# Engineering Characteristics Prioritization in Quality Function Deployment Using an Improved ORESTE Method with Double Hierarchy Hesitant Linguistic Information

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Literature Review

## 3. Preliminaries

#### 3.1. The DHHLTSs

**Definition**

**1**

**.**Let $\dot{S}=\left\{{\dot{s}}_{t}|t=-\tau ,\dots ,-1,0,1,\dots ,\tau \right\}$ and $\ddot{S}=\left\{{\ddot{s}}_{a}|a=-\varsigma ,\dots ,-1,0,1,\dots ,\varsigma \right\}$ be the first hierarchy and the second hierarchy linguistic term sets, respectively. Then, a DHLTS ${\dot{S}}_{\ddot{S}}$ is defined as:

**Definition**

**2**

**.**Let X be a fixed set, and ${\dot{S}}_{\ddot{S}}=\left\{{\dot{s}}_{t\langle {\ddot{s}}_{a}\rangle}|t=-\tau ,\dots ,-1,0,1,\dots ,\tau ;a=-\varsigma ,\dots ,-1,0,1,\dots ,\varsigma \right\}$ be a DHLTS. A DHHLTS on X, ${H}_{{\dot{S}}_{\ddot{S}}}$, is a mathematical form of

**Definition**

**3**

**.**Let ${\dot{S}}_{\ddot{S}}$ be a DHLTS, ${h}_{{\dot{S}}_{\ddot{S}}}$ be a DHHLE, and ${h}_{\gamma}=\left\{{\gamma}_{l}|{\gamma}_{l}\in \left[0,1\right];l=1,\dots ,L\right\}$ be a hesitant fuzzy element (HFE). The subscript ${\varphi}_{l}\langle {\phi}_{l}\rangle $ of the DHLT can express the equivalent information to the membership degree ${\gamma}_{l}$. They can be transformed into each other by the functions f and f

^{−}

^{1}.

**Definition**

**4**

**.**Let ${\dot{S}}_{\ddot{S}}=\left\{{\dot{s}}_{t\langle {\ddot{s}}_{a}\rangle}|t=-\tau ,\dots ,-1,0,1,\dots ,\tau ;a=-\varsigma ,\dots ,-1,0,1,\dots ,\varsigma \right\}$ be a DHLTS, ${h}_{{\dot{S}}_{\ddot{S}}}^{1}$ and ${h}_{{\dot{S}}_{\ddot{S}}}^{2}$ be two DHHLEs, and λ is a real number. Then the operational laws of the DHHLEs are given as follows:

- (1)
- ${h}_{{\dot{S}}_{\ddot{S}}}^{1}\oplus {h}_{{\dot{S}}_{\ddot{S}}}^{2}={F}^{-1}\left(\underset{{\eta}_{1}\in F\left({h}_{{\dot{S}}_{\ddot{S}}}^{1}\right),{\eta}_{2}\in F\left({h}_{{\dot{S}}_{\ddot{S}}}^{2}\right)}{{\displaystyle \cup}}\left\{{\eta}_{1}+{\eta}_{2}-{\eta}_{1}{\eta}_{2}\right\}\right);$
- (2)
- ${h}_{{\dot{S}}_{\ddot{S}}}^{1}\otimes {h}_{{\dot{S}}_{\ddot{S}}}^{2}={F}^{-1}\left(\underset{{\eta}_{1}\in F\left({h}_{{\dot{S}}_{\ddot{S}}}^{1}\right),{\eta}_{2}\in F\left({h}_{{\dot{S}}_{\ddot{S}}}^{2}\right)}{{\displaystyle \cup}}\left\{{\eta}_{1}{\eta}_{2}\right\}\right);$
- (3)
- $\lambda {h}_{{\dot{S}}_{\ddot{S}}}^{1}={F}^{-1}\left(\underset{{\eta}_{1}\in F\left({h}_{{\dot{S}}_{\ddot{S}}}^{1}\right)}{{\displaystyle \cup}}\left\{1-{\left(1-{\eta}_{1}\right)}^{\lambda}\right\}\right);$
- (4)
- ${\left({h}_{{\dot{S}}_{\ddot{S}}}^{1}\right)}^{\lambda}={F}^{-1}\left(\underset{{\eta}_{1}\in F\left({h}_{{\dot{S}}_{\ddot{S}}}^{1}\right)}{{\displaystyle \cup}}\left\{{\eta}_{1}^{\lambda}\right\}\right).$

