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Marks: A New Interval Tool for Uncertainty, Vagueness and Indiscernibility

Author

Listed:
  • Miguel A. Sainz

    (Modeling, Identification and Control Engineering (MICELab) Research Group, Institut d’Informatica i Aplicacions, Universitat de Girona, 17003 Girona, Spain)

  • Remei Calm

    (Modeling, Identification and Control Engineering (MICELab) Research Group, Institut d’Informatica i Aplicacions, Universitat de Girona, 17003 Girona, Spain
    Centro de Investigación Biomédica en Red de Diabetes y Enfermedades Metabólicas Asociadas (CIBERDEM), 28029 Madrid, Spain)

  • Lambert Jorba

    (Department de Matemàtica Econòmica, Financera i Actuarial, University of Barcelona, 08034 Barcelona, Spain)

  • Ivan Contreras

    (Modeling, Identification and Control Engineering (MICELab) Research Group, Institut d’Informatica i Aplicacions, Universitat de Girona, 17003 Girona, Spain)

  • Josep Vehi

    (Modeling, Identification and Control Engineering (MICELab) Research Group, Institut d’Informatica i Aplicacions, Universitat de Girona, 17003 Girona, Spain
    Centro de Investigación Biomédica en Red de Diabetes y Enfermedades Metabólicas Asociadas (CIBERDEM), 28029 Madrid, Spain)

Abstract

The system of marks created by Dr. Ernest Gardenyes and Dr. Lambert Jorba was first published as a doctoral thesis in 2003 and then as a chapter in the book Modal Interval Analysis in 2014. Marks are presented as a tool to deal with uncertainties in physical quantities from measurements or calculations. When working with iterative processes, the slow convergence or the high number of simulation steps means that measurement errors and successive calculation errors can lead to a lack of significance in the results. In the system of marks, the validity of any computation results is explicit in their calculation. Thus, the mark acts as a safeguard, warning of such situations. Despite the obvious contribution that marks can make in the simulation, identification, and control of dynamical systems, some improvements are necessary for their practical application. This paper aims to present these improvements. In particular, a new, more efficient characterization of the difference operator and a new implementation of the marks library is presented. Examples in dynamical systems simulation, fault detection and control are also included to exemplify the practical use of the marks.

Suggested Citation

  • Miguel A. Sainz & Remei Calm & Lambert Jorba & Ivan Contreras & Josep Vehi, 2021. "Marks: A New Interval Tool for Uncertainty, Vagueness and Indiscernibility," Mathematics, MDPI, vol. 9(17), pages 1-15, September.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:17:p:2116-:d:627219
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    Cited by:

    1. Sorin Nădăban, 2022. "Fuzzy Logic and Soft Computing—Dedicated to the Centenary of the Birth of Lotfi A. Zadeh (1921–2017)," Mathematics, MDPI, vol. 10(17), pages 1-3, September.

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