20(3):273–297

    MATH  Google Scholar 

  55. 55.

    Fine TL (1999) Feedforward neural network methodology. Springer, Berlin

    MATH  Google Scholar 

  56. 56.

    Wei Y, Ni N, Liu D, Chen H, Wang M, Li Q, Ye H (2017) An improved grey wolf optimization strategy enhanced SVM and its application in predicting the second major. Math Prob Eng 2017(1):1–12

    Google Scholar 

  57. 57.

    Nika SS (2015) a comparative study of classification techniques in data mining algorithms. Orient J Comput Sci Technol 8(1):13–19

    Google Scholar 

  58. 58.

    Dasgupta D, Michalewicz Z (2001) Evolutionary algorithms in engineering applications. Springer, Berlin

    MATH  Google Scholar 

  59. 59.

    Parmee IC (2001) Evolutionary and adaptive computing in engineering design. Springer, Berlin

    Google Scholar 

  60. 60.

    Simon D (2008) Biogeography-based optimization. IEEE Trans Evol Comput 12(2008):702–713

    Google Scholar 

  61. 61.

    Wang G-G, Gandomi AH, Alavi AH (2013) A chaotic particle-swarm krill herd algorithm for global numerical optimization. Kybernetes 42(6):962–978

    MathSciNet  Google Scholar 

  62. 62.

    Wang G-G, Gandomi AH, Alavi AH (2013) An effective krill herd algorithm with migration operator in biogeography-based optimization. Appl Math Model.

    Article  MATH  Google Scholar 

  63. 63.

    Wang G-G, Gandomi AH, Alavi AH (2014) Stud krill herd algorithm. Neurocomputing 128:363–370.

    Article  Google Scholar 

  64. 64.

    Wang G-G, Gandomi AH, Alavi AH, Hao G-S (2013) Hybrid krill herd algorithm with differential evolution for global numerical optimization. Neural Comput Appl.

    Article  Google Scholar 

  65. 65.

    Wang G, Guo L, Wang H, Duan H, Liu L, Li J (2012) Incorporating mutation scheme into krill herd algorithm for global numerical optimization. Neural Comput Appl.

    Article  Google Scholar 

  66. 66.

    Mirjalili S, Lewis A, Sadiq AS (2014) Autonomous particles groups for particle swarm optimization. Arab J Sci Eng 39(6):4683–4697

    MATH  Google Scholar 

  67. 67.

    Haykin S (1994) Neural networks: a comprehensive foundation. Prentice Hall PTR

  68. 68.

    Zhang N (2009) An online gradient method with momentum for two-layer feedforward neural networks. Appl Math Comput 212(2009):488–498

    MathSciNet  MATH  Google Scholar 

  69. 69.

    Ammu PK, Sivakumar KC, Rejimoan R (2013) Biogeography-based optimization - A survey. Int J Electron Comput Sci Eng 2(1):154–160

    Google Scholar 

  70. 70.

    Blum C, Socha K (2005) Training feed-forward neural networks with ant colony optimization: an application to pattern classification. In: IEEE

  71. 71.

    Baluja S (1994) Population-based ıncremental learning: a method for ıntegrating genetic search based function optimization and competitive learning. Technical Report CMU-CS-94-163(Computer Science Department, Carnegie Mellon University, Pittsburgh)

  72. 72.

    Kong Z, Jia W, Zhang G, Wang L (2015) Normal parameter reduction in soft set based on particle swarm optimization algorithm. J Appl Math Model 39(16):4808–4820

    MathSciNet  MATH  Google Scholar 

  73. 73.

    Mirjalili S, Gandomi AH (2017) Chaotic gravitational constants for the gravitational search algorithm. Appl Soft Comput 53:407–419

    Google Scholar 

  74. 74.

    Mirjalili S, Mirjalili SM, Lewis A (2014) Let a biogeography-based optimizer train your multi-layer perceptron. Inf Sci 269:188–209

    MathSciNet  Google Scholar 

  75. 75.

    Kennedy J, Eberhart R (1997) A discrete binary version of the particle swarm algorithm. In: Proceedings of the IEEE international conference on computational cybernetics and simulation

  76. 76.

    Mirjalili S, Lewis A (2013) S-shaped versus V-shaped transfer functions for binary particle swarm optimization. Swarm Evolut Comput 9(pp1–14):2013

    Google Scholar 

  77. 77.

    Herawan T, Rose ANM, Deris MM (2009) Soft set theoretic approach for dimensionality reduction. In: International Conference on Database Theory and Application, Springer, Berlin, Heidelberg, pp 171–178

  78. 78.

    Mirjalili S, Mohd Hashim SZ (2012) BMOA: binary magnetic optimization algorithm. Int J Mach Learn Comput 2(3):204–208

    Google Scholar 

  79. 79.

    Mirjalili S, Hashim SZM (2010) A new hybrid PSOGSA algorithm for function optimization. In: 2010 international conference on computer and information application (ICCIA), 3–5 Dec 2010, pp 374, 377

  80. 80.

    Ma H, Simon D, Fei M, Xie Z (2013) Variations of biogeography-based optimization and Markov analysis. Inform Sci 220(2013):492–506.

    Article  Google Scholar 

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Correspondence to Ali Safaa Sadiq.

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Sadiq, A.S., Tahir, M.A., Ahmed, A.A. et al. Normal parameter reduction algorithm in soft set based on hybrid binary particle swarm and biogeography optimizer. Neural Comput & Applic 32, 12221–12239 (2020).

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  • Classification
  • Markov chain model
  • Binary particle swarm optimization
  • Biogeography-based optimizer
  • Decision-making