Abstract
We introduce the concept of (γ, δ)-bifuzzy Lie subalgebra, where γ, δ are any two of {∈, q, ∈∨q, ∈∧q} with γ ≠ ∈∧q, by using belongs to relation (∈) and quasi-coincidence with relation (q) between bifuzzy points and bifuzzy sets and discuss some of its properties. Then we introduce bifuzzy soft Lie subalgebras and investigate some of their properties.
Highlights
The concept of Lie groups was first introduced by Sophus Lie in nineteenth century through his studies in geometry and integration methods for differential equations
In 1999, Molodtsov [5] initiated the novel concept of soft set theory to deal with uncertainties which can not be handled by traditional mathematical tools
A large number of these models are based on an extension of the ordinary set theory such as bifuzzy sets and soft sets
Summary
The concept of Lie groups was first introduced by Sophus Lie in nineteenth century through his studies in geometry and integration methods for differential equations. The elements of the bifuzzy sets are featured by an additional degree which is called the degree of uncertainty This kind of fuzzy sets have gained a wide recognition as a useful tool in the modeling of some uncertain phenomena. In 1999, Molodtsov [5] initiated the novel concept of soft set theory to deal with uncertainties which can not be handled by traditional mathematical tools. He successfully applied the soft set theory several disciplines, such as game theory, Riemann integration, Perron integration, and measure theory. Maji et al [6] gave first practical application of soft sets in decision making problems They presented the definition of intuitionistic fuzzy soft set [7].
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