Innovative ExpTODIM algorithm for interval-valued Pythagorean fuzzy information and new-media information communication influence evaluation

Abstract

Undoubtedly, the Internet is an indispensable part of daily life in this era. In this context, the emergence of new media has played a disruptive role in information dissemination, and has also provided new definitions and evaluation standards for the impact of information dissemination. In an environment where excellent research is constantly emerging, it is of research value to redefine the elements of new media information dissemination from a new perspective and provide specific examples to analyze their information dissemination paths. The new-media information communication influence evaluation from super intellectual property (IP) perspective is a multipleattribute group decisionmaking (MAGDM) problem. Recently, the Exponential TODIM (an acronym in Portuguese of interactive and multicriteria decision making) method has been used to cope with MAGDM issues. The interval-valued Pythagorean fuzzy sets (IVPFSs) are used as a tool for characterizing uncertain information during the new-media information communication influence evaluation from super intellectual property. In this manuscript, the interval-valued Pythagorean fuzzy Exponential TODIM (ExpTODIM) (IVPFExpTODIM) method is built to solve the MAGDM under IVPFSs. In the end, a numerical case study for new-media information communication influence evaluation from super intellectual property is given to validate the proposed method. The main research contribution of this paper is constructed: (1) the Exponential TODIM (ExpTODIM) method is extended to the IVPFSs; (2) the interval-valued Pythagorean fuzzy Exponential TODIM (ExpTODIM) (IVPF-ExpTODIM) method is built to solve the MAGDM under IVPFSs; (3) the information Entropy is used to obtain the weight values based on the score value and accuracy value under IVPFSs; (4) Finally, a numerical case study for new-media information communication influence evaluation from super intellectual property is given to validate the proposed method.

Keywords

Multiple attribute group decision making (MAGDM)interval-valued Pythagorean fuzzy sets (IVPFSs)Exponential TODIM (ExpTODIM) method information communication influence evaluation

1. Introduction

Weibo has become an important medium for generating online public opinion, and timely detection, effective monitoring, and reasonable guidance of Weibo public opinion are of great significance to both the government and enterprises [1, 2, 3]. From the perspective of Communication studies, 140 characters microblog information has become the hot spot of online public opinion because of the continuous spread of information on the microblog network [4, 5, 6]. Unlike traditional two-way social relationships, Weibo networks built with a focus on one-way social relationships serve as a platform for information dissemination, while individual communication behavior on Weibo is the driving force behind information dissemination on the platform [7, 8, 9]. Researchers have found that there are some key individuals in Weibo networks that affect communication, and when information is forwarded by them, it can cause sustained and larger scale dissemination. These individuals with strong information dissemination influence have had a huge impact on the evolution of online public opinion. If they can intervene and intervene in a timely manner, it plays an important role in suppressing the spread of rumors and guiding information dissemination, which is conducive to the monitoring, warning, guidance and control of online public opinion [10, 11, 12]. Information dissemination is defined as the transmission and exchange of spiritual content such as knowledge, judgment, emotions, and consciousness between two or more actors. It is a process of exchanging or sharing opinions, attitudes, and other aspects through a certain information dissemination medium. With the continuous development of information technology, the information environment has also changed [13, 14, 15]. Under the traditional perspective of Communication studies and information science, the information dissemination elements of new media can be summarized as follows: (1) Information dissemination subject. This subject can be an individual or an organization, and can be divided into producers of information, disseminators of information, consumers of information, and regulators of information in specific environments. In the new media environment represented by Sina Weibo, the information producer can be every user who participates in the interaction of the platform. At the same time, because of the particularity of the Weibo platform, People who can express their opinions and opinions in the forwarding comment function can also serve as information producers, but the forwarding user is also the information transmitter [16, 17, 18]. The communicators of information in Weibo are mainly concentrated in the fan group. Due to the special nature of Weibo as a social platform, everyone may be followed and followed by others, that is, having fans and being fans [19, 20, 21]. Therefore, everyone can be a producer of information or a communicator of information. Those who engage in forwarding behavior during browsing Weibo content can be defined as information communicators; Information consumers refer to those who have information needs and are able to accept and utilize consumption information. In Sina Weibo, they mainly refer to people who only read and browse Weibo content, but do not engage in information sharing activities such as forwarding or liking; Information regulators mainly refer to platform operators or other administrative law enforcement departments. Regulators mainly control information that may generate online public opinion and timely control the dissemination of information on Weibo platforms. It is worth mentioning that among the information dissemination entities in the pan entertainment field, the relationship between Big V and fans, as well as the relationship between fans and information producers and transmitters, is extremely significant and close [22, 23, 24]. (2) Information, the information resource itself, is also the event object of communication behavior, the object of information dissemination, described and presented in the form of sound, images, graphics, and text. In the field of information dissemination in the new media pan entertainment field, information mainly refers to the film information, text information, or image information that users want to convey through the platform, which is the core element to achieve dissemination and diffusion. (3) Information technology is a general term for equipment and methods related to the collection, dissemination, and processing of information. It can be divided into two categories: support technology and application technology. It is the support for information transmission in the new media environment, and the supporting technology mainly refers to the mobile or non-mobile devices that the information dissemination subject relies on, such as mobile phones and non-mobile devices such as desktop computers [25, 26, 27]. (4) The sum of various elements related to the information environment, information exchange, and information activities. According to the vertical impact category, it can be divided into social information environment, organizational information environment and personal information environment. According to the horizontal impact category, it can be divided into cultural environment, economic environment, technological environment, etc [26, 27, 28]. Content is the core of Super IP, and most scholars generally believe that content plays a decisive role in the concept of Super IP. High quality content can actively ferment, which is the most crucial fundamental driving force for promoting Super IP; Personality refers to the sufficiently differentiated personality required to build a super IP, and unique personality charm plays a crucial role in attracting and stabilizing audiences; Originality is the foundation of derivation and re-creation, and is the key factor determining whether a high-quality IP can continue to spread across cultures, eras, and still be sought after [29, 30]. However, the most crucial aspect in the dissemination and development of IP lies in the chain of traffic, which enables the entire wheel of super IP to truly rotate; Commercialization is one of the most driving characteristics of Super IP, and it is an unavoidable dimension. It is undeniable that only with monetization value can Super IP achieve more long-term and sustainable development. The dissemination of information in the new media environment, whether on mobile or non-mobile devices, requires the use of a certain platform, and platform users, as the active initiators of all information, are the source of all information dissemination behavior. In the process of new media information dissemination, information can be seen as gradually diverging based on three layers: the basic layer, the accumulation layer, and the diffusion layer. The elements contained in each layer together constitute an indispensable factor in the dissemination of new media information. In the stage of information generation, the two important factors of originality and content power form the basic level of information dissemination. In the new media environment, the lifecycle of information is very short compared to traditional communication models, and the key to generating long-term vitality is content power and originality. Content is the starting point of Super IP, and content power can be seen as the beginning of pan entertainment information dissemination in the new media environment. What we need to share is whether it can reflect the state of things, whether it can meet people’s needs, and whether it has substantial information. In the deepening stage of communication, from the perspective of super IP, the human element is the most dominant factor. The positioning of personality in the super IP elements has been explained in the previous text. The human power element that is pulled into the information dissemination of the pan entertainment field is an expression of emotions, a label of characteristics, and a guarantee of stabilizing the audience [31, 32]. Taking Sina Weibo as a representative of new media in the field of pan entertainment information dissemination as an example, the implementation rate of information dissemination among users with the same or similar interest tags is relatively high, which plays a deepening role in promoting the content of information resources. For example, anime enthusiasts prefer to share anime information, while film and television star followers are more willing to share information such as film stars, At the same time, human power is also reflected in other factors that reflect user characteristics, such as emotional states such as approval. In the stage of information dissemination, based on super IP, it can be understood as the generation of traffic, the implementation of information “viral” diffusion, and in the field of pan entertainment, it mainly refers to the late performance behavior of information dissemination based on the number of fans of users, and information diffusion based on topics that originally had a certain influence or actively mentioning more users [33, 34].

