Bipolar Fuzzy Lie Structures

  • Muhammad AkramEmail author
Part of the Infosys Science Foundation Series book series (ISFS)


In this chapter, we present properties of bipolar fuzzy Lie ideals, bipolar fuzzy Lie sub-superalgebras, bipolar fuzzy bracket product, solvable bipolar fuzzy Lie ideals, and nilpotent bipolar fuzzy Lie ideals. We describe some properties of nilpotency of bipolar fuzzy Lie ideals. We deal the concept of bipolar fuzzy adjoint representation of Lie algebras and discuss the relationship between this representation and nilpotent bipolar fuzzy Lie ideals.

Copyright information

© Springer Nature Singapore Pte Ltd. 2018

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of the PunjabLahorePakistan

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