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Abstract

Computer multimedia technology first appeared in the late 1980s, which is a functional upgrade based on the development of digital technology. It can achieve functions such as information collection, processing, and storage. Multimedia technology has received widespread attention in the entire computer field and has become a popular technology. Against the backdrop of continuous technological development, various electronic products are presented to people, bringing convenience to their lives. At the same time, they also play a huge role in the work of some industries. The application of multimedia technology, advanced editing software, and digital equipment in the production of video works can present good results and showcase excellent film and television works for people. The application effect evaluation of multimedia technology in the film and television post-production is frequently viewed as a multi-attribute group decision-making (MAGDM) issue. The maximizing deviation method was used to obtain the weight information under intuitionistic fuzzy sets (IFSs). Depending on the MABAC (multi-attributive border approximation area comparison) method and IFSs, this paper design the intuitionistic fuzzy MABAC (IF-MABAC) method to assess the application effect evaluation of multimedia technology in the film and television post-production. Eventually, an example about application effect evaluation of multimedia technology in the film and television post-production and some comparative analysis have been employed to verify the superiority of the designed IF-MABAC method.

Keywords

MAGDM issues intuitionistic fuzzy sets (IFSs)MABAC method maximizing deviation method application effect evaluation

1. Introduction

The application of computer multimedia technology in the post production of film and television works has various meanings and significant application advantages, among which the most obvious is the ability to improve the overall quality of film and television works [1, 2]. For traditional film and television post processing techniques, a large amount of film is used in actual production. Usually, a magnetic tape camera is used first for shooting, which is limited by technical conditions and hardware equipment. The shooting process is relatively simple and requires full depth editing and other work after shooting. Therefore, the quality of the final presentation of film and television works largely depends on the post production effect [3, 4, 5]. Traditional editing techniques are relatively backward, resulting in weak continuity and poor quality of the final film and television editing works [6, 7, 8]. The application of advanced computer multimedia technology in the post production of film and television works can greatly reduce the amount of film used, achieve a complete data transmission and capture process, ensure the integrity of materials, and optimize the post production process of film and television works [9, 10]. For relevant technical staff, it simplifies the operation steps and has more functional options to meet diverse production requirements. The use of computer multimedia technology can greatly improve the efficiency of film and television production work, and achieve greater benefits for enterprises. In the traditional post production of film and television works, it is influenced by various factors, resulting in low production efficiency. The main reasons for this include both technical and personnel aspects. In previous post production techniques, linear editing was commonly used, and the production process was relatively rigid, which could only be completed in a sequence from beginning to end [10, 11]. This was a lengthy task for relevant staff and required a lot of time. In order to achieve good editing and production results, under limited technical conditions, high requirements are placed on the staff, and the responsibility of improving the quality of the work falls on the editing and production staff [12, 13, 14]. Post production personnel need to have a high professional level and professional literacy, carry out targeted operations according to different editing requirements, and require precise control to meet various editing requirements. During this process, if there are editing errors or operational errors, a significant amount of time is required to correct them, resulting in a significant reduction in post-production efficiency [15, 16, 17]. However, with the support of new technologies, the progress requirements of post-production film and television can be met, and work efficiency can be significantly improved [18, 19]. In response to operational errors and other issues, improvements and adjustments can be made at any time, and targeted choices can be made, resulting in a significant reduction in the entire work duration, reducing the work pressure and burden of staff, and saving work time and human resources [20, 21]. For the post production of film and television works, the application of computer multimedia technology can not only improve the quality and work efficiency of film and television works, but also enhance the expressive ability of film and television works, achieving the sublimation and optimization of film and television works [22, 23, 24]. Due to the fact that during the filming process, film and television works are all completed by actors in some basic and simple scenes, the overall film and television effect is very single and one-sided, resulting in unsatisfactory results presented by the film and television works [25, 26]. Therefore, many scenes require post production to be completed, effectively integrating diverse elements through computer multimedia technology and ensuring the smooth completion of a series of shooting activities, making the entire film and television work colorful and enhancing the expressive tension of the work.

Similar to multi-attribute decision-making (MADM) [27, 28, 29, 30, 31], the Multicriteria Decision Analysis (MCDA) is an important research domain in modern management science [32, 33, 34, 35, 36]. In many realistic MCDA issues, due to the limitations of the decision maker’s ability to recognize the problem, it is often impossible to supply the accurate information and could only be portrayed through the uncertainty, which constitutes an uncertain MCDA issue [37, 38, 39, 40, 41, 42, 43]. According to the different number of experts participating in decision-making issues, multi-attribute decision-making (MADM) is subdivided into multi-attribute group decision-making (MAGDM) [44, 45, 46, 47, 48, 49]. In order to improve the accuracy of decision-making, Zadeh [50] presented the fuzzy sets (FSs). Atanassov [51] presented intuitionistic fuzzy sets (IFSs). Garg [52] presented intuitionistic fuzzy multiplicative preference relations and presented some geometric operators. Liu [53] presented the BM operator on the basis of the Dombi operations for IFSs. Cali and Balaman [54] extended ELECTRE I with VIKOR method with IFSs. Zeng et al. [55] presented some distance measure between IFSs. Verma and Merigo [56] presented the Sharma-Mittal’s Entropy under IFSs. Xie et al. [57] presented the information quality for IFSs. Verma [58] presented intuitionistic fuzzy order- $\alpha$ divergence and entropy measures with MABAC method for MAGDM. However, the MABAC method under IFSs [58] doesn’t consider the psychological behavior of decision-makers.

