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Fuzzy Cognitive Maps for Applied Sciences and Engineering pp 237–252Cite as

Using Fuzzy Grey Cognitive Maps for Industrial Processes Control

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Part of the book series: Intelligent Systems Reference Library ((ISRL,volume 54))

Abstract

Recently, Fuzzy Grey Cognitive Maps (FGCM) has been proposed as a Grey System theory-based FCM extension. Grey systems have become a very effective theory for solving problems within environments with high uncertainty, under discrete small and incomplete data sets. The benefits of FGCMs over conventional FCMs make evident the significance of developing a greyness-based cognitive model such as FGCM. In this chapter, the FGCM model and the proposed NHL learning algorithm were applied within an industrial problem, concerning a chemical process control process with two tanks, three valves, one heating element and two thermometers for each tank. The proposed mathematical formulation of FGCMs and the implementation of the NHL algorithm have been successfully applied. This type of learning rule accompanied with the good knowledge of the given system, guarantee the successful implementation of the proposed technique in industrial process control problems.

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Author information

Authors and Affiliations

  1. Computational Intelligence Lab, University Pablo de Olavide, 1st km. Utrera Road, Seville, Spain

    Jose L. Salmeron

  2. Department of Computer Engineering, Technological Educational Institute of Central Greece, 3rd Km Old National Road Lamia-Athens, 35100, Lamia, Greece

    Elpiniki I. Papageorgiou

Authors
  1. Jose L. Salmeron
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  2. Elpiniki I. Papageorgiou
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Corresponding author

Correspondence to Jose L. Salmeron .

Editor information

Editors and Affiliations

  1. Department of Computer Engineering, Technological Educational Institute of Central Greece, Lamia, Greece

    Elpiniki I. Papageorgiou

1 Electronic supplementary material

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Appendix

Appendix

$$\begin{aligned} A_1= \left[ \begin{array}{cccccccc} &{}[0.52,0.53] [0.56,0.56] [0.48,1.00] [0.63,1.00] [0.65,0.66] [0.57,0.58] [0.52,0.53] [0.64,0.70] \\ &{}[0.53,0.54] [0.57,0.57] [0.67,0.71] [0.79,1.00] [0.72,1.00] [0.58,0.59] [0.53,0.54] [0.66,0.71] \\ &{}[0.24,1.00] [0.55,0.61] [0.64,0.77] [0.64,0.77] [0.65,0.73] [0.56,0.63] [0.51,0.57] [0.63,0.77] \\ &{}[0.51,0.57] [0.50,1.00] [0.64,0.77] [0.64,0.78] [0.66,0.73] [0.56,0.63] [0.01,1.00] [0.63,0.78] \\ &{}[0.53,0.54] [0.56,0.57] [0.66,0.73] [0.66,0.73] [0.67,0.69] [0.58,0.59] [0.53,0.54] [0.65,0.74] \\ &{}[0.54,0.54] [0.57,0.58] [0.60,1.00] [0.67,0.72] [0.67,0.68] [0.59,0.59] [0.54,0.54] [0.66,1.00] \\ &{}[0.52,0.53] [0.56,0.56] [0.65,0.69] [0.59,1.00] [0.65,0.66] [0.57,0.58] [0.52,0.53] [0.64,0.70] \\ &{}[0.51,0.58] [0.54,0.62] [0.63,0.77] [0.63,0.78] [0.65,0.73] [0.18,1.00] [0.51,0.58] [0.62,0.78] \end{array} \right] \end{aligned}$$
(16)
$$\begin{aligned} A_2= \left[ \begin{array}{cccccccc} &{}[0.55,0.57] [0.60,0.61] [0.49,1.00] [0.65,1.00] [0.70,0.72] [0.61,0.63] [0.56,0.57] [0.68,0.75] \\ &{}[0.56,0.58] [0.61,0.62] [0.70,0.76] [0.80,1.00] [0.72,1.00] [0.62,0.63] [0.57,0.58] [0.69,0.77] \\ &{}[0.20,1.00] [0.57,0.65] [0.65,0.82] [0.66,0.83] [0.68,0.78] [0.58,0.67] [0.53,0.62] [0.64,0.83] \\ &{}[0.53,0.62] [0.48,1.00] [0.65,0.83] [0.65,0.84] [0.68,0.78] [0.58,0.68] [0.00,1.00] [0.64,0.84] \\ &{}[0.55,0.58] [0.59,0.62] [0.68,0.78] [0.68,0.79] [0.70,0.75] [0.61,0.64] [0.55,0.58] [0.67,0.79] \\ &{}[0.57,0.58] [0.61,0.62] [0.60,1.00] [0.70,0.78] [0.71,0.73] [0.62,0.64] [0.57,0.58] [0.66,1.00] \\ &{}[0.55,0.57] [0.60,0.61] [0.69,0.74] [0.60,1.00] [0.69,0.71] [0.61,0.62] [0.56,0.57] [0.67,0.75] \\ &{}[0.52,0.62] [0.56,0.67] [0.64,0.83] [0.65,0.84] [0.67,0.79] [0.16,1.00] [0.52,0.63] [0.63,0.84] \\ \end{array} \right] \end{aligned}$$
(17)
$$\begin{aligned} A_3= \left[ \begin{array}{cccccccc} &{}[0.58,0.61] [0.62,0.65] [0.50,1.00] [0.66,1.00] [0.74,0.77] [0.64,0.67] [0.58,0.61] [0.72,0.81] \\ &{}[0.59,0.61] [0.64,0.65] [0.73,0.81] [0.82,1.00] [0.75,1.00] [0.65,0.68] [0.60,0.62] [0.72,0.82] \\ &{}[0.17,1.00] [0.59,0.69] [0.66,0.87] [0.67,0.89] [0.70,0.84] [0.60,0.72] [0.55,0.66] [0.66,0.89] \\ &{}[0.54,0.66] [0.44,1.00] [0.65,0.88] [0.65,0.90] [0.70,0.85] [0.59,0.73] [0.00,1.00] [0.65,0.91] \\ &{}[0.56,0.61] [0.60,0.64] [0.68,0.82] [0.69,0.83] [0.73,0.79] [0.61,0.67] [0.57,0.62] [0.69,0.84] \\ &{}[0.58,0.62] [0.63,0.66] [0.60,1.00] [0.72,0.84] [0.74,0.80] [0.64,0.69] [0.59,0.63] [0.68,1.00] \\ &{}[0.58,0.61] [0.62,0.65] [0.71,0.80] [0.61,1.00] [0.73,0.78] [0.63,0.67] [0.58,0.62] [0.71,0.81] \\ &{}[0.53,0.66] [0.56,0.69] [0.63,0.88] [0.64,0.90] [0.69,0.84] [0.12,1.00] [0.53,0.67] [0.64,0.90] \end{array} \right] \end{aligned}$$
(18)

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Salmeron, J.L., Papageorgiou, E.I. (2014). Using Fuzzy Grey Cognitive Maps for Industrial Processes Control. In: Papageorgiou, E. (eds) Fuzzy Cognitive Maps for Applied Sciences and Engineering. Intelligent Systems Reference Library, vol 54. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-39739-4_14

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  • DOI: https://doi.org/10.1007/978-3-642-39739-4_14

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