This paper aims to extend the notion of group to inside the algebraic structures of L-fuzzy soft sets. We firstly give some new notions such as product, extended product, restricted product of two L-fuzzy soft sets. By using these new notions we then introduce concept of L-fuzzy soft groups and study some of their properties. We also compare L-fuzzy soft groups to the related concept of soft groups. Furthermore, we show that L-fuzzy soft groups are more general concept than soft groups. We finally define L-fuzzy soft function and L-fuzzy soft group homomorphism, and then give theorem of homomorphic image and homomorphic pre-image under a L-fuzzy soft function.
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