The application effect evaluation of multimedia technology in the film and television post-production is frequently viewed as the MAGDM issue. Through the study of the literatures, it can be found that it is an interesting research topic to combine the MABAC method [59, 60, 61, 62, 63, 64] and maximizing deviation method (MDM) [65, 66, 67, 68, 69, 70] with the prospect theory (PT) [71] under intuitionistic fuzzy sets (IFSs) [72]. The traditional MAGDM method assumes that people are rational people and calculates the rational optimal solution. However, in the actual MAGDM process, decision-makers will be affected by their own risk appetite and loss aversion. The prospect theory (PT) [71] is added to the MAGDM method, so that the obtained results are more in line with the preferences of the decision-makers, and the results that are more satisfactory to the decision-makers can be obtained. Depending on the MABAC method [59] and intuitionistic fuzzy sets (IFSs) [72], this paper design the IF-MABAC method to assess the application effect evaluation of multimedia technology in the film and television post-production. Finally, an example about application effect evaluation of multimedia technology in the film and television post-production and some comparative analysis has been given to demonstrate the superiority of the designed method.

The reminder framework proceeds as follows. The IFSs is reviewed in Section 2. The IF-MABAC method is constructed under IFSs in Section 3. A numerical example about application effect evaluation of multimedia technology in the film and television post-production is given and some comparative analysis is also offered in Section 4. At last, the conclusion is given in Section 5.

2. Preliminaries

2.1 Intuitionistic fuzzy sets

Definition 1 [51]. An IFS on the universe $X$ is

$\displaystyle SI=\{{\langle{\theta,\mu_{SI}(\theta),\nu{}_{SI}(\theta)}\rangle% |{\theta\in\Theta}}\}$ (1)

where $\mu_{SI}(\theta)\in[{0,1}]$ is membership and $\nu_{SI}(\theta)\in[{0,1}]$ is non-membership, and $\mu_{SI}(\theta)$ , $\nu_{SI}(\theta)$ meet: $0\leqslant\mu_{SI}(\theta)+\nu_{SI}(\theta)\leqslant 1$ , $\forall\theta\in\Theta$ .

Definition 2 [73]. Let $SI_{1}=({s\mu_{1},s\nu_{1}})$ and $SI_{2}=({s\mu_{2},s\nu_{2}})$ be two intuitionistic fuzzy numbers (IFNs), the operation laws are defined:

$\displaystyle SI_{1}\oplus SI_{2}=({s\mu_{1}+s\mu_{2}-s\mu_{1}s\mu_{2},s\nu_{1% }s\nu_{2}})$ (2) $\displaystyle SI_{1}\otimes SI_{2}=({s\mu_{1}s\mu_{2},s\nu_{1}+s\nu_{2}-s\nu_{% 1}s\nu_{2}})$ (3) $\displaystyle\lambda SI_{1}=({1-({1-s\mu_{1}})^{\lambda},s\nu_{1}^{\lambda}}),% \lambda>0$ (4) $\displaystyle SI_{1}^{\lambda}=({s\mu_{1}^{\lambda},1-({1-s\nu_{1}})^{\lambda}% }),\lambda>0$ (5)

From Definition 2, the operation laws are obtained.

$\displaystyle(1)SI_{1}\oplus SI_{2}=SI_{2}\oplus SI_{1},SI_{1}\otimes SI_{2}=% SI_{2}\otimes SI_{1},({({SI_{1}})^{\lambda_{1}}})^{\lambda_{2}}=({SI_{1}})^{% \lambda_{1}\lambda_{2}};(2)\lambda({SI_{1}\oplus SI_{2}})=\lambda SI_{1}\oplus% \lambda SI_{2},({SI_{1}\otimes SI_{2}})^{\lambda}=({SI_{1}})^{\lambda}\otimes(% {SI_{2}})^{\lambda};(3)\lambda_{1}SI_{1}\oplus\lambda_{2}SI_{1}=({\lambda_{1}+% \lambda{}_{2}})SI_{1},({SI_{1}})^{\lambda_{1}}\otimes({SI_{1}})^{\lambda_{2}}=% ({SI_{1}})^{({\lambda_{1}+\lambda_{2}})}.$

Definition 3 [74]. Let $SI_{1}=({s\mu_{1},s\nu_{1}})$ and $SI_{2}=({s\mu_{2},s\nu_{2}})$ , the score and accuracy values are constructed:

$\displaystyle SV({SI_{1}})=s\mu_{1}+s\mu_{1}({1-s\mu_{1}-s\nu_{1}}),SV({SI_{2}% })=s\mu_{2}+s\mu_{2}({1-s\mu_{2}-s\nu_{2}})$ (6) $\displaystyle AV({I_{1}})=s\mu_{1}+s\nu_{1},AV({I_{2}})=s\mu_{2}+s\nu_{2}$ (7)

For two IFNs and the Definition 3, then

$\displaystyle(1)\text{if }SV({SI_{1}})<SV({SI_{2}}),\text{then }SI_{1}<SI_{2};% (2)\text{if }SV({SI_{1}})=SV({SI_{2}}),AV({SI_{1}})<AV({SI_{2}}),\text{then }% SI_{1}<SI_{2};(3)\text{if }SV({SI_{1}})=SV({SI_{2}}),AV({SI_{1}})>AV({SI_{2}})% ,\text{then }SI_{1}>SI_{2};(4)\text{if }SV({SI_{1}})=SV({SI_{2}}),AV({SI_{1}})% =AV({SI_{2}}),\text{then }SI_{1}=SI_{2}.$