**Definition**

**5**

**.**Let ${\dot{S}}_{\ddot{S}}=\left\{{\dot{s}}_{t\langle {\ddot{s}}_{a}\rangle}|t=-\tau ,\dots ,-1,0,1,\dots ,\tau ;a=-\varsigma ,\dots ,-1,0,1,\dots ,\varsigma \right\}$ be a DHLTS, ${h}_{{\dot{S}}_{\ddot{S}}}=\left\{{\dot{s}}_{{\varphi}_{l}\langle {\ddot{s}}_{{\phi}_{l}}\rangle}|{\dot{s}}_{{\varphi}_{l}\langle {\ddot{s}}_{{\phi}_{l}}\rangle}\in {\dot{S}}_{\ddot{S}};l=1,2,\dots ,L;{\varphi}_{l}=\left[-\tau ,\tau \right];{\phi}_{l}=\left[-\varsigma ,\varsigma \right]\right\}$ be a DHHLE. Then the expected value of ${h}_{{\dot{S}}_{\ddot{S}}}$ is defined as

**Definition**

**6**

- (1)
- If $E\left({h}_{{\dot{S}}_{\ddot{S}}}^{1}\right)>E\left({h}_{{\dot{S}}_{\ddot{S}}}^{2}\right)$, then ${h}_{{\dot{S}}_{\ddot{S}}}^{1}$ is bigger than ${h}_{{\dot{S}}_{\ddot{S}}}^{2}$, denoted by ${h}_{{\dot{S}}_{\ddot{S}}}^{1}>{h}_{{\dot{S}}_{\ddot{S}}}^{2}$;
- (2)
- If $E\left({h}_{{\dot{S}}_{\ddot{S}}}^{1}\right)=E\left({h}_{{\dot{S}}_{\ddot{S}}}^{2}\right)$, then
- (a)
- if $v\left({h}_{{\dot{S}}_{\ddot{S}}}^{1}\right)<v\left({h}_{{\dot{S}}_{\ddot{S}}}^{2}\right)$, ${h}_{{\dot{S}}_{\ddot{S}}}^{1}$ is bigger than ${h}_{{\dot{S}}_{\ddot{S}}}^{2}$, denoted by ${h}_{{\dot{S}}_{\ddot{S}}}^{1}>{h}_{{\dot{S}}_{\ddot{S}}}^{2}$;
- (b)
- if $v\left({h}_{{\dot{S}}_{\ddot{S}}}^{1}\right)=v\left({h}_{{\dot{S}}_{\ddot{S}}}^{2}\right)$, ${h}_{{\dot{S}}_{\ddot{S}}}^{1}$ is equivalent than ${h}_{{\dot{S}}_{\ddot{S}}}^{2}$, denoted by ${h}_{{\dot{S}}_{\ddot{S}}}^{1}={h}_{{\dot{S}}_{\ddot{S}}}^{2}$.

**Definition**

**7**

**.**Let ${\dot{S}}_{\ddot{S}}=\left\{{\dot{s}}_{t\langle {\ddot{s}}_{a}\rangle}|t=-\tau ,\dots ,-1,0,1,\dots ,\tau ;a=-\varsigma ,\dots ,-1,0,1,\dots ,\varsigma \right\}$ be a DHLTS, ${H}_{{\dot{S}}_{\ddot{S}}}^{1}=\left\{{h}_{{\dot{S}}_{\ddot{S}}}^{11},{h}_{{\dot{S}}_{\ddot{S}}}^{12},\dots ,{h}_{{\dot{S}}_{\ddot{S}}}^{1n}\right\}$ and ${H}_{{\dot{S}}_{\ddot{S}}}^{2}=\left\{{h}_{{\dot{S}}_{\ddot{S}}}^{21},{h}_{{\dot{S}}_{\ddot{S}}}^{22},\dots ,{h}_{{\dot{S}}_{\ddot{S}}}^{2n}\right\}$ be two DHHLEs. Meanwhile, ${h}_{{\dot{S}}_{\ddot{S}}}^{1j}=\left\{{\dot{s}}_{{\varphi}_{l}\langle {\ddot{s}}_{{\phi}_{l}}\rangle}^{1j}|{\dot{s}}_{{\varphi}_{l}\langle {\ddot{s}}_{{\phi}_{l}}\rangle}^{1j}\in {\dot{S}}_{\ddot{S}};l=1,2,\dots ,L\right\}$ and ${h}_{{\dot{S}}_{\ddot{S}}}^{2j}=\left\{{\dot{s}}_{{\varphi}_{l}\langle {\ddot{s}}_{{\phi}_{l}}\rangle}^{2j}|{\dot{s}}_{{\varphi}_{l}\langle {\ddot{s}}_{{\phi}_{l}}\rangle}^{2j}\in {\dot{S}}_{\ddot{S}};l=1,2,\dots ,L\right\}$. Then, the distance between ${H}_{{\dot{S}}_{\ddot{S}}}^{1}$ and ${H}_{{\dot{S}}_{\ddot{S}}}^{2}$ can be calculated by

