Multiple criteria decision analysis (MCDA) approaches are via expert insights to create frameworks for better decision making [

35]. In this section, the fuzzy Delphi method, DEMATEL, ANP, and TOPSIS are explained for determining the optimal variety show hosts for television stations in the social media era.

#### 3.1. Conceptual Framework

This study can assist television stations managers in selecting the optimal variety show hosts in the social media era, and the conceptual framework of this research is as follows:

(1) First level: Objective

Select the optimal variety show hosts for television stations in the era of social media.

(2) Second level: Perspectives

Crucial criteria are classified into several perspectives according to the relevant literature and interviews with the program department supervisors of television stations.

(3) Third level: Criteria

Review relevant studies of television hosts. Additionally, investigate relevant conditions and abilities of hosts in the social media era as well as the criteria that create an Internet celebrity. Subsequently, the selection criteria for hosts of television variety shows are compiled, and a 9-item questionnaire is designed according to the fuzzy Delphi method, which is then distributed to program department supervisors and senior producers of television stations. Respondents rate the importance of criteria with a score of 1 to 9 according to their personal, professional, and practical work experiences. Crucial criteria are retained according to their geometric mean from experts.

(4) Fourth level: Alternatives

Alternatives are the variety show hosts of the case company.

#### 3.3. Fuzzy Delphi Method

The Delphi method has proven to be effective in forecasting technological trends [

36]. It attempts to reach expert consensus via behavioral feedback in brainstorming. Through results from sequential rounds of survey administration, the group members begin to understand other experts’ perspectives, adjusting their knowledge, and developing a full understanding of the topic. The success of the Delphi method relies on whether the experts are fully committed. To ensure a smooth implementation of the Delphi method, it is necessary to establish a list of experts, discuss the research issues with the invited experts, and obtain a commitment from the potential group members. The expert members of a Delphi method do not change across questionnaire administration. Members cannot suddenly withdraw and cannot have direct face-to-face discussions. By repeatedly eliciting opinions and encouraging opinion modification, the decision-making group reaches a consensus [

37,

38].

However, studies [

10,

11,

36,

39,

40,

41] have the declared the disadvantages of the Delphi method. For example, the research time can be quite long, especially as the number of iterations increases. Respondents may drop out of the process. Even when the narrative text of the questionnaire is clear, it is difficult to avoid ambiguity. Besides, it is easy for the participants to misunderstand unclear instructions from the questionnaire.

To overcome such disadvantages, researchers [

42,

43,

44] have improved it by the fuzzy concept. Chang et al. [

45] presented that the Delphi method fails to deal with the fuzziness in respondents’ opinions. The fuzzy Delphi method can identify the criteria for resolving many uncertain problems. Zhang [

14] also expressed that the conclusions acquired by the fuzzy Delphi method are objective and reasonable. Moreover, the investigation time and costs are reduced. This study used the fuzzy Delphi method to obtain the selection criteria. The geometric mean can better represent the majority of the decision-makers and can better represent more objective and fair criteria. The criterion is considered significant when its importance is over 80% [

46]. In other words, if a 9-point Likert scale questionnaire is used, a geometric mean that is greater than 7.2 is classified as an important criterion.

where

L_{i} denotes the importance rating of the criteria by the

i-th expert (

i = 1, 2,...,

n).

L_{G} = geometric mean value.

#### 3.4. DEMATEL

DEMATEL uses complex systems by directly comparing the relationship between factors to utilize matrices to calculate the causal relationships between them. Based on professional knowledge, the decision-makers give scores of “no influence”, “low influence”, “medium influence”, “high influence”, and “very high influence” to the relationship between factors. DEMATEL assists in decision making by expressing the causal relationship between factors in complicated systems and the intensity of their effects. In other words, this method transforms complicated systems into well-defined causal relationships. The following is the procedure for operating DEMATEL [

12,

31,

47,

48,

49,

50].

(1) Build the initial direct-relation matrix

The decision-makers determine the extent of influence of the two factors and fill in the corresponding position, which generates a direct-relation table and integrates the decision-makers’ results to produce an initial direct-relation matrix. The average matrix is constructed

$A=\left[{a}_{ij}\right]$:

x_{ij} is the degree to which the decision-maker evaluation factor i influences factor j. For i = j, all the diagonal elements values are 0. For each decision-maker, a n $\times $ n positive matrix can be developed as ${X}^{k}=\left[{X}_{ij}^{k}\right]$, where k is the number of decision-makers with 1 $\le $ k $\le $ H, and n is the number of perspectives.

(2) Establish the normalized initial direct-relation matrix

Normalize the initial direct-relation matrix obtained by the previous step to obtain the matrix X. X is generated from A. X = A × S where $S=\frac{1}{\underset{1\le i\le n}{\mathrm{max}}{\sum}_{j=1}^{n}{a}_{ij}}$. Each element in X falls between 0 and 1.

(3) Establish the total-influence relation matrix

When matrix X is known, the total-influence relation matrix T can be obtained from the formula (T = X(I − X)^{−1}), where I is an identity matrix with a diagonal value of 1.