Definition 4 [75]. Let $SI_{1}=({s\mu_{1},s\nu_{1}})$ and $SI_{2}=({s\mu_{2},s\nu_{2}})$ , the IFN distance measure is defined:

$\displaystyle\textit{IFNDM}({SI_{1},SI_{2}})=\frac{1}{{2}}\left({\begin{array}% []{l}s\mu_{1}\log\frac{2s\mu_{1}}{s\mu_{1}+s\mu_{2}}+s\mu_{2}\log\frac{2s\mu_{% 2}}{s\mu_{1}+s\mu_{2}}\\ \\ {}+s\nu_{1}\log\frac{2s\nu_{1}}{s\nu_{1}+s\nu_{2}}+s\nu_{2}\log\frac{2s\nu_{2}% }{s\nu_{1}+s\nu_{2}}\\ \\ {}+s\pi_{1}\log\frac{2s\pi_{1}}{s\pi_{1}+s\pi_{2}}+s\pi_{2}\log\frac{2s\pi_{2}% }{s\pi_{1}+s\pi_{2}}\\ \end{array}}\right)$ (8)

where $s\pi_{1}=1-s\mu_{1}-s\nu_{1}$ , $s\pi_{2}=1-s\mu_{2}-s\nu_{2}$ .

2.2 Intuitionistic fuzzy aggregation operators

The intuitionistic fuzzy weighted averaging (IFWA) operator and intuitionistic fuzzy weighted geometric (IFWG) operator are introduced.

Definition 5 [73]. Let $SI_{j}=({s\mu_{I_{j}},s\nu_{I_{j}}})({j=1,2,\ldots,n})$ , the IFWA operator is defined:

$\displaystyle\textit{IFWA}_{s\omega}(SI_{1},SI_{2},\ldots,SI_{n})=\mathop{% \oplus}\limits_{j=1}^{n}({s\omega_{j}SI_{j}})$

(9) $\displaystyle{}=\left({1-\prod\limits_{j=1}^{n}{({1-s\mu_{I_{j}}})}^{s\omega_{% j}},\prod\limits_{j=1}^{n}{({s\nu_{I_{j}}})^{s\omega_{j}}}}\right)$

where $s\omega=({s\omega_{1},s\omega_{2},\ldots,s\omega_{n}})^{T}$ be the weight of $SI_{j}({j=1,2,\ldots,n})$ , $s\omega_{j}>0$ , $\sum\limits_{j=1}^{n}{s\omega_{j}}=1$ .

Definition 6 [73]. Let $SI_{j}=({s\mu_{I_{j}},s\nu_{I_{j}}})({j=1,2,\ldots,n})$ , the IFWG operator is defined:

$\displaystyle\textit{IFWG}_{s\omega}(SI_{1},SI_{2},\ldots,SI_{n})=\mathop{% \otimes}\limits_{j=1}^{n}({SI_{j}})^{s\omega_{j}}=\left({\prod\limits_{j=1}^{n% }{({s\mu_{I_{j}}})}^{s\omega_{j}},1-\prod\limits_{j=1}^{n}{({1-s\nu_{I_{j}}})^% {s\omega_{j}}}}\right)$ (10)

where $s\omega=({s\omega_{1},s\omega_{2},\ldots,s\omega_{n}})^{T}$ be the weight of $SI_{j}({j=1,2,\ldots,n})$ , $s\omega_{j}>0$ , $\sum\limits_{j=1}^{n}{s\omega_{j}}=1$ .
3. MABAC method for MAGDM with IFNs

Then, the IF-MABAC method is constructed for MAGDM with IFNs. Let $SZ=\{{SZ_{1},SZ_{2},\ldots,SZ_{n}}\}$ be attributes, $s\omega=\{{s\omega_{1},s\omega_{2},\ldots,s\omega_{n}}\}$ be the weight of attributes $SZ_{j}$ , where $s\omega_{j}\in[{0,1}]$ , $\sum\nolimits_{j=1}^{n}{s\omega_{j}}=1$ . Assume $SH=\{{SH_{1},SH_{2},\ldots,SH_{l}}\}$ be a set of decision makers with weight values of $sw=\{{sw_{1},sw_{2},\ldots,sw_{l}}\}$ , $sw_{k}\in[{0,1}]$ , $\sum\nolimits_{k=1}^{l}{sw_{k}}=1$ . Let $SP=\{{SP_{1},SP_{2},\ldots,SP_{m}}\}$ be alternatives. And $SQ^{(k)}=({SQ_{ij}^{k}})_{m\times n}=({s\mu_{ij}^{(k)},s\nu_{ij}^{(k)}})$ is the IF-matrix. Subsequently, the calculating procedures are constructed.

Step 1. Construct the IF-matrix $SQ^{(k)}=({SQ_{ij}^{k}})_{m\times n}=({s\mu_{ij}^{(k)},s\nu_{ij}^{(k)}})$ and calculate the overall IF-matrix $SQ=({SQ_{ij}})_{m\times n}=({s\mu_{ij},s\nu_{ij}})$ through IFWG operator.

