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Combining Fuzzy Cognitive Maps and Discrete Random Variables

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Artificial Intelligence and Soft Computing (ICAISC 2016)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 9692))

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Abstract

In this paper we propose an extension to the Fuzzy Cognitive Maps (FCMs) that aims at aggregating a number of reasoning tasks into a one parallel run. The described approach consists in replacing real-valued activation levels of concepts (and further influence weights) by random variables. Such extension, followed by the implemented software tool, allows for determining ranges reached by concept activation levels, sensitivity analysis as well as statistical analysis of multiple reasoning results. We replace multiplication and addition operators appearing in the FCM state equation by appropriate convolutions applicable for discrete random variables. To make the model computationally feasible, it is further augmented with aggregation operations for discrete random variables. We discuss four implemented aggregators, as well as we report results of preliminary tests.

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Notes

  1. 1.

    Convolution is often defined as \(p_z(z)=\sum _x p_x(x)p_y(z-x)\). Formula (2) is an equivalent definition.

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Author information

Authors and Affiliations

  1. AGH University of Science and Technology, Kraków, Poland

    Piotr Szwed

Authors
  1. Piotr Szwed
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Correspondence to Piotr Szwed .

Editor information

Editors and Affiliations

  1. Częstochowa University of Technology, Czestochowa, Poland

    Leszek Rutkowski

  2. Częstochowa University of Technology, Czestochowa, Poland

    Marcin Korytkowski

  3. Częstochowa University of Technology, Czestochowa, Poland

    Rafał Scherer

  4. AGH University of Science and Technology, Krakow, Poland

    Ryszard Tadeusiewicz

  5. University of California, Berkeley, California, USA

    Lotfi A. Zadeh

  6. University of Louisville, Louisville, Kentucky, USA

    Jacek M. Zurada

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Szwed, P. (2016). Combining Fuzzy Cognitive Maps and Discrete Random Variables. In: Rutkowski, L., Korytkowski, M., Scherer, R., Tadeusiewicz, R., Zadeh, L., Zurada, J. (eds) Artificial Intelligence and Soft Computing. ICAISC 2016. Lecture Notes in Computer Science(), vol 9692. Springer, Cham. https://doi.org/10.1007/978-3-319-39378-0_30

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  • DOI: https://doi.org/10.1007/978-3-319-39378-0_30

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-39377-3

  • Online ISBN: 978-3-319-39378-0

  • eBook Packages: Computer ScienceComputer Science (R0)

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