(4) Establish the threshold value

Establish the threshold value according to the total-influence relation matrix. By doing so, the influence that is too small in the matrix can be eliminated, and a more concise causal relationship between factors can be obtained.

Recently, practitioners and researchers are interested in DEMATEL and it is applied it widely due to its ability to handle complicated relationships [

51]. In this paper, DEMATEL was utilized to verify interdependencies between the perspectives.

#### 3.5. ANP

ANP, an extension of AHP, is a comprehensive approach that can capture the outcome of dependencies between elements [

52]. Comparing to AHP, ANP ponders interdependence and thus is superior for solving real-world situations [

53]. There are four major steps of ANP:

(1) Construct the hierarchy

The problem is structured in a hierarchy including a goal, perspectives, criteria, and alternatives. The contents of the hierarchy can be determined by appropriate methods, such as eliciting brainstormed opinions from decision-makers, or by a literature survey.

(2) Complete pairwise comparison

Decision-makers make a series of pairwise comparisons to obtain the relative importance of factors. A 9-point scale is applied to compare two factors according to their interdependency. All decision-makers’ preferences should be inputs to a geometric mean calculation to establish each pairwise comparison. We compare a set of

n factors pairwise based on their relative importance weights, where the factors are presented by

a_{1},

a_{2}, …,

a_{n} and the weights are indicated by

w_{1},

w_{2}, …,

w_{n}. The pairwise comparisons can be shown by questionnaires with subjective perception as:

where

a_{ij} is 1/

a_{ji} and

a_{ij} =

a_{ik}/

a_{jk}.

A weight matrix is illustrated as:

The eigenvector of the observable pairwise comparison matrix provides the weights of the factors at this level, which will be used in the supermatrix.

where

A is defined as the matrix of pairwise comparison values;

w is the priority vector, also called the principal eigenvector, and

${\lambda}_{max}$ is the maximum eigenvalue of matrix

A.

The consistency ratio (CR) is proposed to verify the consistency of the pairwise comparison matrix. If the CR value is less than 0.1, the pairwise comparison matrix is accepted as consistent.

CI and RI represent the consistency index and random index, respectively, and n is the number of factors in the matrix.

(3) Solve the supermatrix

ANP utilizes the supermatrix to deal with dependencies among factors. The factors weights are applied to obtain the columns of the supermatrix. A general form of the supermatrix is presented in

Figure 2.

C_{m} denotes the

mth cluster,

e_{mn} is the

nth factor in the

mth cluster, and

W_{ij} is the principal eigenvector of the influence of the factors compared in the

jth cluster to the

ith cluster. If the

jth cluster has no impact on the

ith cluster, then W

_{ij} is 0. The eigenvector obtained in Step 2 is grouped and located in appropriate positions in the supermatrix based on the influences.

The unweighted supermatrix

W, containing the weights derived from the pairwise comparisons throughout the network, can be also presented as follows:

W_{21} is a matrix that illustrates the weights of cluster 2 concerning cluster 1; W_{33} shows that there is an inner dependence within cluster 3.

Finally, the weighted supermatrix is stabilized by multiplying the weighted supermatrix by itself until its row values converge to the same value (limiting matrix).

Here, k = an arbitrarily large number.

(4) Choose the optimal alternative

Through a synthesis of the limiting matrix and the weights of the alternatives, the global weight of each alternative can be derived. Then, the identified alternatives are ranked per their weights.

We employed ANP here to get weights according to the interdependencies obtained by DEMATEL.

#### 3.6. TOPSIS

TOPSIS is an MCDM method developed by Hwang and Yoon in 1981 [

54]. The method assumes that all criteria are either monotonically increasing or monotonically decreasing and selects a solution that is closest to the positive ideal solution (PIS) and farthest from the negative ideal solution (NIS) as the ideal solution. Criteria that are benefit criteria exhibit more favorable performance and higher preference values, whereas those that are cost criteria exhibit less favorable performance and lower preference values. A PIS is derived by combining the optimal values of all criteria, whereas an NIS is determined by the worst values of all criteria. When determining the alternative to be implemented, Euclidean distance is adopted to get the distance between each alternative and the ideal solution. The TOPSIS procedure is as follows:

(1) Build a normalized evaluation matrix

where

i is the alternatives,

j is the selection criteria, and

x_{ij} is the

i alternative under the

j criterion to be measured.

(2) Construct a weighted evaluation matrix

Multiply the weight vector by the normalized evaluation matrix to obtain the weighted evaluation matrix. In other words, the weights of selection criteria,

$w=\left({w}_{1},{w}_{2},\cdots ,{w}_{n}\right)$, multiplied by the normalized evaluation matrix can be expressed as:

(3) Identify PIS (

A*) and NIS (

A^{−})

(4) Compute the Euclidean distance of each alternative from PIS

$\left({S}_{i}^{\ast}\right)$ and NIS

$\left({S}_{i}^{-}\right)$(5) Compute the closeness coefficient of each alternative

We rank the alternatives in descending order of ${C}_{i}^{\ast}$.