$\displaystyle SQ^{(k)}=[{SQ_{ij}^{k}}]_{m\times n}=\left[{{\begin{array}[]{*{2% 0}c}{SQ_{11}^{k}}&{SQ_{12}^{k}}&\ldots&{SQ_{1n}^{k}}\\ {SQ_{21}^{k}}&{SQ_{22}^{k}}&\ldots&{SQ_{2n}^{k}}\\ \vdots&\vdots&\vdots&\vdots\\ {SQ_{m1}^{k}}&{SQ_{m2}^{k}}&\ldots&{SQ_{mn}^{k}}\\ \end{array}}}\right]$ (11) $\displaystyle SQ=[{SQ{}_{ij}}]_{m\times n}=\left[{{\begin{array}[]{*{20}c}{SQ_% {11}}&{SQ_{12}}&\ldots&{SQ_{1n}}\\ {SQ_{21}}&{SQ_{22}}&\ldots&{SQ_{2n}}\\ \vdots&\vdots&\vdots&\vdots\\ {SQ_{m1}}&{SQ_{m2}}&\ldots&{SQ_{mn}}\\ \end{array}}}\right]$ (12) $\displaystyle SQ_{ij}=({s\mu_{ij},s\nu_{ij}})=\left({\prod\limits_{k=1}^{l}{({% s\mu_{ij}^{(k)}})^{sw_{k}}},1-\prod\limits_{k=1}^{l}{({1-s\nu_{ij}^{(k)}})}^{% sw_{k}}}\right)$ (13)

Step 2. Normalize the overall IF-matrix $SQ=({SQ_{ij}})_{m\times n}=({s\mu_{ij},s\nu_{ij}})$ to $NQ=[{NQ_{ij}}]_{m\times n}=({n\mu_{ij},n\nu_{ij}})_{m\times n}$ .

$\displaystyle({n\mu_{ij},n\nu_{ij}})=\left\{{{\begin{array}[]{ll}({s\mu_{ij},s% \nu_{ij}}),SZ_{j}\textit{ is a benefit criterion}\\ ({s\nu_{ij},s\mu_{ij}}),SZ_{j}\textit{ is a cost criterion}\\ \end{array}}}\right.$ (14)

Step 3. Utilize the maximizing deviation method (MDM) to determine the weight values.

The MDM was constructed through Wang [65]. Subsequently, the calculating procedures of this method was constructed.

(1) According to $NQ=[{NQ_{ij}}]_{m\times n}=({n\mu_{ij},n\nu_{ij}})_{m\times n}$ , the deviation $SP_{i}$ to other alternatives is constructed.

$\displaystyle\textit{IFHD}_{ij}=\sum\limits_{t=1}^{m}s\omega_{j}\cdot\textit{% IFNDM}({NQ_{ij},NQ_{tj}})$ (15)

where

$\displaystyle\textit{IFNDM}({NQ_{ij},NQ_{tj}})=\frac{1}{2}\left({\begin{array}% []{l}s\mu_{ij}\log\frac{2s\mu_{ij}}{s\mu_{ij}+s\mu_{tj}}+s\mu_{tj}\log\frac{2s% \mu_{tj}}{s\mu_{ij}+s\mu_{tj}}\\ \\ {}+s\nu_{ij}\log\frac{2s\nu_{ij}}{s\nu_{ij}+s\nu_{tj}}+s\nu_{tj}\log\frac{2s% \nu_{tj}}{s\nu_{ij}+s\nu_{tj}}\\ \\ {}+s\pi_{ij}\log\frac{2s\pi_{ij}}{s\pi_{ij}+s\pi_{tj}}+s\pi_{tj}\log\frac{2s% \pi_{tj}}{s\pi_{ij}+s\pi_{tj}}\\ \end{array}}\right).$

(2) Construct the total weighted deviation values.

$\displaystyle\textit{IFNDM}_{j}({s\omega})=\sum\limits_{i=1}^{m}{\textit{IFNDM% }_{ij}}({s\omega})$ (16) $\displaystyle{}=\sum\limits_{i=1}^{m}{\sum\limits_{t=1}^{m}{s\omega_{j}}}\left% ({\frac{1}{2}\left({\begin{array}[]{l}s\mu_{ij}\log\frac{2s\mu_{ij}}{s\mu_{ij}% +s\mu_{tj}}+s\mu_{tj}\log\frac{2s\mu_{tj}}{s\mu_{ij}+s\mu_{tj}}\\ \\ {}+s\nu_{ij}\log\frac{2s\nu_{ij}}{s\nu_{ij}+s\nu_{tj}}+s\nu_{tj}\log\frac{2s% \nu_{tj}}{s\nu_{ij}+s\nu_{tj}}\\ \\ {}+s\pi_{ij}\log\frac{2s\pi_{ij}}{s\pi_{ij}+s\pi_{tj}}+s\pi_{tj}\log\frac{2s% \pi_{tj}}{s\pi_{ij}+s\pi_{tj}}\\ \end{array}}\right)}\right)$

(3) Construct a non-linear programming with IFNs.

$\displaystyle({M-1})\left\{{\begin{array}[]{l}\max\textit{IFNDM}({s\omega})=% \sum\limits_{j=1}^{n}\sum\limits_{i=1}^{m}{\sum\limits_{t=1}^{m}{s\omega_{j}}}% \\ \left({\frac{1}{2}\left({\begin{array}[]{l}s\mu_{ij}\log\frac{2s\mu_{ij}}{s\mu% _{ij}+s\mu_{tj}}+s\mu_{tj}\log\frac{2s\mu_{tj}}{s\mu_{ij}+s\mu_{tj}}\\ \\ {}+s\nu_{ij}\log\frac{2s\nu_{ij}}{s\nu_{ij}+s\nu_{tj}}+s\nu_{tj}\log\frac{2s% \nu_{tj}}{s\nu_{ij}+s\nu_{tj}}\\ \\ {}+s\pi_{ij}\log\frac{2s\pi_{ij}}{s\pi_{ij}+s\pi_{tj}}+s\pi_{tj}\log\frac{2s% \pi_{tj}}{s\pi_{ij}+s\pi_{tj}}\\ \end{array}}\right)}\right)\\ s.t.\,z_{j}\geqslant 0,j=1,2,\ldots,n,\sum\limits_{j=1}^{n}{s\omega_{j}^{2}=1}% \\ \end{array}}\right.$ (17)

