IJPAM: Volume 105, No. 3 (2015)

A NEW APPROACH TO GROUP THEORY VIA
SOFT SETS AND $L$-FUZZY SOFT SETS

Yıldıray Çelik
Department of Mathematics
Ordu University
52200, Ordu, TURKEY


Abstract. 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.

Received: October 2, 2015

AMS Subject Classification: 08A72, 20N25

Key Words and Phrases: $L$-fuzzy subsets, soft sets, soft groups, $L$-fuzzy soft sets, $L$-fuzzy soft groups

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DOI: 10.12732/ijpam.v105i3.14 How to cite this paper?

Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2015
Volume: 105
Issue: 3
Pages: 459 - 475


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