Hesitant Fuzzy Soft Group

S. Mahalakshmi; A. Solairaju

doi:https://doi.org/10.14445/22315373/IJMTT-V54P549

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 54 | Number 5 | Year 2018 | Article Id. IJMTT-V54P549 | DOI : https://doi.org/10.14445/22315373/IJMTT-V54P549

Hesitant Fuzzy Soft Group

S. Mahalakshmi, A. Solairaju

Abstract

Maji et. al. [2] firstly presented the concept of fuzzy soft set by combining the theories of fuzzy set and soft set together. Rosenfeld [3] proposed the concept of fuzzy groups in order to establish the algebraic structures of fuzzy sets.Aktas and Çagman [6] introduced the notion of soft groups, which extends the notion of group to include the algebraic structures of soft sets. Recently, in order to tackle the difficulty in establishing the degree of membership of an element in a set, Torra and Narukawa [7] and Torra [8] proposed the concept of a hesitant fuzzy set.The purpose of this paper is to extend the soft groups to the hesitant fuzzy set, and, thus, we establish a new soft group model named hesitant fuzzy soft group. The rest of this paper is organized as follows. We first review some background on soft set, fuzzy soft set, and hesitant fuzzy set, hesitant fuzzy soft set in Section 2. In Section 3, the concepts and operations of hesitant fuzzy soft groups are proposed and their properties are discussed in detail.In Section 4, we define the image and pre-image of a hesitant soft set under a soft function, and then define soft homomorphism between hesitant fuzzy soft groups. We prove the image and pre-image of a hesitant fuzzy soft group are also hesitant fuzzy soft groups. In Section 5, we give the definition of a normal hesitant fuzzy soft group and study some of their properties.

Keywords

In Section 5, we give the definition of a normal hesitant fuzzy soft group and study some of their properties.

References

1. Aktas. H and N. Cagman, Soft sets and soft group, Information Science 177 (2007), PP 2726-2735.
2. AbdülkadirAygüno_glu, HalisAygün,Introduction to fuzzy soft groups,computers and Mathematics with Applications 58,(2009) 1279_1286.
3. Fuqiang Wang,Hihua Li, and Xiaowong chen, ―Hesitant Fuzzy soft set and its Application in Multicriteria Decision making, Journal of Applied Mathematics, Volume 2014 (2014).
4. D. Molodtsov, ―Soft set theory—first results, Computers & Mathematics with Applications, vol. 37, no. 4-5, pp. 19–31, 1999.
5. D. Molodtsov, ―Soft set theory—first results, Computers & Mathematics with Applications, vol. 37, no. 4-5, pp. 19–31, 1999.
6. A. Rosenfeld, Fuzzy groups, Journal of Mathematical Analysis and Applications 35 (1971) 512_517.
7. A.Solairaju and R.Nagarajan,A New Structure and Construction of Q-Fuzzy Groups, Advances in fuzzy mathematics , Volume 4 , Number 1 (2009) pp.23-29.
8. V. Torra and Y. Narukawa, ―On hesitant fuzzy sets and decision, in Proceedings of the IEEE International Conference on Fuzzy Systems, pp. 1378–1382, Jeju-do, Republic of Korea, August 2009.
9. V. Torra, ―Hesitant fuzzy sets, International Journal of Intelligent Systems, vol. 25, no. 6, pp. 529–539, 2010.
10. Xia Yin, Study on Soft Groups ,Journal of computers, vol. 8, no. 4, April 2013.

Citation :

S. Mahalakshmi, A. Solairaju, "Hesitant Fuzzy Soft Group," International Journal of Mathematics Trends and Technology (IJMTT), vol. 54, no. 5, pp. 404-414, 2018. Crossref, https://doi.org/10.14445/22315373/IJMTT-V54P549