To solve this decision model, the Lagrange function is constructed

$\displaystyle L({s\omega,\xi})=\sum\limits_{j=1}^{n}\sum\limits_{i=1}^{m}{\sum% \limits_{t=1}^{m}{s\omega_{j}}}\left({\frac{1}{2}\left({\begin{array}[]{l}s\mu% _{ij}\log\frac{2s\mu_{ij}}{s\mu_{ij}+s\mu_{tj}}+s\mu_{tj}\log\frac{2s\mu_{tj}}% {s\mu_{ij}+s\mu_{tj}}\\ \\ {}+s\nu_{ij}\log\frac{2s\nu_{ij}}{s\nu_{ij}+s\nu_{tj}}+s\nu_{tj}\log\frac{2s% \nu_{tj}}{s\nu_{ij}+s\nu_{tj}}\\ \\ {}+s\pi_{ij}\log\frac{2s\pi_{ij}}{s\pi_{ij}+s\pi_{tj}}+s\pi_{tj}\log\frac{2s% \pi_{tj}}{s\pi_{ij}+s\pi_{tj}}\\ \end{array}}\right)}\right){}+\frac{\xi}{2}\left({\sum\limits_{j=1}^{n}{s% \omega_{j}^{2}-1}}\right)$ (18)

where $\xi$ is the Lagrange multiplier. Then the partial derivatives of $L$ is constructed.

$\displaystyle\left\{{\begin{array}[]{l}\frac{\partial L}{\partial s\omega_{j}}% =\sum\limits_{i=1}^{m}{\sum\limits_{t=1}^{m}{\left({\frac{1}{2}\left({\begin{% array}[]{l}s\mu_{ij}\log\frac{2s\mu_{ij}}{s\mu_{ij}+s\mu_{tj}}+s\mu_{tj}\log% \frac{2s\mu_{tj}}{s\mu_{ij}+s\mu_{tj}}\\ \\ {}+s\nu_{ij}\log\frac{2s\nu_{ij}}{s\nu_{ij}+s\nu_{tj}}+s\nu_{tj}\log\frac{2s% \nu_{tj}}{s\nu_{ij}+s\nu_{tj}}\\ \\ {}+s\pi_{ij}\log\frac{2s\pi_{ij}}{s\pi_{ij}+s\pi_{tj}}+s\pi_{tj}\log\frac{2s% \pi_{tj}}{s\pi_{ij}+s\pi_{tj}}\\ \end{array}}\right)}\right)+\xi s\omega_{j}=0}}\\ \frac{\partial L}{\partial\xi}=\frac{1}{2}\left({\sum\limits_{j=1}^{n}{s\omega% _{j}^{2}-1}}\right)=0\\ \end{array}}\right..$ (19)

And then the weight is constructed through solving the above model.

$\displaystyle s\omega_{j}^{*}=\frac{\sum\limits_{i=1}^{m}{\sum\limits_{t=1}^{m% }{\left({\frac{1}{2}\left({\begin{array}[]{l}s\mu_{ij}\log\frac{2s\mu_{ij}}{s% \mu_{ij}+s\mu_{tj}}+s\mu_{tj}\log\frac{2s\mu_{tj}}{s\mu_{ij}+s\mu_{tj}}\\ \\ {}+s\nu_{ij}\log\frac{2s\nu_{ij}}{s\nu_{ij}+s\nu_{tj}}+s\nu_{tj}\log\frac{2s% \nu_{tj}}{s\nu_{ij}+s\nu_{tj}}\\ \\ {}+s\pi_{ij}\log\frac{2s\pi_{ij}}{s\pi_{ij}+s\pi_{tj}}+s\pi_{tj}\log\frac{2s% \pi_{tj}}{s\pi_{ij}+s\pi_{tj}}\\ \end{array}}\right)}\right)}}}{\sqrt{\sum\limits_{j=1}^{n}{\left({\sum\limits_% {i=1}^{m}{\sum\limits_{t=1}^{m}{\left({\frac{1}{2}\left({\begin{array}[]{l}s% \mu_{ij}\log\frac{2s\mu_{ij}}{s\mu_{ij}+s\mu_{tj}}+s\mu_{tj}\log\frac{2s\mu_{% tj}}{s\mu_{ij}+s\mu_{tj}}\\ \\ {}+s\nu_{ij}\log\frac{2s\nu_{ij}}{s\nu_{ij}+s\nu_{tj}}+s\nu_{tj}\log\frac{2s% \nu_{tj}}{s\nu_{ij}+s\nu_{tj}}\\ \\ {}+s\pi_{ij}\log\frac{2s\pi_{ij}}{s\pi_{ij}+s\pi_{tj}}+s\pi_{tj}\log\frac{2s% \pi_{tj}}{s\pi_{ij}+s\pi_{tj}}\\ \end{array}}\right)}\right)}}}\right)^{2}}}}$ (20)

Finally, the normalized weight values are determined.

