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" Fuzzy lie algebras / "
Muhammad Akram.
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BL
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| Record Number
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891408
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| Main Entry
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Akram, Muhammad
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| Title & Author
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Fuzzy lie algebras /\ Muhammad Akram.
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| Publication Statement
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Singapore :: Springer,, [2018]
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| Series Statement
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Infosys Science Foundation Series in Mathematical Sciences,
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| Page. NO
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1 online resource
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| ISBN
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9789811332203
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: 9789811332210
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: 9811332207
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: 9811332215
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9789811332203
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| Contents
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Intro; Foreword; Preface; Contents; About the Author; List of Figures; List of Tables; 1 Fuzzy Lie Structures; 1.1 Introduction; 1.1.1 Fuzzy Sets; 1.1.2 Lie Algebras; 1.1.3 Lie Superalgebras; 1.2 Fuzzy Lie Ideals; 1.3 Anti-fuzzy Lie Ideals; 1.4 Fuzzy Lie Sub-superalgebras; 1.5 Hesitant Fuzzy Lie Ideals; 2 Intuitionistic Fuzzy Lie Ideals; 2.1 Introduction; 2.2 Intuitionistic Fuzzy Lie Subalgebras; 2.3 Lie Homomorphism of Intuitionistic Fuzzy Lie Subalgebras; 2.4 Intuitionistic Fuzzy Lie Ideals; 2.5 Special Types of Intuitionistic Fuzzy Lie Ideals; 2.6 Intuitionistic (S, T)-Fuzzy Lie Ideals
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9.1 Introduction9.2 Rough Fuzzy Lie Ideals; 9.3 Fuzzy Rough Lie Algebras; 9.4 Rough Intuitionistic Fuzzy Lie Algebras; 10 Fuzzy n-Lie Algebras; 10.1 Introduction; 10.2 Fuzzy Subalgebras and Ideals; 10.3 Fuzzy Quotient n-Lie Algebras; 10.4 Pythagorean Fuzzy n-Lie Algebras; References; Glossary of Symbols; Index
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| Abstract
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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.--
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| Subject
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Fuzzy mathematics.
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Lie algebras.
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Fuzzy mathematics.
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Lie algebras.
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General Algebraic Systems.
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Mathematical Logic and Foundations.
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| Dewey Classification
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512/.482
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| LC Classification
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QA252.3.A37 2018
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