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Algebraic Formalization of Smart Systems

Theory and Practice

  • Book
  • © 2018

Overview

Authors:
  1. Natalia Serdyukova

    1. Plekhanov Russian University of Economics, Moscow, Russia

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  2. Vladimir Serdyukov

    1. and Institute of Education Management of the Russian Academy of Education, Bauman Moscow State Technical University, Moscow, Russia

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    You can also search for this author in PubMed   Google Scholar

  • Presents an excellent framework for the implementation of smart systems
  • Focuses on the algebraic formalization of smart systems
  • Combines theory and practice

Part of the book series: Smart Innovation, Systems and Technologies (SIST, volume 91)

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Table of contents (10 chapters)

  1. Front Matter

    Pages i-xxxvii
    Download chapter PDF

  2. The Problem of General Systems Theory’s Formalization

    • Natalia Serdyukova, Vladimir Serdyukov
    Pages 1-20

  3. The Performance of a System by Using an Algebraic System of Factors Determining the System. P-Properties of a System

    • Natalia Serdyukova, Vladimir Serdyukov
    Pages 21-39

  4. The Simulation of the System with the Help of Finite Group of Factors Determining the System. P-Properties of the System. Cayley Tables and Their Role in Modeling Associative Closed System with Feedback

    • Natalia Serdyukova, Vladimir Serdyukov
    Pages 41-55

  5. External and Internal Properties of a System. Integrity and P-Integrity of a System by Predicate P. Formalization Smart Systems’ Axiomatic

    • Natalia Serdyukova, Vladimir Serdyukov
    Pages 57-78

  6. Formalization of System Links: Different Approaches. Duality in Smart Systems Theory

    • Natalia Serdyukova, Vladimir Serdyukov
    Pages 79-96

  7. P-Innovative and P-Pseudo-Innovative Systems on the Predicate P and Their Properties

    • Natalia Serdyukova, Vladimir Serdyukov
    Pages 97-116

  8. Algebraic Approach to the Risk Description. Linear Programming Models with Risk

    • Natalia Serdyukova, Vladimir Serdyukov
    Pages 117-136

  9. The Transition from an Infinite Model of Factors that Determine the System to a Finite Model. The Model of Algebraic Formalization of Risks of Changing the Scenarios of the Long-Term Development of a Smart System of Six Factors on the Example of a Smart University

    • Natalia Serdyukova, Vladimir Serdyukov
    Pages 137-147

  10. Pro-P-Groups and Algebraically Closed Groups: Application to Smart Systems

    • Natalia Serdyukova, Vladimir Serdyukov
    Pages 149-169

  11. P-Sustainability of a System. Algebraic Formalization of Sustainability Concept. Sustainability of Ranking Systems in Education

    • Natalia Serdyukova, Vladimir Serdyukov
    Pages 171-189
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Keywords

About this book

This book reveals the general laws of the theory of smart systems with the help of a very powerful and expressive language of algebraic formalization. It also shows how this language can be used to substantiate practical results in the field of smart systems, which previously had only an empirical justification. Further, it proposes a translation of the theory of smart systems from verbal language to a much more expressive language of algebraic formalization, allowing the laws of the theory of smart systems to be seen in a different light.

In 1937 L. Bertalanffy proposed the concept of an algebraic system and the development of a mathematical apparatus for describing systems. In the 1970s, A.I. Mal'tsev developed a theory of algebraic systems connecting algebra and logic for studying algebraic and logical objects. In the 1990s, the concept of purities by predicates was introduced by one of the authors, and the book includes some of its applications. The concept, which is basedon the theory of algebraic systems, allows clarification of the connections between quantitative and qualitative analysis of a system.

The book is intended for readers who use elements of artificial intelligence in their work.

Authors and Affiliations

  • Plekhanov Russian University of Economics, Moscow, Russia

    Natalia Serdyukova

  • and Institute of Education Management of the Russian Academy of Education, Bauman Moscow State Technical University, Moscow, Russia

    Vladimir Serdyukov

Bibliographic Information

  • Book Title: Algebraic Formalization of Smart Systems

  • Book Subtitle: Theory and Practice

  • Authors: Natalia Serdyukova, Vladimir Serdyukov

  • Series Title: Smart Innovation, Systems and Technologies

  • DOI: https://doi.org/10.1007/978-3-319-77051-2

  • Publisher: Springer Cham

  • eBook Packages: Engineering, Engineering (R0)

  • Copyright Information: Springer International Publishing AG, part of Springer Nature 2018

  • Hardcover ISBN: 978-3-319-77050-5Published: 19 March 2018

  • Softcover ISBN: 978-3-030-08358-8Published: 24 January 2019

  • eBook ISBN: 978-3-319-77051-2Published: 08 March 2018

  • Series ISSN: 2190-3018

  • Series E-ISSN: 2190-3026

  • Edition Number: 1

  • Number of Pages: XXXVII, 189

  • Topics: Computational Intelligence, Artificial Intelligence

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