# Prediction of Knowledge Management for Success of Franchise Hospitality in a Post-Pandemic Economy

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## Abstract

**:**

## 1. Introduction

## 2. The Review of the Professional and Academic Literature

#### 2.1. Headquarters System

#### 2.2. Human Resources

#### 2.3. Corporate Imagination

#### 2.4. Location Advantage

#### 2.5. Innovation and Transformation

#### 2.6. Marketing Strategy

#### 2.7. Crisis Management

## 3. Research Methodology

- (1)
- What definition do you use to describe knowledge management of routine operation as franchise hospitality stakeholders?
- (2)
- What processes do you use to implement KM strategies for market performance and competitiveness?
- (3)
- What specific technology do you use to identify the influential criteria within the COVID-19 outbreak?
- (4)
- What additional comments or insights would you suggest discussing?
- (5)
- Moreover, seven major influential criteria were designed into a set of pairwise comparisons, to collect the experts’ preference opinions.

#### 3.1. Fuzzy Preference Relations

**Definition**

**1.**

**Proposition**

**1.**

#### 3.2. Consistency of Fuzzy Preference Relations

**Proposition**

**2.**

**Proof.**

**Definition**

**2.**

#### 3.3. Additive Transitivity Consistency of the Fuzzy Preference Relations

**Proposition**

**3.**

**Proposition**

**4.**

**Proposition**

**5.**

## 4. Framework to Evaluate the Influence of Criteria to Implement Knowledge Management (KM)

#### 4.1. Evaluated Influential Criteria and Framework of the Evaluation Model

_{1}headquarters system; C

_{2}human resources; C

_{3}corporate imagination; C

_{4}location advantage; C

_{5}innovation and transformation C

_{6}marketing strategy; C

_{7}crisis management. An analytic hierarchy framework reliant upon seven major influential criteria is illustrated in Figure 2 [12,53].

#### 4.2. The Analytic Hierarchy Process for Evaluating the Influence of Criteria

#### 4.2.1. Linguistic Variables

#### 4.2.2. Consistent Fuzzy Preference Relations for Weighting the Influential Criteria

- (1)
- This study established pairwise comparison matrices for n criteria (${C}_{i}$, i = 1, 2, …, n) in the dimension of a hierarchical system. Evaluators (${C}_{k}$, k = 1, 2, …, m) provided the essential pairwise criteria for a set of n − 1 preference values $\left({a}_{12},{a}_{23},\dots ,{a}_{\left(n-1\right)n}\right),$ as shown below.$$\begin{array}{l}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\begin{array}{c}{c}_{1}\end{array}\stackrel{}{{\displaystyle}}\begin{array}{cccc}\hspace{1em}{c}_{2}& \hspace{1em}\dots & {c}_{n-1}& {c}_{n}\end{array}\\ {A}^{k}=\begin{array}{c}{c}_{1}\\ {c}_{2}\\ \vdots \\ {c}_{n-1}\\ {c}_{n}\end{array}\begin{array}{r}\hfill \left[\begin{array}{ccccc}1& {a}_{12}^{k}& \dots & \times & \times \\ \times & 1& {a}_{23}^{k}& \times & \times \\ \vdots & \vdots & \ddots & \ddots & \vdots \\ \times & \times & \dots & 1& {a}_{(n-1)n}^{k}\\ \times & \times & \dots & \times & 1\end{array}\right]\end{array}\end{array}$$
- (2)
- The preference value ${a}_{ij}^{k}$ was transformed into ${p}_{ij}^{k}$ utilizing an interval scale $\left[0,1\right]$ before deriving the preserved ${p}_{ij}^{k}$ on the basis of the reciprocal transitivity property, as shown below.$$\begin{array}{l}\begin{array}{cc}& \begin{array}{cccc}& & & \end{array}\begin{array}{c}\hspace{1em}{c}_{1}\end{array}\end{array}\begin{array}{ccc}\hspace{1em}\hspace{1em}{c}_{2}& \hspace{1em}\dots & \hspace{1em}{c}_{n}\end{array}\\ {A}^{k}\stackrel{\frac{1}{2}(1+{\mathrm{log}}_{9}{a}_{ij})}{\Rightarrow}{p}^{k}=\begin{array}{c}{c}_{1}\\ {c}_{2}\\ \vdots \\ {c}_{n}\end{array}\begin{array}{r}\hfill \left[\begin{array}{cccc}0.5& {p}_{12}^{k}& \times & \times \\ 1-{p}_{12}^{k}& 0.5& {p}_{23}^{k}& \times \\ \vdots & 1-{p}_{23}^{k}& \vdots & \vdots \\ \times & \times & \dots & 0.5\end{array}\right]\end{array}\end{array}$$$$f:\left[-\mathrm{a},1+\mathrm{a}\right]\to \left[0,1\right]\phantom{\rule{0ex}{0ex}}f\left(x\right)=\frac{\chi +\mathrm{a}}{1+2\mathrm{a}}$$$$f\left({p}_{ij}^{k}\right)=\frac{{p}_{ij}^{k}+\mathrm{a}}{1+2\mathrm{a}}$$
- (3)
- The evaluators’ opinions were pulled to acquire the aggregated priority weights of influential criteria. In addition, ${p}_{ij}^{k}$ was used to indicate transformed the fuzzy preference value of evaluator k for evaluating the criteria i and j. The notation of the average integrated values of m evaluators is described below [72].$${p}_{ij}=\frac{1}{m}\left({p}_{ij}^{1}+{p}_{ij}^{2}+\dots +{p}_{ij}^{m}\right)$$
- (4)
- Normalized fuzzy preference relation matrix ${q}_{ij}$ was aggregated to refer to the normalized fuzzy preference values of each criterion as follows:$${{\displaystyle q}}_{ij}=\frac{1}{n}{\displaystyle \sum _{i=1}^{n}{p}_{ij}}$$
- (5)
- The variable ${\overline{\omega}}_{i}$ represents the average priority weight of influential criteria, whereas n denotes the number of influential criteria; thus, the priority of each criterion can be defined as$${\overline{\omega}}_{i}=\frac{{q}_{ij}}{{\displaystyle \sum _{i=1}^{n}{q}_{ij}}}$$