**Definition**

**8**

**.**Let ${H}_{{\dot{S}}_{\ddot{S}}}=\left\{{h}_{{\dot{S}}_{\ddot{S}}}^{1},{h}_{{\dot{S}}_{\ddot{S}}}^{2},\dots ,{h}_{{\dot{S}}_{\ddot{S}}}^{n}\right\}$ be a DHHLE, and ${w}_{i}={\left({w}_{1},{w}_{2},\dots ,{w}_{n}\right)}^{T}$ be their associated weights with ${w}_{i}\in \left[0,1\right]$ and $\sum _{i=1}^{n}{w}_{i}}=1$, where ${h}_{{\dot{S}}_{\ddot{S}}}^{i}=\left\{{\dot{s}}_{{\varphi}_{l}\langle {\ddot{s}}_{{\phi}_{l}}\rangle}^{i}|{\dot{s}}_{{\varphi}_{l}\langle {\ddot{s}}_{{\phi}_{l}}\rangle}^{i}\in {\dot{S}}_{\ddot{S}};l=1,2,\dots ,L\right\}$ and L indicates the number of DHLTS in ${h}_{{\dot{S}}_{\ddot{S}}}^{i}$. Then, the double-hierarchy hesitant linguistic weighted average (DHHLWA) operator is defined as

#### 3.2. The ORESTE Method

**Step 1:**Calculate the global preference scores for alternatives.

_{j}and r

_{j}(A

_{i}) represent a preference structure and a merit of A

_{i}under C

_{j}, respectively. The global preference scores D(a

_{ij}) of the A

_{i}regarding the C

_{j}can be calculated by

**Step 2:**Identify the global weak rank r(a

_{ij}).

_{ij}) > D(a

_{kv}), then r(a

_{ij}) > r(a

_{kv}); If D(a

_{ij}) = D(a

_{kv}), then r(a

_{ij}) = r(a

_{kv}), where i, k = 1, 2, …, m and j, v = 1, 2, …, n.

**Step 3:**Obtain the global weak ranking.

**Step 4:**Compute the preference intensities.

_{i}and A

_{k}is defined as

_{i}and A

_{k}is defined as:

**Step 5:**Establish the PIR relation.

- (1)
- If $\left|\Delta T\left({A}_{i},{A}_{k}\right)\right|\le \sigma $, then
- (a)
- if $\left|T\left({A}_{i},{A}_{k}\right)\right|\le \eta $ and $\left|T\left({A}_{k},{A}_{i}\right)\right|\le \eta $, then A
_{i}IA_{k}, - (b)
- if $\left|T\left({A}_{i},{A}_{k}\right)\right|>\eta $ or $\left|T\left({A}_{k},{A}_{i}\right)\right|>\eta $, then A
_{i}RA_{k}.

- (2)
- If $\left|\Delta T\left({A}_{i},{A}_{k}\right)\right|>\sigma $, then
- (a)
- if $\frac{\mathrm{min}\left(T\left({A}_{i},{A}_{k}\right),T\left({A}_{k},{A}_{i}\right)\right)}{\left|\Delta T\left({A}_{i},{A}_{k}\right)\right|}\ge \rho $, then A
_{i}RA_{k}; - (b)
- if $\frac{\mathrm{min}\left(T\left({A}_{i},{A}_{k}\right),T\left({A}_{k},{A}_{i}\right)\right)}{\left|\Delta T\left({A}_{i},{A}_{k}\right)\right|}<\rho $ and $\Delta T\left({A}_{i},{A}_{k}\right)>0$, then A
_{i}PA_{k}; - (c)
- if $\frac{\mathrm{min}\left(T\left({A}_{i},{A}_{k}\right),T\left({A}_{k},{A}_{i}\right)\right)}{\left|\Delta T\left({A}_{i},{A}_{k}\right)\right|}<\rho $ and $\Delta T\left({A}_{k},{A}_{i}\right)>0$, then A
_{i}PA_{k}.

## 4. The Proposed QFD Approach

_{j}on EC

_{i}based on the linguistic term sets $\dot{S}=\left\{{\dot{s}}_{t}|t=-\tau ,\dots ,-1,0,1,\dots ,\tau \right\}$ and $\ddot{S}=\left\{{\ddot{s}}_{a}|a=-\varsigma ,\dots ,-1,0,1,\dots ,\varsigma \right\}$.

**Stage 1:**Assess the correlations between CRs and ECs based on DHHLTSs.

**Step 1:**Compute the collective relationship assessment matrix.

**Stage 2:**Determine the importance prioritization of ECs with the ORESTE method.

**Step 2:**Calculate the global preference scores for ECs.

_{j}and r

_{j}(EC

_{i}) represent a preference structure and a merit of the EC

_{i}under the CR

_{j}, respectively. r

_{j}can be determined by the weights of CRs, and r

_{j}(EC

_{i}) can be realized by the pairwise comparisons between DHHLEs in the matrix A. Then the global preference score D(a

_{ij}) of the EC

_{i}regarding the CR

_{j}can be calculated by

**Step 3:**Obtain the global weak ranking of ECs.

**Step 4:**Compute the preference intensities among ECs.

_{i}over EC

_{p}is defined as:

_{i}over EC

_{p}is defined as:

**Step 5:**Establish the PIR structure of ECs.

- (1)
- If $\left|\Delta T\left(E{C}_{i},E{C}_{p}\right)\right|\le \sigma $, then
- (a)
- EC
_{i}I EC_{p}, if $\left|T\left(E{C}_{i},E{C}_{p}\right)\right|\le \eta $ and $\left|T\left(E{C}_{p},E{C}_{i}\right)\right|\le \eta $; - (b)
- EC
_{i}R EC_{p}, if $\left|T\left(E{C}_{i},E{C}_{p}\right)\right|>\eta $ or $\left|T\left(E{C}_{p},E{C}_{i}\right)\right|>\eta $.