In decision-making practice, due to the complexity of the socio-economic environment, in order to consider a decision-making problem as comprehensively as possible, single person decision-making cannot meet the multiple attribute decision making (MADM) needs [35, 36, 37]. Similar to the MADM, the multicriteria Decision Analysis (MCDA) is the important research parts in practical management science [38, 39, 40, 41, 42]. In many MCDA problems, due to the limitations which recognizing the practical decision-making problem, it is often impossible to depict the accurate information and could only be portrayed through the uncertainty which constitutes the uncertain MCDA issue [43, 44, 45, 46]. Multiple attribute group decision making (MAGDM), which aggregates the information of multiple decision-makers according to certain rules, has become a commonly used decision-making mode [47, 48, 49, 50]. In practical decision-making, due to differences in the knowledge, experience, status, and information collection methods accumulated by different decision-makers in their professional fields, their cognition of the decision object may also vary. If the preferences and opinions of various experts are simply aggregated and the differences between experts are ignored, it may lead to lower acceptability or reliability of the decision plan. For uncertain group decision-making, the reliability of decision information is a key indicator to measure the effectiveness of decision results [51, 52, 53, 54]. As human beings’ ability to understand and transform the world continues to strengthen, decision-makers perceive more and more content, and the information involved becomes more complex [51, 52, 53, 54, 55, 56, 57, 58]. With the increasing complexity of the MAGDM issues [59, 60, 61, 62], it is of great necessity to consider the decisiom makers’ (DMs’) psychological factors [63]. Tversky and Kahneman [64] designed the prospect theory (PT) under risk. Gomes and Lima [65] designed the TODIM for MADM issues under risk. Wei, Ren and Rodriguez [66] defined the hesitant fuzzy linguistic TODIM method. Leoneti and Gomes [67] put forward the Exponential TODIM (ExpTODIM) method. Sun et al. [68] put forward the extended Exp-TODIM method for MADM based on the Z-Wasserstein distance. The new-media information communication influence evaluation from super intellctual property is classical MAGDM. Recently, the Exponential TODIM (ExpTODIM) method [67] has been used to cope with MAGDM issues. Compared with other fuzzy sets, the IVPFSs [69] are used as a tool for characterizing uncertain information during the new-media information communication influence evaluation from super intellctual property. Until now, there is not related research works to investigate the ExpTODIM method [67]under IVPFSs [69]. Thus, the main aim of this paper is to investigate the ExpTODIM method under IVPFSs and construct the corresponding MAGDM method for new-media information communication influence evaluation from super intellectual property. In this manuscript, the interval-valued Pythagorean fuzzy Exponential TODIM (ExpTODIM) (IVPF-ExpTODIM) method is built to solve the MAGDM under IVPFSs. The information Entropy is used to obtain the weight values based on the score value and accuracy value under IVPFSs. In the end, a numerical case study for new-media information communication influence evaluation from super intellectual property is given to validate the proposed method. The main research aim and motivation of this paper is constructed: (1) the Exponential TODIM (ExpTODIM) method is extended to the IVPFSs; (2) the interval-valued Pythagorean fuzzy Exponential TODIM (ExpTODIM) (IVPF-ExpTODIM) method is built to solve the MAGDM under IVPFSs; (3) the information Entropy is used to obtain the weight values based on the score value and accuracy value under IVPFSs; (4) Finally, a numerical case study for new-media information communication influence evaluation from super intellectual property is given to validate the proposed method.

The structure of this paper is listed below. In Section 2, the IVPFSs is introduced. In Section 3, IVPF-ExpTODIM method is designed under IVPFSs with entropy. Section 4 gives an illustrative case for new-media information communication influence evaluation from super intellctual property and some comparative analysis. Some remarks are given in Section 5.

2. Preliminaries

The PFSs and IVPFSs are introduced.

Definition 1 [70]. Let $Θ$ be a fix set. A PFS is defined

$T = {⟨ θ, (M_{T} (θ), M_{T} (θ)) ⟩ | θ \in Θ}$ (1)

where $M_{T} (θ) \subseteq [0, 1]$ , $N_{T} (θ) \subseteq [0, 1]$ denotes the membership non-membership of $θ \in Θ$ to $T$ , and, for $θ \in Θ$ , it has the defined condition

${(M_{T} (θ))}^{2} + {(N_{T} (θ))}^{2} ⩽ 1 .$ (2)

Definition 2 [70]. Let $T_{1} = (M_{1}, N_{1})$ , $T_{2} = (M_{2}, N_{2})$ , and $T = (M, N)$ be three PFNs, and some operations are given.

$(1) T_{1} \oplus T_{2} = (\sqrt{{(M_{1})}^{2} + {(M_{2})}^{2} - {(M_{1})}^{2} {(M_{2})}^{2}}, N_{1} N_{2}); (2) T_{1} \otimes T_{2} = (M_{1} M_{2}, \sqrt{{(N_{1})}^{2} + {(N_{2})}^{2} - {(N_{1})}^{2} {(N_{2})}^{2}}); (3) λ T = (\sqrt{1 - {(1 - M^{2})}^{λ}}, N^{λ}), λ > 0; (4) {(T)}^{λ} = (M^{λ} \sqrt{1 - {(1 - N^{2})}^{λ}}), λ > 0 .$

Liang, Zhang and Liu [69] developed the interval-valued PFSs (IVPFSs).