$\displaystyle s\omega_{j}=\frac{\sum\limits_{i=1}^{m}{\sum\limits_{t=1}^{m}{% \left({\frac{1}{2}\left({\begin{array}[]{l}s\mu_{ij}\log\frac{2s\mu_{ij}}{s\mu% _{ij}+s\mu_{tj}}+s\mu_{tj}\log\frac{2s\mu_{tj}}{s\mu_{ij}+s\mu_{tj}}\\ \\ {}+s\nu_{ij}\log\frac{2s\nu_{ij}}{s\nu_{ij}+s\nu_{tj}}+s\nu_{tj}\log\frac{2s% \nu_{tj}}{s\nu_{ij}+s\nu_{tj}}\\ \\ {}+s\pi_{ij}\log\frac{2s\pi_{ij}}{s\pi_{ij}+s\pi_{tj}}+s\pi_{tj}\log\frac{2s% \pi_{tj}}{s\pi_{ij}+s\pi_{tj}}\\ \end{array}}\right)}\right)}}}{\sum\limits_{j=1}^{n}{\sum\limits_{i=1}^{m}{% \sum\limits_{t=1}^{m}{\left({\frac{1}{2}\left({\begin{array}[]{l}s\mu_{ij}\log% \frac{2s\mu_{ij}}{s\mu_{ij}+s\mu_{tj}}+s\mu_{tj}\log\frac{2s\mu_{tj}}{s\mu_{ij% }+s\mu_{tj}}\\ \\ {}+s\nu_{ij}\log\frac{2s\nu_{ij}}{s\nu_{ij}+s\nu_{tj}}+s\nu_{tj}\log\frac{2s% \nu_{tj}}{s\nu_{ij}+s\nu_{tj}}\\ \\ {}+s\pi_{ij}\log\frac{2s\pi_{ij}}{s\pi_{ij}+s\pi_{tj}}+s\pi_{tj}\log\frac{2s% \pi_{tj}}{s\pi_{ij}+s\pi_{tj}}\\ \end{array}}\right)}\right)}}}}$ (21)

Step 4. Construct the border approximation area (BAA) for each attribute with Eq. (22).

$\displaystyle BQ_{j}=({b\mu_{j},b\nu_{j}})=\mathop{\otimes}\limits_{i=1}^{m}({% NQ_{ij}})^{1/m}=\left({\prod\limits_{i=1}^{m}{({n\mu_{ij}})^{\frac{1}{m}}},1-% \prod\limits_{i=1}^{m}{({1-n\nu_{ij}})^{\frac{1}{m}}}}\right)$ (22)

Step 5. Construct the IFN distance matrix $\textit{IFNDM}=({\textit{IFNDM}_{ij}})_{m\times n}$ . The alternatives’ distances from BAA are constructed using the Eq. (23) based on the prospect theory (PT) [58].

$\displaystyle\textit{IFNDM}_{ij}=\left\{{\begin{array}[]{l}({\textit{IFNDM}({% NQ_{ij},BQ_{j}})})^{\vartheta},\text{if }SV({NQ_{ij}})\geqslant SV({BQ_{j}}),% \\ -\rho({\textit{IFNDM}({NQ_{ij},BQ_{j}})})^{\varsigma},\text{if }SV({NQ_{ij}})<% SV({BQ_{j}}),\\ \end{array}}\right.$ (23)

where $\vartheta$ and $\varsigma$ are the parameters of DMs’ risk attitudes, $\rho$ is the loss aversion’s parameter. In this paper, $\vartheta=$ 0.88, $\varsigma=$ 0.88 and $\rho=$ 2.25 from Tversky [76].

Step 6. Construct the IFN final value $\textit{IFNFV}_{i}$ .

$\displaystyle\textit{IFNFV}_{i}=\sum\limits_{j=1}^{n}s\omega_{j}\times\textit{% IFNDM}_{ij},i=1,2,\ldots,m.$ (24)

Step 7. According to $\textit{IFNFV}_{i}$ , all the alternatives is ranked. The higher $\textit{IFNFV}_{i}$ is, the optimal alternative will be.

4. The empirical example and comparative analysis

4.1 An empirical example

In the post-production of film and television, the application of multimedia technology should adhere to three principles. First of all, the application of multimedia technology should ensure that the overall structure of the film is complete and rigorous, because the film is usually shot with a lot of material. In order to highlight the theme center of the film, the structure of the film needs to be adjusted, and the film should be dealt with in the post-production of the film and television. The content of the film is simplified and concentrated, so that the essence is presented in the film, but the structure of the film must be kept complete and classic; secondly, the application of multimedia technology in the post-production of film and television should control the overall structure of the film, and edit the film in post-production. It will affect the overall flow of the film. The use of scene transitions and lens switching will disrupt the rhythm of the film. The special effects of post-production will cause the audience’s emotions to fluctuate. For this reason, in terms of the rhythm control of the film, it is necessary to ensure that the scene transitions, lens switching, music and music. Storytelling matches; finally, multimedia technology in post-production of film and television should be noted that it is only an auxiliary tool, and should not dominate. The application of computer multimedia technology has promoted the development of modern film and television technology, and also promoted the development of my country’s cultural industry. At present, my country’s film and television works have encountered a series of bottlenecks in post-production, mainly manifested in the lack of imagination and creativity of the works. These problems restrict my country’s film and television works from entering the international stage and winning more awards. In the post-production of film and television works, efforts should be made to enrich the picture and sound experience with the help of computer multimedia technology from the perspective of innovation, fully mobilize the audience’s vision and hearing, so that the audience can obtain rich imagination through the film and television works, and feel the richness of the film and television works. The tension transmitted and the advantages of computer multimedia technology are brought into play. The application effect evaluation of multimedia technology in the film and television post-production is frequently viewed as a MAGDM issue. There are five potential multimedia technology enterprises $SP_{i}({i=1,2,3,4,5})$ preparing to evaluate their application effect evaluation. In order to assess these enterprises fairly, three experts $SH=\{{SH_{1},SH_{2},SH_{3}}\}$ are invited. All experts give their assessment information depending on the four subsequently attributes: ⟀ $SZ_{1}$ is picture texture; ⟁ $SZ_{2}$ is production cost of multimedia technology; ⟂ $SZ_{3}$ is the audience satisfaction; ⟃ $SZ_{4}$ is economic benefits. Evidently, $SZ_{2}$ is the cost attribute, while $SZ_{1}$ , $SZ_{2}$ and $SZ_{4}$ are the benefit attributes.

