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Revised convexity, normality and stability properties of the dynamical feedback fuzzy state space model (FFSSM) of insulin–glucose regulatory system in humans

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Abstract

This research tries to explore more important structural properties of the insulin–glucose regulatory system in humans. Consequently, an important theorem, namely “revised modified optimized defuzzified value theorem” for feedback systems is derived and then proved. Moreover, the properties concerning the convexity, normality and the bounded-input bounded-output stability of the induced solution of FFSSM are researched. The proposed theorems and lemmas are successfully implemented and verified for the insulin–glucose system in humans. The successful and promising results and proofs of the theorems of the relevant properties improve the credibility and reliability of the FFSSM model of the insulin–glucose regulatory system in humans.

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Acknowledgements

We are thankful to the respectable editors and reviewers for their relevant, credible and useful reviews and suggestions. Thanks are due to COMSATS University Islamabad, Abbottabad Campus, Pakistan, and UTM Malaysia.

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Authors and Affiliations

  1. Department of Mathematics, COMSATS University Islamabad, Abbottabad Campus, Abbottabad, Pakistan

    Izaz Ullah Khan

  2. Department of Mathematical Sciences, Faculty of Science, Universiti Teknologi Malaysia, 81310, Skudai, Johor Darul Ta’zim, Malaysia

    Tahir Ahmad & Normah Maan

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  1. Izaz Ullah Khan
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  2. Tahir Ahmad
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Correspondence to Izaz Ullah Khan.

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This article does not contain any studies with human participants performed by any of the authors. The data presented are obtained from the widely accepted published research Sturis (1991), Sturis et al. (1991) and Tolić et al. (2000).

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Communicated by V. Loia.

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Khan, I.U., Ahmad, T. & Maan, N. Revised convexity, normality and stability properties of the dynamical feedback fuzzy state space model (FFSSM) of insulin–glucose regulatory system in humans. Soft Comput 23, 11247–11262 (2019). https://doi.org/10.1007/s00500-018-03682-w

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