Definition 3 [69]. Let $Θ$ be a fix set. An IVPFS is defined

$V T = {⟨ θ, (V M_{V T} (θ), V N_{V T} (θ)) ⟩ | θ \in Θ}$ (3)

where $V M_{V T} (θ) \subseteq [0, 1]$ , $V N_{V T} (θ) \subseteq [0, 1]$ are interval values, $V M_{V T} (θ) = [V M_{V T}^{L} (θ), V M_{V T}^{R} (θ)]$ , $V N_{V T} (θ) = [V N_{V T}^{L} (θ), V N_{V T}^{R} (θ)]$ , $0 ⩽ V M_{V T}^{R} (θ) + V N_{V T}^{R} (θ) ⩽ 1$ , $\forall θ \in Θ$ . $V M_{V T} (θ)$ , $V N_{V T} (θ)$ denote the membership and no-membership.

For convenience, $V T = ([V M^{L}, V M^{R}], [V N^{L}, V N^{R}])$ is an interval-valued Pythagorean fuzzy number (IVPFN), and $[V M^{L}, V M^{R}], [V N^{L}, V N^{R}] \subset [0, 1]$ , ${(V M^{R})}^{2} + {(V M^{R})}^{2} ⩽ 1$ .

Definition 4 [71]. Let $V T_{1} = ([V M_{1}^{L}, V M_{1}^{R}], [V N_{1}^{L}, V N_{1}^{R}])$ , $V T_{2} = ([V M_{2}^{L}, V M_{2}^{R}], [V N_{2}^{L}, V N_{2}^{R}])$ , and $V T = ([V M^{L}, V M^{R}], [V N^{L}, V N^{R}])$ be three IVPFNs, and some operations are given.

$(1) V T_{1} \oplus V T_{2} = (\begin{matrix} [\begin{matrix} \sqrt{{(V M_{1}^{L})}^{2} + {(V M_{2}^{L})}^{2} - {(V M_{1}^{L})}^{2} {(V M_{2}^{L})}^{2}}, \\ \sqrt{{(V M_{1}^{R})}^{2} + {(V M_{2}^{R})}^{2} - {(V M_{1}^{R})}^{2} {(V M_{2}^{R})}^{2}} \end{matrix}], \\ [V N_{1}^{L} V N_{2}^{L}, V N_{1}^{R} V N_{2}^{R}] \end{matrix}); (2) V T_{1} \otimes V T_{2} = (\begin{matrix} [V M_{1}^{L} V M_{2}^{L}, V M_{1}^{R} V M_{2}^{R}], \\ [\begin{matrix} \sqrt{{(V N_{1}^{L})}^{2} + {(V N_{2}^{L})}^{2} - {(V N_{1}^{L})}^{2} {(V N_{2}^{L})}^{2}}, \\ \sqrt{{(V N_{1}^{R})}^{2} + {(V N_{2}^{R})}^{2} - {(V N_{1}^{R})}^{2} {(V N_{2}^{R})}^{2}} \end{matrix}] \end{matrix}); (3) λ V T = ([\sqrt{1 - {(1 - {(V M^{L})}^{2})}^{λ}}, \sqrt{1 - {(1 - {(V M^{R})}^{2})}^{λ}}], [{(V N^{L})}^{λ}, {(V N^{R})}^{λ}]), λ > 0; (4) {(V T)}^{λ} = ([{(V M^{L})}^{λ}, {(V M^{R})}^{λ}] [\sqrt{1 - {(1 - {(V N^{L})}^{2})}^{λ}}, \sqrt{1 - {(1 - {(V N^{R})}^{2})}^{λ}}]), λ > 0; (5) V T^{c} = ([V N^{L}, V N^{R}], [V M^{L}, V M^{R}]) .$

Definition 5 [71]. Let $V T_{1} = ([V M_{1}^{L}, V M_{1}^{R}], [V N_{1}^{L}, V N_{1}^{R}])$ , $V T_{2} = ([V M_{2}^{L}, V M_{2}^{R}], [V N_{2}^{L}, V N_{2}^{R}])$ ,

$S V (V T_{1}) = \frac{1}{4} [(1 + {(V M_{1}^{L})}^{2} - {(V N_{1}^{L})}^{2}) + (1 + {(V M_{1}^{R})}^{2} - {(V N_{1}^{R})}^{2})]$

and

$S V (V T_{2}) = \frac{1}{4} [(1 + {(V M_{2}^{L})}^{2} - {(V N_{2}^{L})}^{2}) + (1 + {(V M_{2}^{R})}^{2} - {(V N_{2}^{R})}^{2})]$

is the scores value of $V T_{1} = ([V M_{1}^{L}, V M_{1}^{R}], [V N_{1}^{L}, V N_{1}^{R}])$ and $V T_{2} = ([V M_{2}^{L}, V M_{2}^{R}], [V N_{2}^{L}, V N_{2}^{R}])$ ,

$A V (V T_{1}) = \frac{1}{2} [({(V M_{1}^{L})}^{2} + {(V N_{1}^{L})}^{2}) + {(V M_{1}^{R})}^{2} + {(V N_{1}^{R})}^{2}]$

and

$A V (V T_{2}) = \frac{1}{2} [({(V M_{2}^{L})}^{2} + {(V N_{2}^{L})}^{2}) + {(V M_{2}^{R})}^{2} + {(V N_{2}^{R})}^{2}]$

is the accuracy value of $V T_{1} = ([V M_{1}^{L}, V M_{1}^{R}], [V N_{1}^{L}, V N_{1}^{R}])$ and $V T_{2} = ([V M_{2}^{L}, V M_{2}^{R}], [V N_{2}^{L}, V N_{2}^{R}])$ , then if $S V (V T_{1}) < S V (V T_{2})$ , $V T_{1} < V T_{2}$ ; if $S V (V T_{1}) = S V (V T_{2})$ , (1) if $A V (V T_{1}) = A V (V T_{2})$ , $V T_{1} = V T_{2}$ ; (2) if $A V (V T_{1}) < A V (V T_{2})$ , $V T_{1} < V T_{2}$ .

Definition 6 [72]. Let $V T_{1} = ([V M_{1}^{L}, V M_{1}^{R}], [V N_{1}^{L}, V N_{1}^{R}])$ , $V T_{2} = ([V M_{2}^{L}, V M_{2}^{R}], [V N_{2}^{L}, V N_{2}^{R}])$ , the normalized Hamming distance is:

$H D (V T_{1}, V T_{2}) = \frac{1}{4} (\begin{matrix} | {(V M_{1}^{L})}^{2} - {(V M_{2}^{L})}^{2} | + | {(V M_{1}^{R})}^{2} - {(V M_{2}^{R})}^{2} | \\ + | {(V L_{1}^{L})}^{2} - {(V L_{2}^{L})}^{2} | + | {(V N_{1}^{R})}^{2} - {(V N_{2}^{R})}^{2} | \end{matrix})$ (4)

3. IVPF-ExpTODIM method for MAGDM with entropy weight

In this section, IVPF-ExpTODIM method is built for MAGDM. Let $V A = {V A_{1}, V A_{2}, \dots, V A_{m}}$ be alternatives, and the attributes set $V G = {V G_{1}, V G_{2}, \dots, V G_{n}}$ with weight $v w$ , where $v w_{j} \in [0, 1]$ , $\sum_{j = 1}^{n} v w_{j} = 1$ and a set of invited experts $D E = {D E_{1}, D E_{2}, \dots, D E_{q}}$ , let expert’s weight be ${d w_{1}, d w_{2}, \dots, d w_{q}} d w_{t} \in [0, 1]$ , $\sum_{t = 1}^{q} d w_{t} = 1$ .

