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Fuzzy Lie Algebras

  • Book
  • © 2018

Overview

Authors:
  1. Muhammad Akram

    1. Department of Mathematics, University of the Punjab, Lahore, Pakistan

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  • Provides a crisp review of fuzzy set theory, Lie algebras, and Lie superalgebras
  • Presents the properties of interval-valued fuzzy Lie ideals, Noetherian Lie algebras, quotient Lie algebras, and interval-valued fuzzy Lie superalgebras
  • Characterizes the Artinian and Noetherian Lie algebras by considering their fuzzy Lie ideals over a fuzzy field
  • Discusses the concepts of m-polar fuzzy Lie subalgebras and m-polar fuzzy Lie ideals

Part of the book series: Infosys Science Foundation Series (ISFS)

Part of the book sub series: Infosys Science Foundation Series in Mathematical Sciences (ISFM)

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Table of contents (10 chapters)

  1. Front Matter

    Pages i-xix
    Download chapter PDF

  2. Fuzzy Lie Structures

    • Muhammad Akram
    Pages 1-32

  3. Intuitionistic Fuzzy Lie Ideals

    • Muhammad Akram
    Pages 33-73

  4. Interval-Valued Fuzzy Lie Structures

    • Muhammad Akram
    Pages 75-106

  5. Generalized Fuzzy Lie Subalgebras

    • Muhammad Akram
    Pages 107-141

  6. Fuzzy Lie Structures Over a Fuzzy Field

    • Muhammad Akram
    Pages 143-174

  7. Bipolar Fuzzy Lie Structures

    • Muhammad Akram
    Pages 175-202

  8. m-Polar Fuzzy Lie Ideals

    • Muhammad Akram
    Pages 203-219

  9. Fuzzy Soft Lie Algebras

    • Muhammad Akram
    Pages 221-247

  10. Rough Fuzzy Lie Algebras

    • Muhammad Akram
    Pages 249-272

  11. Fuzzy n-Lie Algebras

    • Muhammad Akram
    Pages 273-289

  12. Back Matter

    Pages 291-302
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Keywords

About this book

This book explores certain structures of fuzzy Lie algebras, fuzzy Lie superalgebras and fuzzy n-Lie algebras. In addition, it applies various concepts to Lie algebras and Lie superalgebras, including type-1 fuzzy sets, interval-valued fuzzy sets, intuitionistic fuzzy sets, interval-valued intuitionistic fuzzy sets, vague sets and bipolar fuzzy sets. The book offers a valuable resource for students and researchers in mathematics, especially those interested in fuzzy Lie algebraic structures, as well as for other scientists.


Divided into 10 chapters, the book begins with a concise review of fuzzy set theory, Lie algebras and Lie superalgebras. In turn, Chap. 2 discusses several properties of concepts like interval-valued fuzzy Lie ideals, characterizations of Noetherian Lie algebras, quotient Lie algebras via interval-valued fuzzy Lie ideals, and interval-valued fuzzy Lie superalgebras. Chaps. 3 and 4 focus on various concepts of fuzzy Lie algebras, while Chap. 5 presents the concept of fuzzy Lie ideals of a Lie algebra over a fuzzy field. Chapter 6 is devoted to the properties of bipolar fuzzy Lie ideals, bipolar fuzzy Lie subsuperalgebras, bipolar fuzzy bracket product, solvable bipolar fuzzy Lie ideals and nilpotent bipolar fuzzy Lie ideals. Chap. 7 deals with the properties of m-polar fuzzy Lie subalgebras and m-polar fuzzy Lie ideals, while Chap. 8 addresses concepts like soft intersection Lie algebras and fuzzy soft Lie algebras. Chap. 9 deals with rough fuzzy Lie subalgebras and rough fuzzy Lie ideals, and lastly, Chap. 10 investigates certain properties of fuzzy subalgebras and ideals of n-ary Lie algebras.

Authors and Affiliations

  • Department of Mathematics, University of the Punjab, Lahore, Pakistan

    Muhammad Akram

About the author

MUHAMMAD AKRAM is a  Professor at the Department of Mathematics, University of the Punjab, Pakistan. He earned his PhD in fuzzy mathematics from the Government College University, Pakistan. His research interests include numerical algorithms, fuzzy graphs, fuzzy algebras, and fuzzy decision support systems. He has published five monographs and over 265 research articles in international peer-reviewed journals.

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