Home A novel framework for single-valued neutrosophic MADM and applications to English-blended teaching quality evaluation
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A novel framework for single-valued neutrosophic MADM and applications to English-blended teaching quality evaluation

  • Zhiqiang Miao EMAIL logo
Published/Copyright: April 23, 2024
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Journal of Intelligent Systems
From the journal Journal of Intelligent Systems Volume 33 Issue 1

Abstract

In the context of “Internet plus,” college English-teaching resources are increasingly rich. Research has found that implementing a blended teaching model for college English based on the Super Star Learning Communication and Rain Classroom online teaching platform is beneficial for improving students’ enthusiasm and continuity in English learning. The English-blended teaching quality evaluation is a multiple attribute decision making (MADM). The single-valued neutrosophic set (SVNS) is a useful tool to depict uncertain information during the English-blended teaching quality evaluation. In such an article, the single-valued neutrosophic number Aczel–Alsina power geometric (SVNNAAPG) operator is produced based on the Aczel–Alsina operations and classical power geometric operator under SVNSs. The SVNNAAPG operator is built for MADM. Eventually, an example about English-blended teaching quality evaluation and some selected comparative analysis was used to depict the SVNNAAPG technique.

Keywords: multiple-attribute decision-making; single-valued neutrosophic sets; power geometric; English-blended teaching quality evaluation

1 Introduction

At present, there are many teaching techniques for college English. Traditional college English teaching is taught in the form of blackboard writing or multimedia courseware, allowing students to learn and memorize words, sentence patterns, and grammar [1,2,3]. Currently, the blended teaching model of “online + offline” is popular among college English teachers. Of course, both traditional and blended teaching models have their own advantages and disadvantages [4,5,6]. The blended teaching mode is composed of two parts: online (online teaching platform) teaching and offline (face-to-face teaching) teaching [7,8,9]. There are many online teaching platforms suitable for college English courses now, such as Super-Star Learning Pass, Rain Classroom, Ding-Talk Live Teaching, and China University MOOC Platform. These platforms are based on the current network environment, with extremely rich content, and are convenient and fast teaching tools. Diversified teaching techniques can effectively promote students’ learning of college English courses [10,11,12]. Students can independently learn English courses, complete learning content, tests, and examinations through the Super Star Learning Platform. More importantly, the pre-class and post-class parts of the blended teaching model supplement and actively extend traditional classroom teaching. If students are confused about learning, they can check the platform’s learning materials at any time and repeatedly watch instructional videos, teaching courseware, audio, and other content. In short, the Super-Star Learning Platform is a very suitable teaching platform for students, and teachers should effectively utilize this platform to provide assistance for college English teaching [13,14,15]. Whether it is online teaching based on Superstar Learning Connect or Rain Classroom online teaching platforms, or offline teaching with face-to-face teaching, teachers must find a balance point and effectively combine the two to maximize their effectiveness. In terms of online teaching, teachers and students should master platform usage skills; teachers carefully design the best teaching content and process; teachers supervise and supervise students’ E-learning and encourage students to actively study and review. It is a meaningful exploration to apply blended teaching mode to college English teaching based on the Super Star Learning Communication and Rain Classroom online teaching platform [16,17]. How to cleverly and silently make college English classrooms more efficient and interesting remains an important topic that college English teachers need to explore seriously. In summary, college English teachers should keep up with the pace of the times, constantly explore new teaching models, continuously improve the college English teaching effectiveness, and enhance students’ English literacy [18,19,20].

The multiple attribute decision making (MADM) is the important research technique in modern decision science [21,22,23,24,25,26,27,28,29]. In order to depict uncertain information, Zadeh [30] implemented fuzzy sets. Atanassov [31] structured the intuitionistic fuzzy sets. To depict inconsistency information, Smarandache [32] structured the neutrosophic sets. Wang et al. [33] structured the single-valued neutrosophic sets (SVNSs). Aczél and Alsina [34] structured the Aczel–Alsina t-norm techniques and t-conorm techniques. Yong et al. [35] and Ashraf et al. [36] structured the Aczel–Alsina operations to SVNNs. The English-blended teaching quality evaluation is a MADM. The SVNS [38] is a useful tool to depict uncertain information during the English-blended teaching quality evaluation. The main contribution of this article is to produce the power geometric (PG) operators based on the Aczel–Alsina techniques and classical PG operator [37] under SVNNs. Thus, the SVNN Aczel–Alsina PG (SVNNAAPG) operator is produced based on the Aczel–Alsina techniques and classical PG operator under SVNSs. The SVNNAAPG operator is implemented for MADM. Eventually, an example about English-blended teaching quality evaluation and some selected comparative analysis is implemented. In order to implement so, the framework of this article is implemented. The SVNS is implemented in Section 2. The SVNNAAPG operators are implemented in Section 3. The MADM based on the SVNNAAPG technique is implemented in in Section 4. An example for English-blended teaching quality evaluation is implemented in Section 5. The conclusion is implemented in Section 6.