- (2)
- If $\left|\Delta T\left(E{C}_{i},E{C}_{k}\right)\right|>\sigma $, then
- (a)
- EC
_{i}R EC_{p}, if $\frac{\mathrm{min}\left(T\left(E{C}_{i},E{C}_{p}\right),T\left(E{C}_{p},E{C}_{i}\right)\right)}{\left|\Delta T\left(E{C}_{i},E{C}_{p}\right)\right|}\ge \rho $; - (b)
- EC
_{i}P EC_{p}, if $\frac{\mathrm{min}\left(T\left(E{C}_{i},E{C}_{p}\right),T\left(E{C}_{p},E{C}_{i}\right)\right)}{\left|\Delta T\left(E{C}_{i},E{C}_{p}\right)\right|}<\rho $ and $\Delta T\left(E{C}_{i},E{C}_{p}\right)>0$; - (c)
- EC
_{p}P EC_{i}, if $\frac{\mathrm{min}\left(T\left(E{C}_{i},E{C}_{p}\right),T\left(E{C}_{p},E{C}_{i}\right)\right)}{\left|\Delta T\left(E{C}_{i},E{C}_{p}\right)\right|}<\rho $ and $\Delta T\left(E{C}_{p},E{C}_{i}\right)>0$.

**Step 6:**Determine the strong ranking of ECs.

_{i}) can be determined by the sorted R(EC

_{i}) and its PIR relation, i.e., if global weak ranking orders of two ECs R(EC

_{i}) > R(EC

_{k}), then r(EC

_{i}) > r(EC

_{k}), denoted as a natural number from 1, 2, … and the like; otherwise, R(EC

_{i}) = R(EC

_{k}), then r(EC

_{i}) = r(EC

_{k}) wherein the relationships between r(EC

_{i}) and r(EC

_{k}) can be determined by the PIR rules, for i, k = 1, 2, …, m.

## 5. Case Study

#### 5.1. Implementation and Results

- (1)
- if ${\dot{s}}_{t}\ge {\dot{s}}_{0}$, then$$\begin{array}{l}{\ddot{s}}_{a}=\{{\ddot{s}}_{-3}=\mathrm{far}\mathrm{from},{\ddot{s}}_{-2}=\mathrm{only}\mathrm{a}\mathrm{little},{\ddot{s}}_{-1}=\mathrm{a}\mathrm{little},{\ddot{s}}_{0}=\mathrm{just}\mathrm{right},{\ddot{s}}_{1}=\mathrm{much},\\ {\ddot{s}}_{2}=\mathrm{very}\mathrm{much},{\ddot{s}}_{3}=\mathrm{entirely}\}\end{array}$$
- (2)
- if ${\dot{s}}_{t}<{\dot{s}}_{0}$, then$$\begin{array}{l}{\ddot{s}}_{a}=\{{\ddot{s}}_{-3}=\mathrm{entirely},{\ddot{s}}_{-2}=\mathrm{very}\mathrm{much},{\ddot{s}}_{-1}=\mathrm{much},{\ddot{s}}_{0}=\mathrm{just}\mathrm{right},{\ddot{s}}_{1}=\mathrm{a}\mathrm{little},\\ {\ddot{s}}_{2}=\mathrm{only}\mathrm{a}\mathrm{little},{\ddot{s}}_{3}=\mathrm{far}\mathrm{from}\}\end{array}$$

**Step 1:**The original linguistic assessments for the relationships between ECs and CRs given by five experts are translated into DHHLEs to obtain the DHHL matrices ${A}^{k}={\left({a}_{{\dot{S}}_{{\ddot{S}}_{ij}}}^{k}\right)}_{17\times 7}\left(k=1,2,\dots ,5\right)$. Taking the first expert as an example, its DHHL assessment matrix ${A}^{1}$ is presented in Table 4.

**Step 2:**According to the correlation-based weights of CRs given in Table 5, the Besson’s mean ranks of CRs are obtained as: r

_{1}= 2, r

_{2}= 4.5, r

_{3}= 6, r

_{4}= 7, r

_{5}= 1, r

_{6}= 4.5, and r

_{7}= 3.