#### 4.2.3. Defining the Priority Ratings for Possibility of Outcome Complying with Each Criterion

- (1)
- For each influential criterion, the evaluators selected the two possible outcomes for a set of t − 1 preference data $\left\{{b}_{12},{b}_{23,}\dots ,{b}_{\left(t-1\right)t}\right\}$ as shown below.$$\begin{array}{l}\begin{array}{c}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}{A}_{1}\end{array}\begin{array}{cccc}\hspace{1em}\hspace{1em}{A}_{2}& \dots & {A}_{t-1}& {A}_{t}\end{array}\\ {}_{i}B=\begin{array}{c}{A}_{1}\\ {A}_{2}\\ \vdots \\ {A}_{t-1}\\ {A}_{t}\end{array}\begin{array}{r}\hfill \left[\begin{array}{ccccc}1& {}_{i}{b}_{12}^{k}& \times & \times & \times \\ \times & 1& {}_{i}{b}_{23}^{k}& \times & \times \\ \vdots & \vdots & \ddots & \ddots & \vdots \\ \times & \times & \dots & 1& {}_{i}{b}_{(t-1)t}^{k}\\ \times & \times & \dots & \times & 1\end{array}\right]\end{array}\end{array}$$
- (2)
- Moreover, the preference value ${}_{i}{b}_{uv}^{k}$ was transformed in the range $\left[\frac{1}{5},5\right]$ into ${}_{i}{q}_{uv}^{k}$ using an interval scale [0, 1], whereby the preservation of ${}_{i}{q}_{uv}^{k}$ can be acquired utilizing the reciprocal transitivity property as follows:$$\begin{array}{l}\begin{array}{c}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}{A}_{1}\end{array}\begin{array}{cccc}\hspace{1em}\hspace{1em}{A}_{2}& \dots & \hspace{1em}{A}_{t-1}\stackrel{}{}& {A}_{t}\end{array}\\ {}_{i}B\stackrel{\frac{1}{2}(1+{\mathrm{log}}_{5}{b}_{uv})}{\Rightarrow}{}_{i}Q=\begin{array}{c}{A}_{1}\\ {A}_{2}\\ \vdots \\ {A}_{t-1}\\ {A}_{t}\end{array}\begin{array}{r}\hfill \left[\begin{array}{ccccc}0.5& {}_{i}{q}_{12}^{k}& \times & \times & \times \\ 1-{}_{i}{q}_{12}^{k}& 0.5& {}_{i}{q}_{23}^{k}& \times & \times \\ \vdots & 1-{}_{i}{q}_{23}^{k}& \ddots & \ddots & \vdots \\ \times & \times & \dots & 0.5& {}_{i}{q}_{(t-1)t}^{k}\\ \times & \times & \dots & \times & 0.5\end{array}\right]\end{array}\end{array}$$
- (3)
- The suggestions of evaluators were pulled to rate the synthetically transformed possible outcome. Utilizing ${}_{i}{q}_{uv}^{k}$ represents the transformed fuzzy preference value of evaluator k for evaluating possible outcomes Au and Av in terms of influential criterion i. The average value integrated the assessment values of m evaluators as follows:$${}_{i}{q}_{uv}^{k}=\frac{1}{m}\left({}_{i}{q}_{uv}^{1}+{}_{i}{q}_{uv}^{2}+\dots +{}_{i}{q}_{uv}^{m}\right),$$
- (4)
- For the synthetically normalized fuzzy preference rating of possible outcomes, ${}_{i}{\lambda}_{uv}$ was used to represent the normalized rating of possible outcomes Au and Av in terms of influential criterion i.$${}_{i}{\lambda}_{uv}=\frac{{}_{i}{q}_{uv}}{{\displaystyle \sum _{u=1}^{t}{}_{i}{q}_{uv}}}\stackrel{}{}u,v=1,2,\dots t.$$
- (5)
- As a consequence, ${}_{i}{\overline{\varphi}}_{u}$ representing the average rating of possible outcome Au with respect to influential criterion i was supplied. The appetence rating of each possible outcome could be acquired as follows$${}_{i}{\overline{\varphi}}_{u}=\frac{1}{t}{\displaystyle \sum _{v=1}^{t}{\lambda}_{uv}},$$