Then, IVPF-ExpTODIM method is built for MAGDM. The calculating steps are depicted:

Stage 1: Obtain the decision information with IVPFSs

(1) Build the IVPF-matrix $V R^{(t)} = {[V R_{i j}^{(t)}]}_{m \times n} = {([V M_{i j}^{L (t)}, V M_{i j}^{R (t)}], [V N_{i j}^{L (t)}, V N_{i j}^{R (t)}])}_{m \times n}$ and calculate the average matrix $V R = {[V R_{i j}]}_{m \times n} = {([V M_{i j}^{L}, V M_{i j}^{R}], [V N_{i j}^{L}, V N_{i j}^{R}])}_{m \times n}$ :

$\begin{matrix} V G_{1} & V G_{2} & \dots & V G_{n} \end{matrix}$ $V R^{t} = {[V R_{i j}^{t}]}_{m \times n} = \begin{matrix} V A_{1} \\ V A_{2} \\ ⋮ \\ V A_{m} \end{matrix} [\begin{matrix} V R_{11}^{t} & V R_{12}^{t} & \dots & V R_{1 n}^{t} \\ V R ϕ_{21}^{t} & V R_{22}^{t} & \dots & V R_{2 n}^{t} \\ ⋮ & ⋮ & ⋮ & ⋮ \\ V R_{m 1}^{t} & V R_{m 2}^{t} & \dots & V R_{m n}^{t} \end{matrix}]$ (5) $\begin{matrix} V G_{1} & V G_{2} & \dots & V G_{n} \end{matrix}$ $V R = {[V R_{i j}]}_{m \times n} = \begin{matrix} V A_{1} \\ V A_{2} \\ ⋮ \\ V A_{m} \end{matrix} [\begin{matrix} V R_{11} & V R_{12} & \dots & V R_{1 n} \\ V R_{21} & V R_{22} & \dots & V R_{2 n} \\ ⋮ & ⋮ & ⋮ & ⋮ \\ V R_{m 1} & V R_{m 2} & \dots & V R_{m n} \end{matrix}]$ (6)

Based on IVPFWA, the $V R = {[V R_{i j}]}_{m \times n} = {([V M_{i j}^{L}, V M_{i j}^{R}], [V N_{i j}^{L}, V N_{i j}^{R}])}_{m \times n}$ is:

$V R_{i j} = d w_{1} V R_{i j}^{1} \oplus d w_{2} V R_{i j}^{2} \oplus \dots \oplus d w_{q} V R_{i j}^{q} = (\begin{matrix} [\sqrt{1 - \prod_{t = 1}^{q} {(1 - {(V M_{i j}^{L (t)})}^{2})}^{d w_{t}}}, \sqrt{1 - \prod_{t = 1}^{q} {(1 - {(V M_{i j}^{R (h)})}^{2})}^{d w_{t}}}], \\ [\prod_{t = 1}^{q} {(V N_{i j}^{L (t)})}^{d w_{t}}, \prod_{t = 1}^{q} {(V N_{i j}^{R (t)})}^{d w_{t}}] \end{matrix})$ (7)

(2) Normalize the $V R = {[V R_{i j}]}_{m \times n}$ into

$𝑁𝑉𝑅 = {[{𝑁𝑉𝑅}_{i j}]}_{m \times n} = {([{𝑁𝑉𝑀}_{i j}^{L}, {𝑁𝑉𝑀}_{i j}^{R}], [{𝑁𝑉𝑁}_{i j}^{L}, {𝑁𝑉𝑁}_{i j}^{R}])}_{m \times n} .$

For benefit attributes:

${𝑁𝑉𝑅}_{i j} = ([{𝑁𝑉𝑀}_{i j}^{L}, {𝑁𝑉𝑀}_{i j}^{R}], [{𝑁𝑉𝑁}_{i j}^{L}, {𝑁𝑉𝑁}_{i j}^{R}]) = V R_{i j} = ([V M_{i j}^{L}, V M_{i j}^{R}], [V N_{i j}^{L}, V N_{i j}^{R}])$ (8)

For cost attributes:

${𝑁𝑉𝑅}_{i j} = ([{𝑁𝑉𝑀}_{i j}^{L}, {𝑁𝑉𝑀}_{i j}^{R}], [{𝑁𝑉𝑁}_{i j}^{L}, {𝑁𝑉𝑁}_{i j}^{R}]) = ([V N_{i j}^{L}, V N_{i j}^{R}], [V M_{i j}^{L}, V M_{i j}^{R}])$ (9)

Stage 2: Compute the attributes weight by using information entropy.

The weight is important for MAGDM. Many scholars focused on to obtain the weight information under different environment [56, 73, 74, 75, 76]. Entropy [77] is a conventional theory to derive weight. Firstly, the normalized IVPF-matrix $N N_{i j}$ is obtained:

$N N_{i j} = \frac{\frac{A V ([{𝑁𝑉𝑀}_{i j}^{L}, {𝑁𝑉𝑀}_{i j}^{R}], [{𝑁𝑉𝑁}_{i j}^{L}, {𝑁𝑉𝑁}_{i j}^{R}])}{S V ([{𝑁𝑉𝑀}_{i j}^{L}, {𝑁𝑉𝑀}_{i j}^{R}], [{𝑁𝑉𝑁}_{i j}^{L}, {𝑁𝑉𝑁}_{i j}^{R}])}}{\sum_{i = 1}^{m} \frac{A V ([{𝑁𝑉𝑀}_{i j}^{L}, {𝑁𝑉𝑀}_{i j}^{R}], [{𝑁𝑉𝑁}_{i j}^{L}, {𝑁𝑉𝑁}_{i j}^{R}])}{S V ([{𝑁𝑉𝑀}_{i j}^{L}, {𝑁𝑉𝑀}_{i j}^{R}], [{𝑁𝑉𝑁}_{i j}^{L}, {𝑁𝑉𝑁}_{i j}^{R}])}},$ (10)

Then, the IVPFN Shannon information entropy

$𝐼𝑉𝑃𝐹𝑁𝑆𝐼𝐸 = ({𝐼𝑉𝑃𝐹𝑁𝑆𝐼𝐸}_{1}, {𝐼𝑉𝑃𝐹𝑁𝑆𝐼𝐸}_{2}, \dots, {𝐼𝑉𝑃𝐹𝑁𝑆𝐼𝐸}_{n})$

is derived:

${𝐼𝑉𝑃𝐹𝑁𝑆𝐼𝐸}_{j} = - \frac{1}{\ln m} \sum_{i = 1}^{m} N N_{i j} \ln N N_{i j}$ (11)

and $N N_{i j} \ln N N_{i j} = 0$ if $n ϕ ϕ_{i j} = 0$ .

