Bipolar fuzzy Lie superalgebras

We introduce the notion of bipolar fuzzy Lie sub-superalgebras (resp. bipolar fuzzy ideals) and present some of their properties. First we investigate the properties of bipolar fuzzy Lie sub-superalgebras and bipolar fuzzy ideals under homomorphisms of Lie superalgebras. Next we study bipolar fuzzy bracket product, solvable bipolar fuzzy ideals and nilpotent bipolar fuzzy ideals of Lie superalgebras.

[1]  Keon-Myung Lee,et al.  Comparison of Interval-valued fuzzy sets, Intuitionistic fuzzy sets, and bipolar-valued fuzzy sets , 2004 .

[2]  Wen-Ran Zhang,et al.  Bipolar fuzzy sets and relations: a computational framework for cognitive modeling and multiagent decision analysis , 1994, NAFIPS/IFIS/NASA '94. Proceedings of the First International Joint Conference of The North American Fuzzy Information Processing Society Biannual Conference. The Industrial Fuzzy Control and Intellige.

[3]  Wenjuan Chen,et al.  Intuitionistic fuzzy quotient Lie superalgebras , 2010 .

[4]  Muhammad Akram,et al.  Bipolar fuzzy graphs , 2011, Inf. Sci..

[5]  Muhammad Akram,et al.  Intuitionistic (S,T)-fuzzy Lie ideals of Lie algebras , 2007 .

[6]  Wenjuan Chen,et al.  Intuitionistic fuzzy Lie sub-superalgebras and intuitionistic fuzzy ideals , 2009, Comput. Math. Appl..

[7]  M. Akram Generalized fuzzy Lie subalgebras , 2008 .

[8]  M. Akram Co-fuzzy Lie Superalgebras Over a Co-fuzzy Field , 2009 .

[9]  Muhammad Akram,et al.  Regular bipolar fuzzy graphs , 2011, Neural Computing and Applications.

[10]  Yuval Ne'eman,et al.  Graded Lie algebras in mathematics and physics (Bose-Fermi symmetry) , 1975 .

[11]  Muhammad Akram,et al.  Fuzzy Lie ideals of Lie algebras with interval-valued membership functions , 2008 .

[12]  Wen-Ran Zhang,et al.  Bipolar Fuzzy Sets , 1997 .

[13]  J. Van der Jeugt,et al.  Unimodal polynomials associated with Lie algebras and superalgebras , 1991 .