Then, the IF-MABAC method is constructed for application effect evaluation of multimedia technology in the film and television post-production with IFNs.

Step 1. Set up the decision-makers’ IF-matrix $SQ^{(k)}=({SQ_{ij}^{(k)}})_{5\times 4}$ as in Tables 1–3. The overall IF-matrix is constructed in Table 4.

Table 1
The IF-matrix by $SH_{1}$

	SZ₁	SZ₂	SZ₃	SZ₄
SP₁	(0.19, 0.63)	(0.32, 0.64)	(0.45, 0.36)	(0.49, 0.36)
SP₂	(0.82, 0.23)	(0.27, 0.43)	(0.64, 0.14)	(0.62, 0.23)
SP₃	(0.47, 0.34)	(0.16, 0.62)	(0.48, 0.42)	(0.42, 0.39)
SP₄	(0.43, 0.46)	(0.23, 0.49)	(0.65, 0.32)	(0.63, 0.25)
SP₄	(0.45, 0.32)	(0.24, 0.45)	(0.43, 0.46)	(0.63, 0.17)

Table 2

The IF-matrix by $SH_{2}$

	SZ₁	SZ₂	SZ₃	SZ₄
SP₁	(0.46, 0.24)	(0.32, 0.47)	(0.41, 0.34)	(0.46, 0.24)
SP₂	(0.68, 0.25)	(0.39, 0.64)	(0.42, 0.26)	(0.42, 0.39)
SP₃	(0.43, 0.32)	(0.42, 0.41)	(0.39, 0.41)	(0.45, 0.34)
SP₄	(0.46, 0.34)	(0.26, 0.63)	(0.45, 0.30)	(0.48, 0.41)
SP₄	(0.46, 0.27)	(0.38, 0.44)	(0.26, 0.62)	(0.63, 0.19)

Table 3

The IF-matrix by $SH_{3}$

	SZ₁	SZ₂	SZ₃	SZ₄
SP₁	(0.35, 0.46)	(0.26, 0.68)	(0.46, 0.37)	(0.46, 0.26)
SP₂	(0.62, 0.15)	(0.32, 0.64)	(0.64, 0.24)	(0.62, 0.35)
SP₃	(0.43, 0.41)	(0.23, 0.49)	(0.46, 0.41)	(0.42, 0.36)
SP₄	(0.45, 0.33)	(0.36, 0.43)	(0.61, 0.32)	(0.24, 0.61)
SP₄	(0.41, 0.36)	(0.27, 0.64)	(0.41, 0.38)	(0.36, 0.49)

Table 4

Overall the IF-matrix

	SZ₁	SZ₂	SZ₃	SZ₄
SP₁	(0.4325, 0.4563)	(0.5016, 0.3685)	(0.5016, 0.4124)	(0.2752, 0.5463)
SP₂	(0.5152, 0.3509)	(0.5108, 0.3632)	(0.5462, 0.3178)	(0.3089, 0.5219)
SP₃	(0.4369, 0.4325)	(0.6264, 0.1669)	(0.4869, 0.4023)	(0.3573, 0.5162)
SP₄	(0.5236, 0.3408)	(0.5176, 0.3532)	(0.4763, 0.3168)	(0.3273, 0.5524)
SP₄	(0.6234, 0.2104)	(0.6437, 0.2517)	(0.6304, 0.2035)	(0.2625, 0.6137)

Table 5

The normalized IFNs information

	SZ₁	SZ₂	SZ₃	SZ₄
SP₁	(0.4325, 0.4563)	(0.3685, 0.5016)	(0.5016, 0.4124)	(0.2752, 0.5463)
SP₂	(0.5152, 0.3509)	(0.3632, 0.5108)	(0.5462, 0.3178)	(0.3089, 0.5219)
SP₃	(0.4369, 0.4325)	(0.1669, 0.6264)	(0.4869, 0.4023)	(0.3573, 0.5162)
SP₄	(0.5236, 0.3408)	(0.3532, 0.5176)	(0.4763, 0.3168)	(0.3273, 0.5524)
SP₄	(0.6234, 0.2104)	(0.2517, 0.6437)	(0.6304, 0.2035)	(0.2625, 0.6137)

Table 6

The attributes weights

	SZ₁	SZ₂	SZ₃	SZ₄
$s\omega$	0.2633	0.1538	0.3017	0.2812

Step 2. Normalize the IF-matrix $SQ=[{SQ_{ij}}]_{5\times 4}$ to $NQ=[{NQ_{ij}}]_{5\times 4}$ .

Step 3. Construct the attribute weight values in Table 6.

Step 4. Construct the BAA (Table 7).

Table 7

The BAA

	BAA
SZ₁	(0.2357, 0.4123)
SZ₂	(0.1873, 0.5125)
SZ₃	(0.1987, 0.4267)
SZ₄	(0.2543, 0.5336)

Step 5. Construct the distance matrix IFNDM (Table 8).