Then, the weights $v w = (v w_{1}, v w_{2}, \dots, v w_{n})$ is derived:

$v w_{j} = \frac{1 - {𝐼𝑉𝑃𝐹𝑁𝑆𝐼𝐸}_{j}}{\sum_{j = 1}^{n} (1 - {𝐼𝑉𝑃𝐹𝑁𝑆𝐼𝐸}_{j})}, j = 1, 2, \dots, n .$ (12)

Stage 3: IVPF-ExpTODIM method for MAGDM

In such section, the IVPF-ExpTODIM method is built for MAGDM.

(1) Define relative weight of $V G_{j}$ as:

${𝑟𝑣𝑤}_{j} = v w_{j} / v w_{j}^{*},$ (13)

$v w_{j}^{*}$ is the maximum weight of the attributes, and $0 ⩽ v w_{j} ⩽ 1$ .

(2) The dominance degree $D D_{j} (V A_{i}, V A_{t})$ of $V A_{i}$ over $V A_{t}$ for $V G_{j}$ is obtained:

$D D_{j} (V A_{i}, V A_{t}) = {\begin{matrix} \frac{{𝑟𝑣𝑤}_{j} \times (1 - 10^{- ρ H D ({𝑁𝑉𝑅}_{i j}, {𝑁𝑉𝑅}_{t j})})}{\sum_{j = 1}^{n} {𝑟𝑣𝑤}_{j}} & if S F ({𝑁𝑉𝑅}_{i j}) > S F ({𝑁𝑉𝑅}_{t j}) \\ 0 & if S F ({𝑁𝑉𝑅}_{i j}) = S F ({𝑁𝑉𝑅}_{t j}) \\ - \frac{1}{π} \frac{\sum_{j = 1}^{n} {𝑟𝑣𝑤}_{j} \times (1 - 10^{- ρ H D ({𝑁𝑉𝑅}_{i j}, {𝑁𝑉𝑅}_{t j})})}{{𝑟𝑣𝑤}_{j}} & if S F ({𝑁𝑉𝑅}_{i j}) < S F ({𝑁𝑉𝑅}_{t j}) \end{matrix}$ (14)

where $π$ is the amplification parameter values according to the findings of Tversky and Kahneman [64] and $π \in [1, 5]$ . When assuming higher values $ρ$ indicates that the curvature of the function more accentuate, which could be sensitive to small variations [67].

The dominance degree matrix $D D_{j} (V A_{i}) (j = 1, 2, \dots, n)$ with respect to $V G_{j}$ is defined:

$D D_{j} (V A_{i}) = {[D D_{j} (V A_{i}, V A_{t})]}_{m \times m} t$ $\begin{matrix} V A_{1} & V A_{2} & \dots & V A_{m} \end{matrix}$ (15) $= \begin{matrix} V A_{1} \\ V A_{2} \\ ⋮ \\ V A_{m} \end{matrix} [\begin{matrix} 0 & D D_{j} (V A_{1}, V A_{2}) & \dots & D D_{j} (V A_{1}, V A_{m}) \\ D D_{j} (V A_{2}, V A_{1}) & 0 & \dots & D D_{j} (V A_{2}, V A_{m}) \\ ⋮ & ⋮ & \dots & ⋮ \\ D D_{j} (V A_{m}, V A_{1}) & D D_{j} (V A_{m}, V A_{2}) & \dots & 0 \end{matrix}]$

(3) Produce the $D D_{j} (V A_{i})$ of $V A_{i}$ over other alternatives for $V A_{t}$ :

$D D (V A_{i}, V A_{t}) = \sum_{j = 1}^{n} D D_{j} (V A_{i}, V A_{t})$ (16)

The $D D = D D {(V A_{i}, V A_{t})}_{m \times m}$ is defined:

$D D = D D {(V A_{i}, V A_{t})}_{m \times m}$ $= [\begin{matrix} V A_{1} & V A_{2} & \dots & V A_{m} \\ V A_{1} & \sum_{j = 1}^{n} D D_{j} (V A_{1}, V A_{1}) & \sum_{j = 1}^{n} D D_{j} (V A_{1}, V A_{2}) & \dots & \sum_{j = 1}^{n} D D_{j} (V A_{1}, V A_{m}) \\ V A_{2} & \sum_{j = 1}^{n} D D_{j} (V A_{2}, V A_{1}) & \sum_{j = 1}^{n} D D_{j} (V A_{2}, V A_{2}) & \dots & \sum_{j = 1}^{n} D D_{j} (V A_{2}, V A_{m}) \\ ⋮ & ⋮ & ⋮ & ⋮ & ⋮ \\ V A_{m} & \sum_{j = 1}^{n} D D_{j} (V A_{m}, V A_{1}) & \sum_{j = 1}^{n} D D_{j} (V A_{m}, V A_{2}) & \dots & \sum_{j = 1}^{n} D D_{j} (V A_{m}, V A_{m}) \end{matrix}]$ (17)

(4) Finally, the overall dominance degree $𝑂𝐷𝐷 (V A_{i})$ of alternative $V A_{i}$ is obtained:

$𝑂𝐷𝐷 (V A_{i}) = \frac{\sum_{t = 1}^{m} D D (V A_{i}, V A_{t}) - min_{i} {\sum_{t = 1}^{m} D D (V A_{i}, V A_{t})}}{max_{i} {\sum_{t = 1}^{m} D D (V A_{i}, V A_{t})} - min_{i} {\sum_{t = 1}^{m} D D (V A_{i}, V A_{t})}}$ (18)

(5) The order could be obtained according to $𝑂𝐷𝐷 (V A_{i}) (i = 1, 2, \dots, m)$ , that is, the larger $𝑂𝐷𝐷 (V A_{i}) (i = 1, 2, \dots, m)$ , the better the alternative $V A_{i}$ is.