#### 4.3. Acquiring the Priority Weight for Prediction

## 5. Empirical Case for Predicting Possibility of Success of KM Implementation

#### 5.1. Weight Calculation of the Influential Criteria

- (1)

- (2)

- (3)
- Then, the linguistic terms were transferred into parallelism scores (see Table 6).

- (4)
- The elements were transformed by applying Equation (2) (listed in Table 7) into an interval [0, 1], as shown below.

_{1}is shown in Table 8.

- (5)
- The calculated procedures illustrated the fuzzy preference relations matrices of another 14 evaluators; moreover, the aggregated pairwise comparison matrix of the 15 evaluators was acquired by applying Equation (16), as shown in Table 10.

- (6)
- Equation (17) was applied to normalize the aggregated pairwise comparison matrix, where an example is shown below using ${q}_{12}$.

#### 5.2. The Influential Criteria Calculated to Acquire Weights for Possibilities of Outcomes

- (1)
- To assess the real situation of franchising hospitality within the pandemic period, the 15 evaluators were interviewed to evaluate which influential criterion can most easily be implemented to become successful. Table 12 lists the selections made by the 15 evaluators in terms of the preference intensity for the probability of success or failure compliant with each influential criterion.
- (2)
- The translation of linguistic variables into parallel numbers is illustrated in Table 3 Then, the function ${}_{i}{q}_{uv}^{k}=\frac{1}{2}\left(1+{\mathrm{log}}_{5}{}_{i}{b}_{uv}^{k}\right)$ was applied to transform the values within the scale [$\frac{1}{5}$, 5] into the interval [0, 1]. The preference data were transformed into the possible outcome of success, as shown in Table 13.
- (3)
- The reciprocal additive transitivity property was then proposed, leading to the opposite comparison for failure shown in Table 14.
- (4)
- The rating of possible outcomes could be synthetically acquired by applying Equation (21), as shown in Table 15. Equations (22) and (23) were then applied to synthesize and normalize the fuzzy preference rating of possible outcomes with respect to the seven influential criteria. The normalized values and priority weights are listed in Table 14. The calculations using ${}_{1}{\lambda}_{SS},{}_{1}{\lambda}_{SF},{}_{1}{\lambda}_{FS}$ and ${}_{1}{\lambda}_{FF}$ as examples are shown below.

#### 5.3. Determining the Prediction Values of Priority Weight

## 6. Discussion

#### 6.1. Factors

#### 6.2. Method

## 7. Conclusions

## 8. Limitations and Future Research Suggestions

## Author Contributions

## Funding

## Conflicts of Interest

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Criteria | Literature Review | Reference |
---|---|---|

Headquarters System | - The franchise system should provide flexible managerial know-how to reach the franchisee’s endeavors and benefits.
- There are various divisions in an organization practicing a diverse KM framework using different knowledge bases and skill sets.
- The headquarters system is based upon explicit knowledge management and transfer mechanisms since an improvement in consistency and standardization can best maintain the current business model, operational procedures, policy guidelines, quality controls, and brand standard documentation.
- The headquarters system can quickly recognize the importance of successful strategic management needed to share knowledge and to enhance a firm’s ability to react faster to challenges and opportunities in the COVID-19 outbreak.
| [25] [26,27] [28] [29] |

Human Resources | - The effects of the COVID-19 outbreak have caused unavoidable labor problems.
- The hospitality sector’s operational model has been forced to modify into a contactless service and delivery platform.
- New knowledge or skills to meet the customer’s continued expectations.
- The KM system vis-á-vis HR performance can be used for decision-making in a rapidly shifting and uncertain environment.
| [30,31] [32] [23,33] [34] |

Corporate Imagination | - Organizational values must be evaluated according to the internal and external environments of the organizations.
- The pandemic requires corporations to exhibit greater imagination and creativity.
- The vibrant imagination of an organization is an essential criterion for reducing franchisee–partner turnover and improving the organization’s reputation as the best franchise opportunity of choice.
| [35,36] [37] [23] |

Location Advantage | - An effective assessment of the business location depends on the nature of the owner’s business according to the establishment of a new sector.
- The conceptual location advantage has had to be rethought and reassessed to determine a marketplace franchise hospitality performance as a unique brand reputation through identified location advantage.
| [39,40] [41] |