Table 8

The IFNDM

	SZ₁	SZ₂	SZ₃	SZ₄
SP₁	0.0326	0.1671	0.1850	0.0099
SP₂	0.2983	0.0507	0.2955	$-$ 0.0393
SP₃	0.0059	0.0789	0.0030	$-$ 0.0074
SP₄	0.0766	0.0881	0.0996	0.0048
SP₄	$-$ 0.0154	0.0559	$-$ 0.0389	$-$ 0.1291

Step 6. Construct the IFNFV in Table 9.

Step 7. According to the IFNFV, the order is: $SP_{2}>SP_{1}>SP_{4}>SP_{3}>SP_{5}$ and $SP_{2}$ is the optimal multimedia technology enterprise.

4.2 Comparative analysis and discussion

Then, the IF-MABAC method is compared with IFWA operator [77], IFWG operator [73], intuitionistic fuzzy normalized weighted Bonferroni mean (IFNWBM) operator [78], generalized intuitionistic fuzzy power geometric (GIFPG) operators [79], generalized intuitionistic fuzzy weighted geometric interaction averaging (GIFWGIA) operator [80], IF-VIKOR method [81], IF-EDAS method [82], IF-TODIM method [83] and the existing IF-MABAC method [58]. The order decision results are depicted in Table 10.

Table 9
The IFNFV

Alternative	IFNFV
SP₁	0.0929
SP₂	0.1644
SP₃	0.0125
SP₄	0.0651
SP₄	$-$ 0.0435

Table 10

Order for different methods

Methods	Ranking order	The optimal alternative
IFWA operator [77]	$SP_{2}>SP_{1}>SP_{4}>SP_{3}>SP_{5}$	$SP_{2}$
IFWG operator [73]	$SP_{2}>SP_{1}>SP_{3}>SP_{4}>SP_{5}$	$SP_{2}$
IFNWBM operator [78]	$SP_{2}>SP_{1}>SP_{3}>SP_{4}>SP_{5}$	$SP_{2}$
GIFPG operators [79]	$SP_{2}>SP_{1}>SP_{3}>SP_{4}>SP_{5}$	$SP_{2}$
GIFWGIA operator [80]	$SP_{2}>SP_{1}>SP_{3}>SP_{4}>SP_{5}$	$SP_{2}$
IF-VIKOR method [81]	$SP_{2}>SP_{1}>SP_{4}>SP_{3}>SP_{5}$	$SP_{2}$
IF-EDAS method [82]	$SP_{2}>SP_{1}>SP_{4}>SP_{3}>SP_{5}$	$SP_{2}$
IF-TODIM method [83]	$SP_{2}>SP_{1}>SP_{4}>SP_{3}>SP_{5}$	$SP_{2}$
Existing IF-MABAC method [58]	$SP_{2}>SP_{1}>SP_{3}>SP_{4}>SP_{5}$	$SP_{2}$
The built IF-MABAC method	$SP_{2}>SP_{1}>SP_{4}>SP_{3}>SP_{5}$	$SP_{2}$

Obtained from Table 10, it is evident that the ordering results of these nine models are slightly different, however, the best optimal multimedia technology enterprise is SP2, while the worst multimedia technology enterprise is SP5. The main difference between existing IF-MABAC method [58] and the built IF-MABAC method is outlined: The main difference between existing IF-MABAC method [58] doesnâ€™t consider the psychological behavior of decision-makers, however, the built IF-MABAC method consider the psychological behavior of decision-makers. The built IF-MABAC method is that This verifies the IF-MABAC method is reasonable and effective. The proposed IF-MABAC method has the following advantages: (1) The proposed IF-MABAC method consider the psychological behavior of decision-makers; (2) The proposed IF-MABAC method takes into account potential losses and returns, and the calculation is simple and the results are stable.

5. Conclusion

Computer multimedia technology has developed at an astonishing speed since the 1980s. Computer multimedia technology is developed by the combination of computer technology and digital technology, and is applied to the collection, processing and storage of information. In the process of continuous innovation of computer technology, the application of multimedia technology is the most comprehensive and covers the widest range. In the film and television industry, post-production has always occupied a very important position. Through post-production, films can be optimized and improved, thereby enhancing the impact of the film on the audience and making up for the regrets and defects that occurred during the shooting of the work. The continuous upgrading and wide application of computer multimedia technology has brought new development opportunities to the film and television industry, and, with the strong help of computer multimedia technology, the innovative thinking and imagination of producers have been brought into full play. It is reflected in the works, and on this basis, the feeling that the film and television works bring to the audience is more and more powerful. Computer multimedia technology plays a prominent role in the post-production of film and television works and the future development of the film and television industry. The application effect evaluation of multimedia technology in the film and television post-production is frequently viewed as the MAGDM issue. Depending on the MABAC method and IFSs, this paper design the IF-MABAC method to assess the application effect evaluation of multimedia technology in the film and television post-production. Eventually, an example about application effect evaluation of multimedia technology in the film and television post-production and some comparative analysis has been given to demonstrate the superiority of the designed method.

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MABAC-based evaluation of multimedia technology application effect in film and television post-production

Abstract

Keywords

1. Introduction

2. Preliminaries

2.1 Intuitionistic fuzzy sets

4.1 An empirical example

Table 1 The IF-matrix by S ⁢ H 1

Table 9 The IFNFV

References

Table 1
The IF-matrix by $SH_{1}$

Table 9
The IFNFV