4. An empirical example and comparative analysis

4.1 An empirical example

Super IP, also known as Intellectual Property with exploitable value, refers to some cross media content operations with long-term vitality and high commercial value. At present, scholars generally agree that super IP can be divided into four levels, namely presentation form, story, universal elements, and values. The presentation form, as the most superficial layer, focuses more on various popular element forms and does not deeply explore the inherent characteristics of Super IP; The importance of story hierarchy as a property engine is self-evident, as it begins to demonstrate the need for characteristic elements such as original content; The layer of universal elements, which is the deep core of developing IP, has entered a core-oriented approach from this level. Unlike the so-called worldview in stories, universal elements emphasize the common identity of the world, which lays the foundation for the dissemination and sharing characteristics of super IP. Universal elements undoubtedly perform well in dissemination and sharing for subjects with high levels of environmental and architectural construction; Values are the most core level, and the accumulation of this level has a profound impact on the dissemination of IP. All dimensional characteristics revolve around this level. Pan entertainment refers to the fan economy based on the symbiosis of the internet and mobile internet in multiple fields, creating celebrity IPs. Combined with the “Internet plus”’ we are currently discussing, pan entertainment can be said to be a new form of Internet plus culture and entertainment. Under the development of this concept, the concept of pan entertainment involves literature, film and television, anime, games, and various derivatives. It is one of the fields that young people generally participate in in in the context of the new media era, and also one of the indispensable fields in today’s era, naturally controlling the key position of information dissemination. The reason why we chose the pan entertainment field for communication influence evaluation is because it is a field with distinct information dissemination characteristics in the current era of new media. The information related to the pan entertainment field has excellent characteristics such as high aggregation, high sharing, and high enrichment, and the research on communication influence from the super IP perspective has a high degree of compatibility. It is more suitable for conducting relevant research from a new perspective. The new-media information communication influence evaluation from super-intellctual property is a classical MAGDM issue. Therefore, the new-media information communication influence evaluation from super intellctual property is presented to demonstrate the approach developed in this paper. There is a panel with five new media platforms for spreading public opinion information on mobile internet networks $C A_{i} (i = 1, 2, 3, 4, 5)$ to choose. The experts select six attributes to assess the five new media platforms for spreading public opinion information on mobile internet networks:

⟀ VG₁ is the content power. For Super IP, good content is the core of a high-quality IP, which is emphasized by many scholars and experts. High quality content can deeply awaken the public’s psychology in the hearts of the information audience. Introducing a super IP perspective to explain the influencing factors of new media information dissemination, in which the scalability, sustainability, and convertibility of content from this perspective increase the importance of the content power in the information dissemination process. The specific parameter elements of content power in the pan entertainment field of Sina Weibo are reflected in the content of Weibo, such as the number of words in Weibo text and the number of Weibo images.

⟁ VG₂ is the originality power. The originality power is the foundation for Super IP to improve its competitiveness. Super IPs that can attract the public and have both derivative and creative properties have persuasive originality, especially in the field of pan entertainment. People’s awareness of intellectual property is constantly strengthening, and only content with originality has dissemination power and can be recognized by people. In the process of information dissemination in the field of pan entertainment, it is reflected in the degree of non- reprinted originality on Weibo. Information with a high level of originality can not only be based on the overall environment, but also occupy communication nodes to further expand its influence.

⟂ VG₃ is the sharing power. Sharing power is rarely emphasized in the research on super IP, but due to the combination of super IP and information dissemination, this element becomes particularly important. In the typical pan entertainment field, sharing power is the most core link, which expands and extends information, and expands the influence of information dissemination. In the previous example of the pan entertainment field, the construction of communication paths is actually generated through effective forwarding, but the specific breadth of communication influence also needs to consider the number of fans that can be influenced by the participating users.

⟃ VG₄ is the liquidity power. The degree of commercialization in super IP determines whether it will last in the information market. In new media information dissemination, this article converts it into monetization, which is the amount of attention triggered by a Weibo account. This also determines the issue of lasting influence in new media dissemination. A low level of attention may indicate that influence is only an “overnight success”’, Weibo, which has a high level of attention, may also have a more profound and long-lasting impact on users.

⟄ VG₅ is the personality charm power. Personality charm power is most prominent in the example of Weibo in the pan entertainment field, is also the most distinctive element level from the perspective of super IP. Having warmth, emotions, and distinct personality traits, one of the characteristic elements of Super IP – personality, is prominently reflected in users’ emotional views on Weibo in the pan entertainment field of information dissemination. It is most evident in emotional likes and comment expressions. At the same time, user characteristics (such as regional gender) have shown an important role in the analysis of communication paths in the previous section, indicating that this also has a certain determining effect on the elements of personality.

⟅ VG₆ is the Social influence. With the advancement of technology, the modernization of society, the advancement of media technology, the socialization of media, and the continuous acceleration of media dissemination speed, the influence of media on society is constantly increasing. At the same time, the development of new technologies has enabled new media to take on more forms. Readers can not only receive information, but also provide and create information, making it a true “human to human” communication. The emergence of new media will inevitably bring new ways of information exchange to people’s thinking, communication, art, and other aspects. The history of media, in a sense, is also a process of social history. The rapid development of new media and its complexity have had multiple impacts on people’s lives.

All attributes are beneficial one. The five possible new media platforms for spreading public opinion information on mobile internet networks $V A_{i} (i = 1, 2, 3, 4, 5)$ are to be evaluated with IVPFNs with the four criteria by three experts $V E_{t} (t = 1, 2, 3)$ (Suppose expert’s weight is (0.2399, 0.2695, 0.4906).

Table 1
Linguistic scale and IVPFNs [78]

Linguistic terms	IVPFNs
Exceedingly Terrible-VET	$⟨ [0.00, 0.10], [0.85, 0.90] ⟩$
Very Terrible-VVT	$⟨ [0.00, 0.10], [0.70, 0.75] ⟩$
Terrible-VT	$⟨ [0.30, 0.40], [0.45, 0.50] ⟩$
Medium-VM	$⟨ [0.40, 0.50], [0.35, 0.40] ⟩$
Well-VW	$⟨ [0.60, 0.70], [0.15, 0.20] ⟩$
Very Well-VVW	$⟨ [0.70, 0.80], [0.05, 0.10] ⟩$
Exceedingly Well-VEW	$⟨ [1.00, 1.00], [0.00, 0.00] ⟩$

The IVPF-ExpTODIM method is used to solve the new-media information communication influence evaluation from super intellctual property.

Step 1. Construct the IVPFN matrix $V R = {[V R_{i j}^{t}]}_{5 \times 6}$ through linguistic scale (see Tables 2–4).

Table 2

Evaluation information through $V E_{1}$

	VG₁	VG₂	VG₃	VG₄	VG₅	VG₆
VA₁	VW	VVW	VVT	VT	VVW	VW
VA₂	VM	VW	VT	VM	VM	VW
VA₃	VW	VVW	VT	VM	VVW	VT
VA₄	VVT	VVT	VM	VW	VM	VVW
VA₅	VM	VT	VVW	VW	VVT	VM

Table 3

Evaluation information through $V E_{2}$

	VG₁	VG₂	VG₃	VG₄	VG₅	VG₆
VA₁	VM	VT	VVW	VW	VW	VVW
VA₂	VVT	VM	VVW	VT	VVT	VVT
VA₃	VT	VW	VM	VVW	VT	VM
VA₄	VVW	VW	VVT	VM	VT	VM
VA₅	VM	VW	VVT	VVW	VM	VW

Table 4

Evaluation information through $V E_{3}$

	VG₁	VG₂	VG₃	VG₄	VG₅	VG₆
VA₁	VW	VVW	VVT	VM	VW	VM
VA₂	VVT	VVW	VM	VVT	VM	VT
VA₃	VVW	VVT	VM	VT	VVW	VVT
VA₄	VW	VM	VVT	VVW	VVW	VM
VA₅	VM	VT	VVW	VW	VVW	VM

Then according to IVPFWA, the $V R = {[V R_{i j}]}_{5 \times 6}$ is obtained (see Table 5).