Innovation and Transformation | - Due to the COVID-19 outbreak, organizations have been forced to implement innovative and transformative sales methods to existing products or services in order to survive in the uncertain market environment.
- Various combinations of contactless service and delivery methods have arisen to deal with consumers’ dissatisfaction with current performance by leveraging novel technological and social opportunities.
- The central element of innovation is crucial to survive critical market battles and to fight the global crisis of the pandemic.
| [38] [32,42,43] [44] |

Marketing Strategy | - Each of the characteristic influences depends on how relevant services and products are developed, marketed, and sold within the pandemic’s duration.
- These assets will allow firms to reduce their investment risk and monitor costs by leveraging their own particular market knowledge.
| [45,46] [23,47,48] |

Crisis Management | - The executive researchers should not only design and implement a crisis recovery model and response strategy, but also build elastic knowledge and the capacity to address future crises.
- Various organizations’ published sources are used to determine the appropriate stages of prescriptive models and to assist organizations in perception of proactive and strategic policies with the best policy and action to be implemented.
- The three phases of action for organizations and decision-makers to follow provide the guiding principles as a management framework in managing the COVID-19 crisis with detailed key phases of action.
- Some studies investigated COVID-19’s impact on the effectiveness of crisis response strategies, while some focused on the role an organization plays in affecting people’s perceptions of a crisis.
- The crisis management should strengthen the relationship between an organization and an industry in order to discuss relevant improvement and accurate proceedings.
| [32,49] [10] [34] [32] [8] |

Definition | Intensity of Importance |
---|---|

Equally important (EQ) | 1 |

Weakly more important (WK) | 3 |

Strongly more important (ST) | 5 |

Very strongly more important (VS) | 7 |

Absolutely more important (AB) | 9 |

Intermediate values used to represent compromise | 2, 4, 6, 8 |

Definition | Intensity of Importance |
---|---|

Fair (F) | 1 |

High (H) | 3 |

Very high (VH) | 5 |

Intermediate values used to represent compromise | 2, 4 |

${\mathbf{E}}_{1}$ | ${\mathbf{E}}_{2}$ | ${\mathbf{E}}_{3}$ | ${\mathbf{E}}_{4}$ | ${\mathbf{E}}_{5}$ | ${\mathbf{E}}_{6}$ | ${\mathbf{E}}_{7}$ | ${\mathbf{E}}_{8}$ | ${\mathbf{E}}_{9}$ | ${\mathbf{E}}_{10}$ | ${\mathbf{E}}_{11}$ | ${\mathbf{E}}_{12}$ | ${\mathbf{E}}_{13}$ | ${\mathbf{E}}_{14}$ | ${\mathbf{E}}_{15}$ | ||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

C_{1} | WK | EQ | LSLV | WK | VT | AB | AV | AB | VS | AB | AV | LAB | LVS | AB | WK | C_{2} |

C_{2} | ST | LVLA | LST | WK | LVS | LVS | VS | VS | LAB | EQ | LSLV | LAB | LVLA | AB | EQ | C_{3} |

C_{3} | VT | WE | EQ | LWLS | VS | LAB | LWK | LAB | LVS | ST | LAB | AB | AV | AB | AB | C_{4} |

C_{4} | WK | ST | VT | WK | LVS | VS | VS | VS | VS | SW | LST | LST | VS | AV | AB | C_{5} |

C_{5} | LSLV | LSLV | LVS | EQ | LVS | LVS | LSLV | EQ | AV | LST | LVLA | LVS | VS | AV | VS | C_{6} |

C_{6} | EQ | LSLV | LSLV | LWK | EQ | LVLA | LVS | LVLA | LAB | WK | LVLA | LVS | LVLA | AV | AB | C_{7} |

${\mathbf{E}}_{1}$ | ${\mathit{C}}_{1}$ | ${\mathit{C}}_{2}$ | ${\mathit{C}}_{3}$ | ${\mathit{C}}_{4}$ | ${\mathit{C}}_{5}$ | ${\mathit{C}}_{6}$ | ${\mathit{C}}_{7}$ |
---|---|---|---|---|---|---|---|

${C}_{1}$ | 1.0000 | WK | - | - | - | - | - |

${C}_{2}$ | - | 1.0000 | ST | - | - | - | - |

${C}_{3}$ | - | - | 1.0000 | VT | - | - | - |

${C}_{4}$ | - | - | - | 1.0000 | WK | - | - |

${C}_{5}$ | - | - | - | - | 1.0000 | LSLV | - |

${C}_{6}$ | - | - | - | - | - | 1.0000 | EQ |

${C}_{7}$ | - | - | - | - | - | - | 1.0000 |

${\mathbf{E}}_{1}$ | ${\mathit{C}}_{1}$ | ${\mathit{C}}_{2}$ | ${\mathit{C}}_{3}$ | ${\mathit{C}}_{4}$ | ${\mathit{C}}_{5}$ | ${\mathit{C}}_{6}$ | ${\mathit{C}}_{7}$ |
---|---|---|---|---|---|---|---|