_{j}(EC

_{i}) is obtained as:

**Step 3:**With Equation (20), the global weak ranking of each EC is calculated as:

**Step 4:**According to Equations (21) and (22), the average preference intensities between the ECs which have the same global weak rankings, as well as EC

_{9}, EC

_{10}, EC

_{11}, and EC

_{17}are presented in Table 6 and Table 7.

**Step 5:**By Equation (23), the three different thresholds are calculated as: σ = 0.0089, ρ = 1.3, η = 0.003, and the parameter λ = 0.1. Thus, the relationships between ECs are derived by their global weak rankings and PIR rules, and the PIR relations are presented in Table 8.

**Step 6:**The strong ranking r(ECi) (i = 1,2,…,17) of ECs can be determined by the sorted R(EC

_{i}) and its PIR relation, which is denoted as: r(EC

_{14}) > r(EC

_{13}) > r(EC

_{9}) = r(EC

_{10}) = r(EC

_{11}) = r(EC

_{17}) > r(EC

_{1}) = r(EC

_{2}) = r(EC

_{5}) = r(EC

_{12}) = r(EC

_{15}) = r(EC

_{16}) > r(EC

_{7}) > r(EC

_{4}) > r(EC

_{6}) > r(EC

_{3}) > r(EC

_{8}). Therefore, EC

_{8}is the most important EC, which should be paid more attention for selecting the most appropriate mobile phone.

#### 5.2. Comparative Analysis

_{7}, EC

_{13}, and EC

_{14}, the importance prioritization of ECs yielded by the HF-QFD method is in line with the result obtained by the proposed QFD approach; except for EC

_{3}, EC

_{4}, EC

_{6}, EC

_{7}, and EC

_{8}, the importance ranking of ECs derived by the ORESTE method is identical with the result obtained by the proposed QFD approach. As there is a good similarity between the proposed approach and the other three methods, the effectiveness and feasibility of our proposed QFD approach are validated in practical applications.

_{7}, EC

_{13}, and EC

_{14}) obtained by the HF-QFD method are different from those determined by the proposed approach. These discrepancies may be explained by the following reasons: The experts’ relationship evaluations of the proposed approach are based on the DHHLTSs. In contrast, the hesitant fuzzy sets are used by the HF-QFD method to deal with the relationship evaluations between CRs and ECs provided by experts.

_{3}, EC

_{4}, EC

_{6}, EC

_{7}, and EC

_{8}determined by the proposed QFD and the classical ORESTE method are different. This could be attributed to the fact that different methods were adopted by the compared methods to represent the relationship evaluations between CRs and ECs. In other words, the proposed QFD approach adopted the DHHLTSs, and the classical ORESTE method applied crisp numbers to depict the qualitative evaluations on “WHATs-HOWs” given by experts.

- (1)
- By applying the DHHLTSs, the hesitant evaluation information from each expert can be expressed more accurately and comprehensively. Thus, the propped approach can reduce information distortion and improve the accuracy of evaluation in the QFD process.
- (2)
- An extended ORESTE method is employed for determining the importance priority of ECs in the proposed QFD. Through calculating information contents to distinguish ECs, the ranking result given by the propped approach is more reasonable and credible.

## 6. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

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Reference | Methods | Advantages |
---|---|---|

Wang [4] | Fuzzy sets | Create more logical and reliable priority rankings for ECs by aggregating their technical importance ratings |

Singh and Kumar [48] | Picture fuzzy sets | Measure the linguistic terms for qualitative analysis and characterize fuzziness and uncertainties more comprehensively |

Efe et al. [49] | IT2FSs | Include expert opinions to describe the applications’ ambiguity more precisely |

Finger and Lima-Junior [11] | HFLTSs | Support experts employ multiple linguistic terms or linguistic expressions |

Efe and Efe [50] | Q-rung orthopair fuzzy numbers | Present more information about the correlations and relationships of CRs and ECs |

Xiao et al. [51] | Linguistic distribution assessments | Model the vague assessments of the relationship between CRs and ECs; lessen QFD team members’ cognitive burden |

Xie et al. [52] | Interval-valued intuitionistic fuzzy sets | Apply the cross-entropy to perform an objective analysis and prioritize the ECs |

Haktanır and Kahraman [53] | Interval-valued Pythagorean fuzzy sets | Handle the fuzzy and vague relationship assessment information provided by QFD team members |

Ping et al. [38] | Linguistic Pythagorean fuzzy; AQM | Express the assessments from experts on the relationships between CRs and ECs; determine the importance prioritization of ECs |

Liu et al. [5] | Interval type-2 fuzzy sets; TODIM | Describe the imprecise and uncertain correlation assessments between CRs and ECs; derive the weights of CRs objectively |

Nie et al. [28] | Linguistic distribution assessments; TODIM | Achieve a simple opinions presentation given by a large-scale of experts; reflect psychological behaviors and real desires of patients in EC prioritization |

Wang et al. [27] | DHHLTSs; axiomatic design approach | Evaluate the relationships between CRs and ECs; derive the prioritization of ECs in QFD |