Table 5

The $V R = {[V R_{i j}]}_{5 \times 6}$

Alternatives	VG₂	VG₂
VA₁	([0.2725, 0.4663], [0.2017, 0.4312])	([0.2758, 0.4362], [0.3893, 0.4917])
VA₂	([0.2845, 0.3216], [0.3319, 0.4921])	([0.2494, 0.4145], [0.2834, 0.5235])
VA₃	([0.2214, 0.4703], [0.4216, 0.6038])	([0.3491, 0.6028], [0.2978, 0.4196])
VA₄	([0.4215, 0.6014], [0.3319, 0.7217])	([0.4032, 0.7034], [0.2531, 0.4265])
VA₅	([0.3027, 0.4615], [0.2598, 0.3523])	([0.3216, 0.7325], [0.2213, 0.3413])
Alternatives	VG₃	VG₄
VA₁	([0.2498, 0.4354], [0.4372, 0.6284])	([0.3489, 0.6536], [0.2836, 0.4874])
VA₂	([0.3721, 0.6323], [0.2938, 0.4753])	([0.4859, 0.8175], [0.2532, 0.3907])
VA₃	([0.4226, 0.7034], [0.2326, 0.3946])	([0.2539, 0.3598], [0.2936, 0.4449])
VA₄	([0.2276, 0.8258], [0.2936, 0.3745])	([0.2327, 0.4337] , [0.2997, 0.4989])
VA₅	([0.6217, 0.7496], [0.3558, 0.4357])	([0.3468, 0.4437], [0.4905, 0.6953])
Alternatives	VG₅	VG₆
VA₁	([0.2054, 0.7136], [0.2714, 0.3523])	([0.2105, 0.4116], [0.2765, 0.4628])
VA₂	([0.6021, 0.5274], [0.3336, 0.4135])	([0.3246, 0.4213], [0.4713, 0.6732])
VA₃	([0.2276, 0.4132], [0.4154, 0.6062])	([0.3267, 0.6314], [0.2614, 0.4226])
VA₄	([0.3509, 0.6101], [0.2715, 0.4532])	([0.4637, 0.7153], [0.2314, 0.3704])
VA₅	([0.4117, 0.5012], [0.2104, 0.3726])	([0.2428, 0.3465], [0.2714, 0.4225])

Step 2. Normalize the $V R = {[V R_{i j}]}_{5 \times 6}$ into $𝑁𝑉𝑅 = {[{𝑁𝑉𝑅}_{i j}]}_{5 \times 6}$ . Because all attributes are ones, Thus, $𝑁𝑉𝑅 = {[{𝑁𝑉𝑅}_{i j}]}_{5 \times 6}$ is equal to $V R = {[V R_{i j}]}_{5 \times 6}$ (see Table 6).

Table 6

The $𝑁𝑉𝑅 = {[{𝑁𝑉𝑅}_{i j}]}_{5 \times 6}$

Alternatives	VG₁	VG₂
VA₁	([0.2725, 0.4663], [0.2017, 0.4312])	([0.2758, 0.4362], [0.3893, 0.4917])
VA₂	([0.2845, 0.3216], [0.3319, 0.4921])	([0.2494, 0.4145], [0.2834, 0.5235])
VA₃	([0.2214, 0.4703], [0.4216, 0.6038])	([0.3491, 0.6028], [0.2978, 0.4196])
VA₄	([0.4215, 0.6014], [0.3319, 0.7217])	([0.4032, 0.7034], [0.2531, 0.4265])
VA₅	([0.3027, 0.4615], [0.2598, 0.3523])	([0.3216, 0.7325], [0.2213, 0.3413])
Alternatives	VG₃	VG₄
VA₁	([0.2498, 0.4354], [0.4372, 0.6284])	([0.3489, 0.6536], [0.2836, 0.4874])
VA₂	([0.3721, 0.6323], [0.2938, 0.4753])	([0.4859, 0.8175], [0.2532, 0.3907])
VA₃	([0.4226, 0.7034], [0.2326, 0.3946])	([0.2539, 0.3598], [0.2936, 0.4449])
VA₄	([0.2276, 0.8258], [0.2936, 0.3745])	([0.2327, 0.4337] , [0.2997, 0.4989])
VA₅	([0.6217, 0.7496], [0.3558, 0.4357])	([0.3468, 0.4437], [0.4905, 0.6953])
Alternatives	VG₅	VG₆
VA₁	([0.2054, 0.7136], [0.2714, 0.3523])	([0.2105, 0.4116], [0.2765, 0.4628])
VA₂	([0.6021, 0.5274], [0.3336, 0.4135])	([0.3246, 0.4213], [0.4713, 0.6732])
VA₃	([0.2276, 0.4132], [0.4154, 0.6062])	([0.3267, 0.6314], [0.2614, 0.4226])
VA₄	([0.3509, 0.6101], [0.2715, 0.4532])	([0.4637, 0.7153], [0.2314, 0.3704])
VA₅	([0.4117, 0.5012], [0.2104, 0.3726])	([0.2428, 0.3465], [0.2714, 0.4225])

Step 3. Compute the weight values (see Table 7).

Table 7

The attribute weight information

	VG₁	VG₂	VG₃	VG₄	VG₅	VG₆
$v w$	0.2058	0.1879	0.2045	0.1410	0.1504	0.1104

Step 4. Produce the relative weight (see Table 8).

Table 8

The relative weight information

	VG₁	VG₂	VG₃	VG₄	VG₅	VG₆
rvw	0.2058	0.1879	0.2045	0.1410	0.1504	0.1104

Step 5. Obtain the $D D = D D {(V A_{i}, V A_{t})}_{5 \times 5}$ matrix (see Table 9).

Table 9

The $D D = D D {(V A_{i}, V A_{t})}_{5 \times 5}$

Alternatives	VA₁	VA₂	VA₃	VA₄	VA₅
VA₁	0.0000	$-$ 3.0716	2.7464	$-$ 3.5794	1.7232
VA₂	$-$ 0.3668	0.0000	2.6734	0.2878	$-$ 3.6325
VA₃	2.6825	$-$ 4.1341	0.0000	$-$ 4.4350	2.5193
VA₄	$-$ 1.2176	$-$ 1.7165	3.2841	0.0000	$-$ 1.1803
VA₅	2.3884	$-$ 4.4248	$-$ 0.2087	$-$ 4.0909	0.0000

Step 6. Calculate the $𝑂𝐷𝐷 (V A_{i}) (i = 1, 2, \dots, 5)$ (Table 10).