${C}_{1}$ | 1.0000 | 3 | - | - | - | - | - |

${C}_{2}$ | - | 1.0000 | 5 | - | - | - | - |

${C}_{3}$ | - | - | 1.0000 | 6 | - | - | - |

${C}_{4}$ | - | - | - | 1.0000 | 3 | - | - |

${C}_{5}$ | - | - | - | - | 1.0000 | 1/6 | - |

${C}_{6}$ | - | - | - | - | - | 1.0000 | 1 |

${C}_{7}$ | - | - | - | - | - | - | 1.0000 |

${\mathbf{E}}_{1}$ | ${\mathit{C}}_{1}$ | ${\mathit{C}}_{2}$ | ${\mathit{C}}_{3}$ | ${\mathit{C}}_{4}$ | ${\mathit{C}}_{5}$ | ${\mathit{C}}_{6}$ | ${\mathit{C}}_{7}$ |
---|---|---|---|---|---|---|---|

${C}_{1}$ | 1.0000 | 3.0000 | - | - | - | - | - |

${C}_{2}$ | - | 1.0000 | 5.0000 | - | - | - | - |

${C}_{3}$ | - | - | 1.0000 | 6.0000 | - | - | - |

${C}_{4}$ | - | - | - | 1.0000 | 3.0000 | - | - |

${C}_{5}$ | - | - | - | - | 1.0000 | 0.1667 | - |

${C}_{6}$ | - | - | - | - | - | 1.0000 | 1.0000 |

${C}_{7}$ | - | - | - | - | - | - | 1.0000 |

${\mathbf{E}}_{1}$ | ${\mathit{C}}_{1}$ | ${\mathit{C}}_{2}$ | ${\mathit{C}}_{3}$ | ${\mathit{C}}_{4}$ | ${\mathit{C}}_{5}$ | ${\mathit{C}}_{6}$ | ${\mathit{C}}_{7}$ |
---|---|---|---|---|---|---|---|

${C}_{1}$ | 0.5000 | 0.7500 | 1.1162 | 1.5240 | 1.7740 | 1.3662 | 1.3662 |

${C}_{2}$ | 0.2500 | 0.5000 | 0.8662 | 1.2740 | 1.5240 | 1.1162 | 1.1162 |

${C}_{3}$ | −0.1162 | 0.1338 | 0.5000 | 0.9077 | 1.1577 | 0.7500 | 0.7500 |

${C}_{4}$ | −0.5240 | −0.2740 | 0.0923 | 0.5000 | 0.7500 | 0.3423 | 0.3423 |

${C}_{5}$ | −0.7740 | −0.5240 | −0.1577 | 0.2500 | 0.5000 | 0.0923 | 0.0923 |

${C}_{6}$ | −0.3662 | −0.1162 | 0.2500 | 0.6577 | 0.9077 | 0.5000 | 0.5000 |

${C}_{7}$ | −0.3662 | −0.1162 | 0.2500 | 0.6577 | 0.9077 | 0.5000 | 0.5000 |

${\mathbf{E}}_{1}$ | ${\mathit{C}}_{1}$ | ${\mathit{C}}_{2}$ | ${\mathit{C}}_{3}$ | ${\mathit{C}}_{4}$ | ${\mathit{C}}_{5}$ | ${\mathit{C}}_{6}$ | ${\mathit{C}}_{7}$ |
---|---|---|---|---|---|---|---|

${C}_{1}$ | 0.5000 | 0.5981 | 0.7419 | 0.9019 | 1.0000 | 0.8400 | 0.8400 |

${C}_{2}$ | 0.4019 | 0.5000 | 0.6437 | 0.8038 | 0.9019 | 0.7419 | 0.7419 |

${C}_{3}$ | 0.2581 | 0.3563 | 0.5000 | 0.6600 | 0.7581 | 0.5981 | 0.5981 |

${C}_{4}$ | 0.0981 | 0.1962 | 0.3400 | 0.5000 | 0.5981 | 0.4381 | 0.4381 |

${C}_{5}$ | 0.0000 | 0.0981 | 0.2419 | 0.4019 | 0.5000 | 0.3400 | 0.3400 |

${C}_{6}$ | 0.1600 | 0.2581 | 0.4019 | 0.5619 | 0.6600 | 0.5000 | 0.5000 |

${C}_{7}$ | 0.1600 | 0.2581 | 0.4019 | 0.5619 | 0.6600 | 0.5000 | 0.5000 |

E | ${\mathit{C}}_{1}$ | ${\mathit{C}}_{2}$ | ${\mathit{C}}_{3}$ | ${\mathit{C}}_{4}$ | ${\mathit{C}}_{5}$ | ${\mathit{C}}_{6}$ | ${\mathit{C}}_{7}$ |
---|---|---|---|---|---|---|---|

