# A Modification on the Hesitant Fuzzy Set Lexicographical Ranking Method

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Lexicographical Ordering of HFSs

**Definition**

**1**

**[2,3].**

**Definition**

**2**

**[3].**

**Definition**

**3**

**[24].**

**Definition**

**4**

**[24].**

- (i)
- ${h}_{1}>{h}_{2}$ if and only if $R({h}_{1}){>}_{lex}R({h}_{2})$,
- (ii)
- ${h}_{1}\ge {h}_{2}$ if and only if $R({h}_{1}){\ge}_{lex}R({h}_{2})$, and
- (iii)
- if ${h}_{1}={h}_{2}$, then $R({h}_{1}){=}_{lex}R({h}_{2})$.

## 2. Modified Lexicographical Ordering of HFSs

**Example**

**1**

**[24].**

**Example**

**2.**

**Example**

**3.**

**Definition**

**5.**

- (i)
- ${h}_{1}>{h}_{2}$ if and only if ${R}_{M}({h}_{1}){>}_{lex}{R}_{M}({h}_{2})$,
- (ii)
- ${h}_{1}\ge {h}_{2}$ if and only if ${R}_{M}({h}_{1}){\ge}_{lex}{R}_{M}({h}_{2})$, and
- (iii)
- if ${h}_{1}={h}_{2}$, then ${R}_{M}({h}_{1}){=}_{lex}{R}_{M}({h}_{2})$.

**Example**

**4.**

**Example**

**5.**

**Example**

**6**.

**Proposition**

**1.**

**Proof.**

**Proposition**

**2.**

**Proof.**

## 3. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

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Liu, X.; Wang, Z.; Zhang, S.
A Modification on the Hesitant Fuzzy Set Lexicographical Ranking Method. *Symmetry* **2016**, *8*, 153.
https://doi.org/10.3390/sym8120153

**AMA Style**

Liu X, Wang Z, Zhang S.
A Modification on the Hesitant Fuzzy Set Lexicographical Ranking Method. *Symmetry*. 2016; 8(12):153.
https://doi.org/10.3390/sym8120153

**Chicago/Turabian Style**

Liu, Xiaodi, Zengwen Wang, and Shitao Zhang.
2016. "A Modification on the Hesitant Fuzzy Set Lexicographical Ranking Method" *Symmetry* 8, no. 12: 153.
https://doi.org/10.3390/sym8120153