### Journals Information

**
Mathematics and Statistics Vol. 9(4), pp. 445 - 455 DOI: 10.13189/ms.2021.090405 Reprint (PDF) (931Kb) **

## Z-Score Functions of Hesitant Fuzzy Sets

**Zahari Md Rodzi ^{1}^{,2}^{,*}, Abd Ghafur Ahmad ^{2}, Norul Fadhilah Ismail ^{3}, Nur Lina Abdullah ^{1}**

^{1}Faculty of Computer and Mathematical Science, UiTM Cawangan Negeri Sembilan, Kampus 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, UiTM Cawangan Negeri Sembilan, Kampus Kuala Pilah, 72000 Seremban, Negeri Sembilan, Malaysia

**ABSTRACT**

The hesitant fuzzy set (HFS) concept as an extension of fuzzy set (FS) in which the membership degree of a given element, called the hesitant fuzzy element (HFE), is defined as a set of possible values. A large number of studies are concentrating on HFE and HFS measurements. It is not just because of their crucial importance in theoretical studies, but also because they are required for almost any application field. The score function of HFE is a useful method for converting data into a single value. Moreover, the scoring function provides a much easier way to determine each alternative's ranking order for multi-criteria decision-making (MCDM). This study introduces a new hesitant degree of HFE and the z-score function of HFE, which consists of z-arithmetic mean, z-geometric mean, and z-harmonic mean. The z-score function is developed with four main bases: a hesitant degree of HFE, deviation value of HFE, the importance of the hesitant degree of HFE, α, and importance of the deviation value of HFE, β. These three proposed scores are compared with the existing scores functions to identify the proposed z-score function's flexibility. An algorithm based on the z-score function was developed to create an algorithm solution to MCDM. Example of secondary data on supplier selection for automated companies is used to prove the algorithms' capability in ranking order for MCDM.

**KEYWORDS**

Hesitant Degree, Z-Arithmetic Mean, Z-Geometric Mean, Z-Harmonic Mean, HFS, Score Function, MCDM

**Cite This Paper in IEEE or APA Citation Styles**

(a). IEEE Format:

[1] Zahari Md Rodzi , Abd Ghafur Ahmad , Norul Fadhilah Ismail , Nur Lina Abdullah , "Z-Score Functions of Hesitant Fuzzy Sets," Mathematics and Statistics, Vol. 9, No. 4, pp. 445 - 455, 2021. DOI: 10.13189/ms.2021.090405.

(b). APA Format:

Zahari Md Rodzi , Abd Ghafur Ahmad , Norul Fadhilah Ismail , Nur Lina Abdullah (2021). Z-Score Functions of Hesitant Fuzzy Sets. Mathematics and Statistics, 9(4), 445 - 455. DOI: 10.13189/ms.2021.090405.