${C}_{1}$ | 0.5000 | 0.6050 | 0.5729 | 0.5655 | 0.6723 | 0.6066 | 0.5040 |

${C}_{2}$ | 0.3950 | 0.5000 | 0.4678 | 0.4604 | 0.5673 | 0.5015 | 0.3990 |

${C}_{3}$ | 0.4271 | 0.5322 | 0.5000 | 0.4926 | 0.5995 | 0.5337 | 0.4311 |

${C}_{4}$ | 0.4345 | 0.5396 | 0.5074 | 0.5000 | 0.6069 | 0.5411 | 0.4386 |

${C}_{5}$ | 0.3277 | 0.4327 | 0.4005 | 0.3931 | 0.5000 | 0.4342 | 0.3317 |

${C}_{6}$ | 0.3934 | 0.4985 | 0.4663 | 0.4589 | 0.5658 | 0.5000 | 0.3974 |

${C}_{7}$ | 0.4960 | 0.6010 | 0.5689 | 0.5614 | 0.6683 | 0.6026 | 0.5000 |

Total | 2.9737 | 3.7089 | 3.4838 | 3.4319 | 4.1801 | 3.7197 | 3.0019 |

E | ${\mathit{C}}_{1}$ | ${\mathit{C}}_{2}$ | ${\mathit{C}}_{3}$ | ${\mathit{C}}_{4}$ | ${\mathit{C}}_{5}$ | ${\mathit{C}}_{6}$ | ${\mathit{C}}_{7}$ | Total | Weight | Ranking |
---|---|---|---|---|---|---|---|---|---|---|

${C}_{1}$ | 0.1681 | 0.1631 | 0.1644 | 0.1648 | 0.1608 | 0.1631 | 0.1679 | 1.1523 | 0.1658 | 1 |

${C}_{2}$ | 0.1328 | 0.1348 | 0.1261 | 0.1342 | 0.1357 | 0.1348 | 0.1329 | 0.9314 | 0.1340 | 5 |

${C}_{3}$ | 0.1436 | 0.1435 | 0.1348 | 0.1435 | 0.1434 | 0.1435 | 0.1436 | 0.9960 | 0.1433 | 4 |

${C}_{4}$ | 0.1461 | 0.1455 | 0.1368 | 0.1457 | 0.1452 | 0.1455 | 0.1461 | 1.0109 | 0.1455 | 3 |

${C}_{5}$ | 0.1102 | 0.1167 | 0.1080 | 0.1145 | 0.1196 | 0.1167 | 0.1105 | 0.7962 | 0.1146 | 7 |

${C}_{6}$ | 0.1323 | 0.1344 | 0.1257 | 0.1337 | 0.1353 | 0.1344 | 0.1324 | 0.9283 | 0.1336 | 6 |

${C}_{7}$ | 0.1668 | 0.1620 | 0.1534 | 0.1636 | 0.1599 | 0.1620 | 0.1666 | 1.1342 | 0.1632 | 2 |

Total | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 6.9493 | 1.0000 |

${\mathbf{E}}_{1}$ | ${\mathbf{E}}_{2}$ | ${\mathbf{E}}_{3}$ | ${\mathbf{E}}_{4}$ | ${\mathbf{E}}_{5}$ | ${\mathbf{E}}_{6}$ | ${\mathbf{E}}_{7}$ | ${\mathbf{E}}_{8}$ | ${\mathbf{E}}_{9}$ | ${\mathbf{E}}_{10}$ | ${\mathbf{E}}_{11}$ | ${\mathbf{E}}_{12}$ | ${\mathbf{E}}_{13}$ | ${\mathbf{E}}_{14}$ | ${\mathbf{E}}_{15}$ | |||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