Mao et al. [24] | Linguistic Z-numbers; EDAS | Deal with the vague evaluation information; estimate the final priority ratings of ECs |

Liu et al. [19] | EHFLTSs; prospect theory | Obtain the hesitant linguistic assessment information of QFD team members; derive the ranking orders of ECs |

Huang et al. [23] | PHFLTSs; prospect theory | Describe the relationships between CRs and ECs; prioritise ECs in the QFD analysis |

Jin et al. [54] | Interval-valued spherical fuzzy sets; ORESTE | Improve the rationality of the ranking method; can deal with various uncertainty and hesitation |

Wu et al. [25] | C-MULTIMOORA | Capture the uncertainty of experts’ assessment information and derive a credible ranking of ECs |

Kutlu Gündoğdu and Kahraman [26] | TOPSIS | Allocate independently and have a greater scope for determining membership, non-membership, and hesitancy degrees |

Mistarihi et al. [55] | Fuzzy ANP | Deal with vague human judgments of the intensity of preference and consider the relations among ECs |

Wang et al. [56] | Cloud model; GRA | Handle uncertain information in the QFD process to produce more accurate analysis results |

Chen et al. [57] | HFLTS; DEMATEL; MULTIMOORA | Analyze the causal relationships among ECs and capture their influence weights; analyze the correlations between ECs and CRs |

Wu et al. [17] | DEMATEL; VIKOR | Analyze the cause-and-effect relationships among CRs and determine their influential weights; merge the dependences between CRs and ECs and derive the priorities of ECs |

CRs | Customer Requirements | ECs | Engineering Characteristics | ECs | Engineering Characteristics |
---|---|---|---|---|---|

CR_{1} | System performance | EC_{1} | Weight | EC_{10} | Optical zoom |

CR_{2} | Visual appeal | EC_{2} | Thickness | EC_{11} | Image sensor |

CR_{3} | Photograph capability | EC_{3} | RAM capacity | EC_{12} | Video chatting |

CR_{4} | Solidity | EC_{4} | Internal memory | EC_{13} | Dimension |

CR_{5} | Price | EC_{5} | Water resistance | EC_{14} | Screen dimension |

CR_{6} | Portability | EC_{6} | Camera resolution | EC_{15} | Screen type |

CR_{7} | Ease of use | EC_{7} | Screen resolution | EC_{16} | Battery life |

EC_{8} | CPU’s performance score | EC_{17} | Selfie quality | ||

EC_{9} | Touch sensitivity |

EC_{S} | CR_{S} | ||||||
---|---|---|---|---|---|---|---|

CR_{1} | CR_{2} | CR_{3} | CR_{4} | CR_{5} | CR_{6} | CR_{7} | |

EC_{1} | Much medium | ||||||

EC_{2} | Much high | ||||||

EC_{3} | Much high | Just right medium | Very much high | ||||

EC_{4} | Very much medium | Very much medium | Just right high | ||||

EC_{5} | Much low | ||||||

EC_{6} | Only a little medium | Just right medium | A little high | ||||

EC_{7} | Just right very high | Entirely high | Entirely medium | Much high | |||

EC_{8} | Much high | Very much high | |||||

EC_{9} | A little low | Just right very high | |||||

EC_{10} | Just right very high | ||||||

EC_{11} | A little very high | ||||||

EC_{12} | A little medium | ||||||

EC_{13} | A little medium | Just right very high | |||||

EC_{14} | Just right very high | Entirely high | Just right very high | Just right very high | |||

EC_{15} | Only a little low | ||||||

EC_{16} | Just right very high | A little medium | |||||

EC_{17} | A little medium |

ECs | CRs | ||||||
---|---|---|---|---|---|---|---|

CR_{1} | CR_{2} | CR_{3} | CR_{4} | CR_{5} | CR_{6} | CR_{7} | |

EC_{1} | ${\dot{s}}_{0\langle {\ddot{s}}_{1}\rangle}$ | ||||||

EC_{2} | ${\dot{s}}_{1\langle {\ddot{s}}_{1}\rangle}$ | ||||||

EC_{3} | ${\dot{s}}_{1\langle {\ddot{s}}_{1}\rangle}$ | ${\dot{s}}_{0\langle {\ddot{s}}_{0}\rangle}$ | ${\dot{s}}_{1\langle {\ddot{s}}_{2}\rangle}$ | ||||

EC_{4} | ${\dot{s}}_{0\langle {\ddot{s}}_{2}\rangle}$ | ${\dot{s}}_{0\langle {\ddot{s}}_{-2}\rangle}$ | ${\dot{s}}_{1\langle {\ddot{s}}_{0}\rangle}$ | ||||

EC_{5} | ${\dot{s}}_{-1\langle {\ddot{s}}_{-1}\rangle}$ | ||||||

EC_{6} | ${\dot{s}}_{0\langle {\ddot{s}}_{-2}\rangle}$ | ${\dot{s}}_{0\langle {\ddot{s}}_{0}\rangle}$ | ${\dot{s}}_{1\langle {\ddot{s}}_{-1}\rangle}$ | ||||