2 Preliminaries

Wang et al. [38] implemented the SVNSs

Definition 1

[38]. The SVNS is implemented:

(1) OA = { ( θ , OT A ( θ ) , OI A ( θ ) , OF A ( θ ) ) ∣ θ ∈ X } ,

where OT A ( θ ) , OI A ( θ ) , OF A ( θ ) is truth-membership, indeterminacy-membership and falsity-membership, OT A ( θ ) , OI A ( θ ) , OF A ( θ ) ∈ [ 0 , 1 ] , 0 ≤ OT A ( θ ) + OI A ( θ ) + OF A ( θ ) ≤ 3 .

The SVNN is structured as OA = ( OT A , OI A , OF A ) , where OT A ∈ [ 0 , 1 ] , OI A ∈ [ 0 , 1 ] , OF A ∈ [ 0 , 1 ] , and 0 ≤ OT A + OI A + OF A ≤ 3 .

Definition 2

[39]. Let OA = ( OT A , OI A , OF A ) , and the score value is as follows:

(2) OSV ( OA ) = ( 2 + OT A − OI A − OF A ) 3 , OSV ( OA ) ∈ [ 0 , 1 ] .

Definition 3

[39]. Let OA = ( OT A , OI A , OF A ) , and the accuracy value is as follows:

(3) OAV ( OA ) = OT A − OF A , OAV ( OA ) ∈ [ − 1 , 1 ] .

Peng et al. [39] implemented the order relation.

Definition 4

[39]. Let OA = ( OT A , OI A , OF A ) and OB = ( OT B , OI B , OF B ) , let OSV ( OA ) = ( 2 + OT A − OI A − OF A ) 3 and OSV ( OB ) = ( 2 + OT B − OI B − OF B ) 3 , and let OAV ( OA ) = OT A − OF A and OAV ( OB ) = OT B − OF B , if OSV ( OA ) < OSV ( OB ) , OA < OB ; if OSV ( OA ) = OSV ( OB ) , (1) if OAV ( OA ) = OAV ( OB ) , OA = OB ; (2) if OAV ( OA ) < OAV ( OB ) , OA < OB .

Definition 5

[36,38]. Let OA = ( OT A , OI A , OF A ) and OB = ( OT B , OI B , OF B ) , a θ ≥ 1 , a λ > 0 , and the structured Aczel–Alsina operations with SVNNs are as follows:

( 1 ) OA ⊕ OB = 1 − e − ( ( − ln ( 1 − OT A ) ) a θ + ( − ln ( 1 − OT B ) ) a θ ) 1 / a θ , e − ( ( − ln ( OI A ) ) a θ + ( − ln ( OI B ) ) a θ ) 1 / a θ , e − ( ( − ln ( OF A ) ) a θ + ( − ln ( OF B ) ) a θ ) 1 / a θ ;

( 2 ) OA ⊗ OB = e − ( ( − ln ( OT A ) ) a θ + ( − ln ( OT B ) ) a θ ) 1 / a θ , 1 − e − ( ( − ln ( 1 − OI A ) ) a θ + ( − ln ( 1 − OI B ) ) a θ ) 1 / a θ , 1 − e − ( ( − ln ( 1 − OF A ) ) a θ + ( − ln ( 1 − OF B ) ) a θ ) 1 / a θ ;

( 3 ) a λ OA = ( 1 − e − ( a λ ( − ln ( 1 − OT A ) ) a θ ) 1 / a θ , e − ( a λ ( − ln ( OI A ) ) a θ ) 1 / a θ , e − ( a λ ( − ln ( OF A ) ) a θ ) 1 / a θ ) ;

( 4 ) ( OA ) a λ = ( e − ( a λ ( − ln ( OT A ) ) a θ ) 1 / a θ , 1 − e − ( a λ ( − ln ( 1 − OI A ) ) a θ ) 1 / a θ , 1 − e − ( a λ ( − ln ( 1 − OF A ) ) a θ ) 1 / a θ ) ;

3 SNNAAPG operator

Yong et al. [35] and Ashraf et al. [36] defined the SVNNAAWG operator.

