03662nam 22004695 450 991030344660332120251113190104.0981-13-3221-510.1007/978-981-13-3221-0(CKB)4100000007334990(DE-He213)978-981-13-3221-0(MiAaPQ)EBC5627161(EXLCZ)99410000000733499020181230d2018 u| 0engurnn|008mamaatxtrdacontentcrdamediacrrdacarrierFuzzy Lie Algebras /by Muhammad Akram1st ed. 2018.Singapore :Springer Nature Singapore :Imprint: Springer,2018.1 online resource (XIX, 302 p. 14 illus., 4 illus. in color.) Infosys Science Foundation Series in Mathematical Sciences,2364-4044981-13-3220-7 Chapter 1. Fuzzy Lie Structures -- Chapter 2. Interval-valued Fuzzy Lie Structures -- Chapter 3. Intuitionistic Fuzzy Lie Ideals -- Chapter 4. Generalized Fuzzy Lie Subalgebras -- Chapter 5. Fuzzy Lie Structures over a Fuzzy Field -- Chapter 6. Bipolar Fuzzy Lie Structures -- Chapter 7. m−Polar Fuzzy Lie Ideals of Lie Algebras -- Chapter 8. Fuzzy Soft Lie algebras -- Chapter 9. Rough Fuzzy Lie Ideals -- Chapter 10. Fuzzy n-Lie Algebras.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.Infosys Science Foundation Series in Mathematical Sciences,2364-4044Algebra, UniversalLogic, Symbolic and mathematicalGeneral Algebraic SystemsMathematical Logic and FoundationsAlgebra, Universal.Logic, Symbolic and mathematical.General Algebraic Systems.Mathematical Logic and Foundations.512Akram Muhammadauthttp://id.loc.gov/vocabulary/relators/aut767976BOOK9910303446603321Fuzzy Lie Algebras1563884UNINA