Table 10

The $𝑂𝐷𝐷 (V A_{i}) (i = 1, 2, \dots, 5)$

Alternatives	VA₁	VA₂	VA₃	VA₄	VA₅
ODD	0.7546	0.9622	0.5392	1.0000	0.0000

Table 11

The $𝑂𝐷𝐷 (V A_{i}) (i = 1, 2, \dots, 5)$ for different $ρ$ values

$ρ$	VA₁	VA₂	VA₃	VA₄
$ρ = 1.0$	0.7546	0.9622	0.5392	1.0000
$ρ = 2.0$	0.7840	0.9648	0.5618	1.0000
$ρ = 3.0$	0.8146	0.9674	0.5844	1.0000
$ρ = 4.0$	0.8464	0.9700	0.6070	1.0000
$ρ = 5.0$	0.8794	0.9726	0.6296	1.0000

Step 6. Finally, the decision order could be obtained: $V A_{4} ≻ V A_{2} ≻ V A_{1} ≻ V A_{3} ≻ V A_{5}$ , and thus the optimal new media platform for spreading public opinion information on mobile internet networks is $V A_{4}$ .

4.2 Sensitivity analysis

Motivated through sensitivity analysis approach [79], in this subsection firstly, sensitivity analysis is managed to show the influence of attenuation parameter $ρ$ on the constructed results of the IVPF-ExpTODIM method technique under IVPFSs environment. The proposed IVPF-ExpTODIM method technique is managed considering two kinds of rational behaviors of DMs (risk aversion and risk seeking). Here, the parameter $ρ$ is primarily implemented as being discrete and varying between [1, 5], with 1 indicating little sensitivity to the result and 5 extreme sensitivity to the final decision result. This choice is justified mainly by the ease of obtaining an estimated value to the parameter $ρ$ from a discrete Likert scale, this scale being a scientifically accepted and validated manner to measure subjectivity [80]. The sensitivity analysis results are constructed in Table 11.

4.3 Comparative analysis

Then, the IVPF-ExpTODIM method is compared with interval-valued Pythagorean fuzzy Aczel-Alsina weighted average (IVPFAAWA) operator [81], interval-valued Pythagorean fuzzy Weighted Aggregated Sum Product Assessment (IVPFWASPAS) method [82] and interval-valued Pythagorean fuzzy Qualitative Flexible Multiple Criteria (IVPF-QUALIFLEX) method [83], interval-valued Pythagorean fuzzy technique for order of preference by similarity to ideal solution (IVPF-TOPSIS) method [84]. The comparative decision results are shown in Table 12.

Table 12
Order of the different methods

Methods	Order
IVPFAAWA operator [81]	$V A_{4} ≻ V A_{2} ≻ V A_{3} ≻ V A_{1} ≻ V A_{5}$
IVPF-WASPAS method [82]	$V A_{4} ≻ V A_{2} ≻ V A_{1} ≻ V A_{3} ≻ V A_{5}$
IVPF-QUALIFLEX method [83]	$V A_{4} ≻ V A_{2} ≻ V A_{1} ≻ V A_{3} ≻ V A_{5}$
IVPF-TOPSIS method [84]	$V A_{4} ≻ V A_{2} ≻ V A_{1} ≻ V A_{3} ≻ V A_{5}$
IVPF-ExpTODIM method	$V A_{4} ≻ V A_{2} ≻ V A_{1} ≻ V A_{3} ≻ V A_{5}$

Figure 1.

The $𝑂𝐷𝐷 (V A_{i}) (i = 1, 2, \dots, 5)$ for different $ρ$ values.

In accordance with WS coefficients [85, 86], the WS coefficient calculation between interval-valued Pythagorean fuzzy Aczel-Alsina weighted average (IVPFAAWA) operator [81], interval-valued Pythagorean fuzzy Weighted Aggregated Sum Product Assessment (IVPF-WASPAS) method [82] and interval-valued Pythagorean fuzzy Qualitative Flexible Multiple Criteria (IVPF-QUALIFLEX) method [83], interval-valued Pythagorean fuzzy technique for order of preference by similarity to ideal solution (IVPF-TOPSIS) method [84] and the proposed IVPF-ExpTODIM method is 0.6250, 1.0000, 1.0000, 1.0000, respectively. The WS coefficient calculation shows that the order result of IVPF-WASPAS method, IVPF-QUALIFLEX method and IVPF-TOPSIS method is same with the order result of the proposed IVPF-ExpTODIM method. From the above detailed analysis, it could be seen that the order of these five models is slightly different, however, these five models have the same optimal new media platform for spreading public opinion information on mobile internet networks and worst new media platform for spreading public opinion information on mobile internet networks. This shows the IVPF-ExpTODIM method is reasonable and effective.

5. Conclusion

The rapid development of mobile internet and social networks has ushered in a new era of information dissemination in human society. Traditional government media is actively exploring new media models based on social networks while maintaining their inherent communication channels. In the new media environment of social networks, users have shifted from obtaining government information in newspapers, magazines, television, and traditional websites to using mobile devices such as smartphones and iPads to obtain information. Government departments and relevant institutions have also established new media platforms such as WeChat official account, institutional microblog account, Tiktok video account to achieve information release, livelihood services, public opinion guidance, government and people communication, and image building. With the continuous development of social network-related technologies, people’s information interaction behavior under social media has also undergone significant changes. Applications such as social networks, cloud computing, mobile networks, and the Internet of Things have had a comprehensive impact on the information production and consumption of network users, changing the relationship between users and information, as well as the relationship between users and users. The academic community has also invested more energy in the research of information behavior related issues of network users in the new generation of internet environment, and is constantly expanding and innovating to propose new discoveries. The new-media information communication influence evaluation from super intellectual property (IP) perspective is a classical multiple attribute group decision making (MAGDM) problems. Recently, the Exponential TODIM (an acronym in Portuguese of interactive and multicriteria decision making) method has been used to cope with MAGDM issues. The interval-valued Pythagorean fuzzy sets (IVPFSs) are used as a tool for characterizing uncertain information during the new-media information communication influence evaluation from super intellectual property. In this manuscript, the interval-valued Pythagorean fuzzy Exponential TODIM(ExpTODIM) (IVPF-ExpTODIM) method is built to solve the MAGDM under IVPFSs. The information Entropy is used to obtain the weight values based on the score value and accuracy value under IVPFSs. In the end, a numerical case study for new-media information communication influence evaluation from super intellectual property is given to validate the proposed method.

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Innovative ExpTODIM algorithm for interval-valued Pythagorean fuzzy information and new-media information communication influence evaluation

Abstract

Keywords

1. Introduction

2. Preliminaries

4.1 An empirical example

Table 1 Linguistic scale and IVPFNs [78]

4.3 Comparative analysis

Table 12 Order of the different methods

References

Table 1
Linguistic scale and IVPFNs [78]

Table 12
Order of the different methods