F | F | F | F | F | F | F | F | F | F | F | F | F | F | F | |||

C_{1} | S | HF | H | VHG | VHG | H | VHG | H | VHG | VHG | H | VHG | VH | VHG | VHG | F | C_{1} |

C_{2} | S | F | H | VHG | H | H | VHG | LHF | LVHG | H | F | H | VHG | VH | VHG | F | C_{2} |

C_{3} | S | VHG | HF | F | F | VHG | HF | LHF | VH | VHG | VHG | HF | VH | VHG | VH | H | C_{3} |

C_{4} | S | HF | H | VHG | VHG | VH | VHG | VHG | VH | VHG | F | VH | H | H | LHF | F | C_{4} |

C_{5} | S | H | VHG | F | F | LHF | F | LHF | LHF | VHG | HF | HF | VHG | H | LH | H | C_{5} |

C_{6} | S | HF | VHG | VHG | HF | HF | HF | F | LH | HF | H | H | VH | VHG | VH | F | C_{6} |

C_{7} | S | H | H | H | H | VHG | VHG | F | VHG | VHG | H | H | VHG | VH | VHG | F | C_{7} |

${\mathbf{E}}_{1}$ | ${\mathbf{E}}_{2}$ | ${\mathbf{E}}_{3}$ | ${\mathbf{E}}_{4}$ | ${\mathbf{E}}_{5}$ | ${\mathbf{E}}_{6}$ | ${\mathbf{E}}_{7}$ | ${\mathbf{E}}_{8}$ | ${\mathbf{E}}_{9}$ | ${\mathbf{E}}_{10}$ | ${\mathbf{E}}_{11}$ | ${\mathbf{E}}_{12}$ | ${\mathbf{E}}_{13}$ | ${\mathbf{E}}_{14}$ | ${\mathbf{E}}_{15}$ | Total | $\mathit{q}{}_{\mathit{SF}}$ | ||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

F | F | F | F | F | F | F | F | F | F | F | F | F | F | F | Average | |||

C_{1} | S | 0.7153 | 0.8413 | 0.9307 | 0.9307 | 0.8413 | 0.9307 | 0.8413 | 0.9307 | 0.9307 | 0.8413 | 0.9307 | 1.0000 | 0.9307 | 0.9307 | 0.5000 | 13.0260 | 0.8684 |

C_{2} | S | 0.5000 | 0.8413 | 0.9307 | 0.8413 | 0.8413 | 0.9307 | 0.2847 | 0.0693 | 0.8413 | 0.5000 | 0.8413 | 0.9307 | 1.0000 | 0.9307 | 0.5000 | 10.7832 | 0.7189 |

C_{3} | S | 0.9307 | 0.7153 | 0.5000 | 0.5000 | 0.9307 | 0.7153 | 0.2847 | 1.0000 | 0.9307 | 0.9307 | 0.7153 | 1.0000 | 0.9307 | 1.0000 | 0.8413 | 11.9254 | 0.7950 |

C_{4} | S | 0.7153 | 0.8413 | 0.9307 | 0.9307 | 1.0000 | 0.9307 | 0.9307 | 1.0000 | 0.9307 | 0.5000 | 1.0000 | 0.8413 | 0.8413 | 0.2847 | 0.5000 | 12.1773 | 0.8118 |

C_{5} | S | 0.8413 | 0.9307 | 0.5000 | 0.5000 | 0.2847 | 0.5000 | 0.2847 | 0.2847 | 0.9307 | 0.7153 | 0.7153 | 0.9307 | 0.8413 | 0.1587 | 0.8413 | 9.2593 | 0.6173 |

C_{6} | S | 0.7153 | 0.9307 | 0.9307 | 0.7153 | 0.7153 | 0.7153 | 0.5000 | 0.1587 | 0.7153 | 0.8413 | 0.8413 | 1.0000 | 0.9307 | 1.0000 | 0.5000 | 11.2100 | 0.7473 |

C_{7} | S | 0.8413 | 0.8413 | 0.8413 | 0.8413 | 0.9307 | 0.9307 | 0.5000 | 0.9307 | 0.9307 | 0.8413 | 0.8413 | 0.9307 | 1.0000 | 0.9307 | 0.5000 | 12.6319 | 0.8421 |

${\mathbf{E}}_{1}$ | ${\mathbf{E}}_{2}$ | ${\mathbf{E}}_{3}$ | ${\mathbf{E}}_{4}$ | ${\mathbf{E}}_{5}$ | ${\mathbf{E}}_{6}$ | ${\mathbf{E}}_{7}$ | ${\mathbf{E}}_{8}$ | ${\mathbf{E}}_{9}$ | ${\mathbf{E}}_{10}$ | ${\mathbf{E}}_{11}$ | ${\mathbf{E}}_{12}$ | ${\mathbf{E}}_{13}$ | ${\mathbf{E}}_{14}$ | ${\mathbf{E}}_{15}$ | Total | ${\mathit{q}}_{\mathit{FS}}$ | ||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

S | S | S | S | S | S | S | S | S | S | S | S | S | S | S | Average | |||

C_{1} | F | 0.2847 | 0.1587 | 0.0693 | 0.0693 | 0.1587 | 0.0693 | 0.1587 | 0.0693 | 0.0693 | 0.1587 | 0.0693 | 0.0000 | 0.0693 | 0.0693 | 0.5000 | 1.9740 | 0.1316 |

C_{2} | F | 0.5000 | 0.1587 | 0.0693 | 0.1587 | 0.1587 | 0.0693 | 0.7153 | 0.9307 | 0.1587 | 0.5000 | 0.1587 | 0.0693 | 0.0000 | 0.0693 | 0.5000 | 4.2168 | 0.2811 |

C_{3} | F | 0.0693 | 0.2847 | 0.5000 | 0.5000 | 0.0693 | 0.2847 | 0.7153 | 0.0000 | 0.0693 | 0.0693 | 0.2847 | 0.0000 | 0.0693 | 0.0000 | 0.1587 | 3.0746 | 0.2050 |

