### Journals Information

Mathematics and Statistics Vol. 9(3), pp. 225 - 232
DOI: 10.13189/ms.2021.090303
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## Z-Score Functions of Dual Hesitant Fuzzy Set and Its Applications in Multi-Criteria Decision Making

Zahari Md Rodzi 1,2,*, Abd Ghafur Ahmad 2, Nur Sa’aidah Ismail 3, Wan Normila Mohamad 4, Sarahiza Mohmad 1
1 Faculty of Computer and Mathematical Science, Universiti Teknologi MARA Campus Seremban, 70300 Seremban, Negeri Sembilan, Malaysia
2 School of Mathematical Science, Faculty of Science and Technology, Universiti Kebangsaan Malaysia, 43600 UKM, Bangi, Selangor, Malaysia
3 Faculty of Computer and Mathematical Science, Universiti Teknologi MARA Campus Dengkil, 43800 Dengkil, Selangor, Malaysia
4 Faculty of Business and Management, Universiti Teknologi MARA Campus Seremban, 70300 Seremban, Negeri Sembilan, Malaysia

ABSTRACT

Dual hesitant fuzzy set (DHFS) consists of two parts: membership hesitant function and non-membership hesitant function. This set supports more exemplary and flexible access to set degrees for each element in the domain and can address two types of hesitant in this situation. It can be considered a powerful tool for expressing uncertain information in the decision-making process. The function of z-score, namely z-arithmetic mean, z-geometric mean, and z-harmonic mean, has been proposed with five important bases, these bases are hesitant degree for dual hesitant fuzzy element (DHFE), DHFE deviation degree, parameter α (the importance of the hesitant degree), parameter β (the importance of the deviation degree) and parameter ϑ (the importance of membership (positive view) or non-membership (negative view). A comparison of the z-score with the existing score function was made to show some of their drawbacks. Next, the z-score function is then applied to solve multi-criteria decision making (MCDM) problems. To illustrate the proposed method's effectiveness, an example of MCDM specifically in pattern recognition has been shown.

KEYWORDS
Z-Arithmetic Mean, Z-Geometric Mean, Z-Harmonic Mean, Score Function, DHFS, MCDM, DHFE

Cite This Paper in IEEE or APA Citation Styles
(a). IEEE Format:
[1] Zahari Md Rodzi , Abd Ghafur Ahmad , Nur Sa’aidah Ismail , Wan Normila Mohamad , Sarahiza Mohmad , "Z-Score Functions of Dual Hesitant Fuzzy Set and Its Applications in Multi-Criteria Decision Making," Mathematics and Statistics, Vol. 9, No. 3, pp. 225 - 232, 2021. DOI: 10.13189/ms.2021.090303.

(b). APA Format:
Zahari Md Rodzi , Abd Ghafur Ahmad , Nur Sa’aidah Ismail , Wan Normila Mohamad , Sarahiza Mohmad (2021). Z-Score Functions of Dual Hesitant Fuzzy Set and Its Applications in Multi-Criteria Decision Making. Mathematics and Statistics, 9(3), 225 - 232. DOI: 10.13189/ms.2021.090303.