EC_{7} | ${\dot{s}}_{2\langle {\ddot{s}}_{0}\rangle}$ | ${\dot{s}}_{1\langle {\ddot{s}}_{3}\rangle}$ | ${\dot{s}}_{0\langle {\ddot{s}}_{3}\rangle}$ | ${\dot{s}}_{1\langle {\ddot{s}}_{1}\rangle}$ | |||

EC_{8} | ${\dot{s}}_{1\langle {\ddot{s}}_{1}\rangle}$ | ${\dot{s}}_{1\langle {\ddot{s}}_{2}\rangle}$ | |||||

EC_{9} | ${\dot{s}}_{-1\langle {\ddot{s}}_{1}\rangle}$ | ${\dot{s}}_{2\langle {\ddot{s}}_{0}\rangle}$ | |||||

EC_{10} | ${\dot{s}}_{2\langle {\ddot{s}}_{0}\rangle}$ | ||||||

EC_{11} | ${\dot{s}}_{2\langle {\ddot{s}}_{-1}\rangle}$ | ||||||

EC_{12} | ${\dot{s}}_{0\langle {\ddot{s}}_{-1}\rangle}$ | ||||||

EC_{13} | ${\dot{s}}_{0\langle {\ddot{s}}_{-1}\rangle}$ | ${\dot{s}}_{2\langle {\ddot{s}}_{0}\rangle}$ | |||||

EC_{14} | ${\dot{s}}_{2\langle {\ddot{s}}_{0}\rangle}$ | ${\dot{s}}_{1\langle {\ddot{s}}_{3}\rangle}$ | ${\dot{s}}_{2\langle {\ddot{s}}_{0}\rangle}$ | ${\dot{s}}_{2\langle {\ddot{s}}_{0}\rangle}$ | |||

EC_{15} | ${\dot{s}}_{-1\langle {\ddot{s}}_{2}\rangle}$ | ||||||

EC_{16} | ${\dot{s}}_{2\langle {\ddot{s}}_{0}\rangle}$ | ${\dot{s}}_{0\langle {\ddot{s}}_{-1}\rangle}$ | |||||

EC_{17} | ${\dot{s}}_{0\langle {\ddot{s}}_{-1}\rangle}$ |

CR_{1} | CR_{2} | CR_{3} | CR_{4} | CR_{5} | CR_{6} | CR_{7} |
---|---|---|---|---|---|---|

0.196 | 0.094 | 0.091 | 0.111 | 0.239 | 0.094 | 0.175 |

**Table 6.**The average preference intensities between EC

_{1}, EC

_{2}, EC

_{5}, EC

_{12}, EC

_{15}, and EC

_{16}.

T(EC_{1}, EC_{i}) | T(EC_{2}, EC_{i}) | T(EC_{5}, EC_{i}) | T(EC_{12}, EC_{i}) | T(EC_{15}, EC_{i}) | T(EC_{16}, EC_{i}) | |
---|---|---|---|---|---|---|

EC_{1} | / | 0 | 0 | 0.0016 | 0.0016 | 0.0016 |

EC_{2} | 0 | / | 0 | 0.0016 | 0.0016 | 0.0016 |

EC_{5} | 0 | 0 | / | 0.0016 | 0.0016 | 0.0016 |

EC_{12} | 0.0016 | 0.0016 | 0.0016 | / | 0.0016 | 0.0033 |

EC_{15} | 0.0016 | 0.0016 | 0.0016 | 0 | / | 0.0033 |

EC_{16} | 0.0033 | 0.0033 | 0.0033 | 0.0033 | 0.0033 | / |

T(EC_{9}, EC_{i}) | T(EC_{10}, EC_{i}) | T(EC_{11}, EC_{i}) | T(EC_{17}, EC_{i}) | |
---|---|---|---|---|

EC_{9} | / | 0.0020 | 0.0020 | 0.0020 |

EC_{10} | 0.0020 | / | 0 | 0 |

EC_{11} | 0.0020 | 0 | / | 0 |

EC_{17} | 0.0020 | 0 | 0 | / |

EC_{1} | EC_{2} | EC_{3} | EC_{4} | EC_{5} | EC_{6} | EC_{7} | EC_{8} | EC_{9} | EC_{10} | EC_{11} | EC_{12} | EC_{13} | EC_{14} | EC_{15} | EC_{16} | EC_{17} | |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