C_{4} | F | 0.2847 | 0.1587 | 0.0693 | 0.0693 | 0.0000 | 0.0693 | 0.0693 | 0.0000 | 0.0693 | 0.5000 | 0.0000 | 0.1587 | 0.1587 | 0.7153 | 0.5000 | 2.8227 | 0.1882 |

C_{5} | F | 0.1587 | 0.0693 | 0.5000 | 0.5000 | 0.7153 | 0.5000 | 0.7153 | 0.7153 | 0.0693 | 0.2847 | 0.2847 | 0.0693 | 0.1587 | 0.8413 | 0.1587 | 5.7407 | 0.3827 |

C_{6} | F | 0.2847 | 0.0693 | 0.0693 | 0.2847 | 0.2847 | 0.2847 | 0.5000 | 0.8413 | 0.2847 | 0.1587 | 0.1587 | 0.0000 | 0.0693 | 0.0000 | 0.5000 | 3.7900 | 0.2527 |

C_{7} | F | 0.1587 | 0.1587 | 0.1587 | 0.1587 | 0.0693 | 0.0693 | 0.5000 | 0.0693 | 0.0693 | 0.1587 | 0.1587 | 0.0693 | 0.0000 | 0.0693 | 0.5000 | 2.3681 | 0.1579 |

**Table 15.**Normalized values and priority weights of possible outcomes with respect to seven criteria.

Success | Failure | Total | Average | ||
---|---|---|---|---|---|

${C}_{1}$ | Success | 0.7916 | 0.6346 | 1.4262 | 0.7131 |

Failure | 0.2084 | 0.3654 | 0.5738 | 0.2869 | |

${C}_{2}$ | Success | 0.6401 | 0.5898 | 1.2299 | 0.6149 |

Failure | 0.3599 | 0.4102 | 0.7701 | 0.3851 | |

${C}_{3}$ | Success | 0.7092 | 0.6139 | 1.3232 | 0.6616 |

Failure | 0.2908 | 0.3861 | 0.6768 | 0.3384 | |

${C}_{4}$ | Success | 0.7266 | 0.6188 | 1.3454 | 0.6727 |

Failure | 0.2734 | 0.3812 | 0.6546 | 0.3273 | |

${C}_{5}$ | Success | 0.5664 | 0.5525 | 1.1189 | 0.5595 |

Failure | 0.4336 | 0.4475 | 0.8811 | 0.4405 | |

${C}_{6}$ | Success | 0.6643 | 0.5991 | 1.2635 | 0.6317 |

Failure | 0.3357 | 0.4009 | 0.7365 | 0.3683 | |

${C}_{7}$ | Success | 0.7600 | 0.6275 | 1.3875 | 0.6937 |

Failure | 0.2400 | 0.3725 | 0.6125 | 0.3063 |

${\mathit{C}}_{1}$ | ${\mathit{C}}_{2}$ | ${\mathit{C}}_{3}$ | ${\mathit{C}}_{4}$ | ${\mathit{C}}_{5}$ | ${\mathit{C}}_{6}$ | ${\mathit{C}}_{7}$ | Prediction Probability | |
---|---|---|---|---|---|---|---|---|

Rank | 1 | 5 | 4 | 3 | 7 | 6 | 2 | |

Priority Weight | 0.1658 | 0.1340 | 0.1433 | 0.1455 | 0.1146 | 0.1336 | 0.1632 | 1.0000 |

Success | 0.7131 | 0.6149 | 0.6616 | 0.6727 | 0.5595 | 0.6317 | 0.6937 | 0.6551 |

Failure | 0.2869 | 0.3851 | 0.3384 | 0.3273 | 0.4405 | 0.3683 | 0.3063 | 0.3449 |

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## Share and Cite

**MDPI and ACS Style**

Hsieh, H.-C.; Nguyen, X.-H.; Wang, T.-C.; Lee, J.-Y.
Prediction of Knowledge Management for Success of Franchise Hospitality in a Post-Pandemic Economy. *Sustainability* **2020**, *12*, 8755.
https://doi.org/10.3390/su12208755

**AMA Style**

Hsieh H-C, Nguyen X-H, Wang T-C, Lee J-Y.
Prediction of Knowledge Management for Success of Franchise Hospitality in a Post-Pandemic Economy. *Sustainability*. 2020; 12(20):8755.
https://doi.org/10.3390/su12208755

**Chicago/Turabian Style**

Hsieh, Hsiu-Chin, Xuan-Huynh Nguyen, Tien-Chin Wang, and Jen-Yao Lee.
2020. "Prediction of Knowledge Management for Success of Franchise Hospitality in a Post-Pandemic Economy" *Sustainability* 12, no. 20: 8755.
https://doi.org/10.3390/su12208755