Author(s)

Li Xin ¹, Zhang Xiaohong ¹

Affiliation(s)

¹ College of Arts and Sciences, Shanghai Maritime University, Shanghai 201306, China

Corresponding Author

Zhang Xiaohong

ABSTRACT

The concept of dual hesitant fuzzy sets (DHFSs), which was first introduced as a new extension of fuzzy sets and hesitant fuzzy sets in 2012, is a useful tool to deal with the vagueness and ambiguity in many practical problems under hesitant fuzzy environment. Normally, we use the definition of distance to describe the relationship of two DHFSs. However, considering that the existing distance measures of DHFSs still have some major shortcomings, so in this paper, we firstly introduce a new concept –hesitance degree of each dual hesitant fuzzy element (DHFE) to these existing distance measures and then develop several novel distance measures in which both the values and the numbers of values of DHFE are taken into account. The properties of these new distance measures are discussed. Finally, we apply our proposed distance measures of DHFSs in pattern recognition making to illustrate their validity and applicability.

KEYWORDS

Dual hesitant fuzzy sets, Distance Measure, Hesitance degree, Pattern recognition.

CITE THIS PAPER

Xin, L. and Xiaohong, Z. (2016) New Distance Measures on Dual Hesitant Fuzzy Sets and Their Application in Pattern Recognition. Journal of Artificial Intelligence Practice (2016) 1: 8-13.

REFERENCES

[1] L.A.Zadeh: Fuzzy Sets, Information and control 8 (1965), p. 338-353.
[2] Xiaohong Zhang, Daowu Pei, Jianhua Dai: Fuzzy Mathematics and Rough Set Theory (Tsinghua University press, Beijing 2013)
[3] Bin Zhu, Zeshui Xu, Meimei Xia: Dual hesitant fuzzy sets, J. Appl. Math. 2012 (2012). p.1-13.
[4] Zhan Su,  Zeshui Xu, Haifeng Liu, Shousheng Liu, Distance and similarity measures for dual hesitant fuzzy sets and their applications in pattern recognition, Journal of Intelligent & Fuzzy Systems 29 (2015) p.731-745.
[5] Qiuyan Zhan, Xiaohong Zhang, Zhenyu Chen: Modified definitions of distance and similarity measures of interval-valued hesitant fuzzy sets, Fuzzy Systems and Mathematics 30 (2016), in press.
[6] Deqing Li, Wenyi Zeng, Junhong Li: New distance and similarity measures on hesitant fuzzy sets and their applications in multiple criteria decision making, Engineering Applications of Artificial Intelligence 40 (2015), p. 11–16.
 

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