EC_{1} | / | I | > | > | I | > | > | > | < | < | < | I | < | < | I | R | < |

EC_{2} | I | / | < | < | I | < | < | < | < | < | < | I | < | < | I | R | < |

EC_{3} | < | > | / | < | < | < | < | > | < | < | < | < | < | < | < | < | < |

EC_{4} | < | < | > | / | < | < | < | > | < | < | < | < | < | < | < | < | < |

EC_{5} | I | I | > | > | / | > | > | > | < | < | < | I | < | < | I | R | < |

EC_{6} | < | < | > | < | < | / | < | > | < | < | < | < | < | < | < | < | < |

EC_{7} | < | < | > | > | < | > | / | > | < | < | < | < | < | < | < | < | < |

EC_{8} | < | < | < | < | < | < | < | / | < | < | < | < | < | < | < | < | < |

EC_{9} | > | > | > | > | > | > | > | > | / | I | I | > | < | < | > | > | I |

EC_{10} | > | > | > | > | > | > | > | > | I | / | I | > | > | > | > | > | I |

EC_{11} | > | > | > | > | > | > | > | > | I | I | / | > | > | > | > | > | I |

EC_{12} | I | I | > | > | I | > | > | > | < | < | < | / | > | < | I | R | < |

EC_{13} | > | > | > | > | > | > | > | > | > | > | > | > | / | < | > | > | > |

EC_{14} | > | > | > | > | > | > | > | > | > | > | > | > | > | / | > | > | > |

EC_{15} | I | I | > | > | I | > | > | > | < | < | < | I | < | < | / | R | < |

EC_{16} | R | R | > | > | R | > | > | > | < | < | < | R | < | < | R | / | < |

EC_{17} | > | > | > | > | > | > | > | > | I | I | I | > | < | < | > | > | / |

ECs | Proposed Method | IT2F QFD Method | HF-QFD Method | ORESTE Method | ||||
---|---|---|---|---|---|---|---|---|

R(EC_{i}) | Ranking | ω_{j} | Ranking | R(EC_{i}) | Ranking | R(EC_{i}) | Ranking | |

EC_{1} | 4.22 | 6 | 0.019 | 16 | 4.22 | 6 | 4.22 | 6 |

EC_{2} | 4.22 | 6 | 0.024 | 15 | 4.22 | 6 | 4.22 | 6 |

EC_{3} | 4.05 | 2 | 0.058 | 6 | 4.05 | 2 | 4.05 | 3 |

EC_{4} | 4.09 | 4 | 0.044 | 8 | 4.11 | 4 | 4.11 | 5 |

EC_{5} | 4.22 | 6 | 0.049 | 7 | 4.22 | 6 | 4.22 | 6 |

EC_{6} | 4.07 | 3 | 0.132 | 3 | 4.07 | 3 | 4.07 | 4 |

EC_{7} | 4.12 | 5 | 0.175 | 1 | 4.11 | 4 | 4.01 | 1 |

EC_{8} | 4.03 | 1 | 0.101 | 4 | 4.04 | 1 | 4.04 | 2 |

EC_{9} | 4.25 | 12 | 0.040 | 9 | 4.25 | 12 | 4.25 | 12 |

EC_{10} | 4.25 | 12 | 0.025 | 14 | 4.25 | 12 | 4.25 | 12 |

EC_{11} | 4.25 | 12 | 0.033 | 10 | 4.25 | 12 | 4.25 | 12 |

EC_{12} | 4.22 | 6 | 0.023 | 14 | 4.22 | 6 | 4.22 | 6 |

EC_{13} | 4.27 | 16 | 0.026 | 11 | 4.58 | 17 | 4.27 | 16 |

EC_{14} | 4.35 | 17 | 0.074 | 5 | 4.30 | 16 | 4.28 | 17 |

EC_{15} | 4.22 | 6 | 0.009 | 17 | 4.22 | 6 | 4.22 | 6 |

EC_{16} | 4.22 | 6 | 0.142 | 2 | 4.22 | 6 | 4.22 | 6 |

EC_{17} | 4.25 | 12 | 0.026 | 11 | 4.25 | 12 | 4.25 | 12 |

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Shi, H.; Mao, L.-X.; Li, K.; Wang, X.-H.; Liu, H.-C.
Engineering Characteristics Prioritization in Quality Function Deployment Using an Improved ORESTE Method with Double Hierarchy Hesitant Linguistic Information. *Sustainability* **2022**, *14*, 9771.
https://doi.org/10.3390/su14159771

**AMA Style**

Shi H, Mao L-X, Li K, Wang X-H, Liu H-C.
Engineering Characteristics Prioritization in Quality Function Deployment Using an Improved ORESTE Method with Double Hierarchy Hesitant Linguistic Information. *Sustainability*. 2022; 14(15):9771.
https://doi.org/10.3390/su14159771

**Chicago/Turabian Style**

Shi, Hua, Ling-Xiang Mao, Ke Li, Xiang-Hu Wang, and Hu-Chen Liu.
2022. "Engineering Characteristics Prioritization in Quality Function Deployment Using an Improved ORESTE Method with Double Hierarchy Hesitant Linguistic Information" *Sustainability* 14, no. 15: 9771.
https://doi.org/10.3390/su14159771