Definition 6

Let OA i = ( OT i , OI i , OF i ) ( i = 1 , 2 , … , n ) be the SVNNs with weight o w i = ( o w 1 , o w 2 , … , o w n ) T , ∑ i = 1 n o w i = 1 , a θ ≥ 1 . If

(4) SVNNAAWG o w ( OA 1 , OA 2 , … , OA n ) = ⊗ i = 1 n ( OA i ) o w i = e − ∑ i = 1 n o w i ( − ln ( 1 − OT j ) ) a θ 1 / a θ , 1 − e − ∑ i = 1 n o w i ( − ln ( OI j ) ) a θ 1 / a θ , 1 − e − ∑ i = 1 n o w i ( − ln ( OF j ) ) a θ 1 / a θ .

The SVNNAAWG has three properties.

Property 1

(idempotency). If OA i = OA = ( OT , OI , OF ) ,

(5) SVNNAAWG o w ( OA 1 , OA 2 , … , OA n ) = OA .

Property 2. (Monotonicity). Let OA i = ( OT A i , OI A i , OF A i ) and OB i = ( OT B i , OI B i , OF B i ) . If OT A i ≤ OT B i , OI A i ≥ OI B i , OF A i ≥ OF B i holds for all i, then

(6) SVNNAAWG o w ( OA 1 , OA 2 , … , OA n ) ≤ SVNNAAWG o w ( OB 1 , OB 2 , ⋯ , OB n ) .

Property 3

(Boundedness). Let OA i = ( OT A i , OI A i , OF A i ) . If

OA + = ( max i ( OT i ) , min i ( OI i ) , min i ( OF i ) ) , OA − = ( min i ( OT i ) , max i ( OI i ) , max i ( OF i ) ) , then

(7) OA − ≤ SVNNAAWG o w ( OA 1 , OA 2 , … , OA n ) ≤ OA + .

Then, the SVNNAAPG operator is implemented on SVNNAAWG technique and PG technique [37].

Definition 7

Let OA i = ( OT i , OI i , OF i ) ( i = 1 , 2 , … , n ) be the SVNNs, a θ ≥ 1 . If

(8) SVNNAAPG ( OA 1 , OA 2 , … , OA n ) = ⊗ i = 1 n ( OA i ) ( 1 + OT ( OA i ) ) / ∑ i = 1 n ( 1 + OT ( OA i ) ) ,

where OT ( OA a ) = ∑ j = 1 a ≠ j m Sup ( OA a , OA j ) , Sup ( OA a , OA j ) is the decision support for OA a from OA j , with given decision conditions: (1) Sup ( OA a , OA b ) ∈ [ 0 , 1 ] ; (2) Sup ( OA b , OA a ) = Sup ( OA a , OA b ) ; (3) Sup ( OA a , OA b ) ≥ Sup ( OA s , OA t ) , if d ( OA a , OA b ) ≥ d ( OA s , OA t ) , where d is the distance information.

Theorem 2 is implemented.

Theorem 2

Let O A i = ( O T i , O I i , O F i ) ( i = 1 , 2 , … , n ) be the SVNNs, a θ ≥ 1 . If

(9) SVNNAAPG ( OA 1 , OA 2 , ⋯ , OA n ) = ⊗ i = 1 n ( O A i ) ( 1 + OT ( OA i ) ) / ∑ i = 1 n ( 1 + OT ( OA i ) ) = e − ∑ i = 1 n ( 1 + OT ( OA i ) ) ∑ i = 1 n ( 1 + OT ( OA i ) ) ( − ln ( 1 − OT j ) ) a θ 1 / a θ , 1 − e − ∑ i = 1 n ( 1 + OT ( OA i ) ) ∑ i = 1 n ( 1 + OT ( OA i ) ) ( − ln ( II j ) ) a θ 1 / a θ , 1 − e − ∑ i = 1 n ( 1 + OT ( OA i ) ) ∑ i = 1 n ( 1 + OT ( OA i ) ) ( − ln ( OF j ) ) a θ 1 / a θ ,

where OT ( OA a ) = ∑ j = 1 a ≠ j m Sup ( OA a , OA j ) , Sup ( OA a , OA j ) is the decision support for OA a from OA j , with given decision conditions: (1) Sup ( OA a , OA b ) ∈ [ 0 , 1 ] ; (2) Sup ( OA b , OA a ) = Sup ( OA a , OA b ) ; (3) Sup ( OA a , OA b ) ≥ Sup ( OA s , OA t ) , if d ( OA a , OA b ) ≥ d ( OA s , OA t ) , where d is the distance information.

Proof:

  1. Let i = 2 , then

    SVNNAAPG ( OA 1 , OA 2 ) = ( OA 1 ) ( 1 + OT ( OA 1 ) ) / ∑ i = 1 2 ( 1 + OT ( OA 1 ) ) ⊗ ( OA 2 ) ( 1 + OT ( OA 2 ) ) / ∑ i = 1 2 ( 1 + OT ( OA 2 ) )

    = e − ( 1 + OT ( OA 1 ) ) ∑ i = 1 2 ( 1 + OT ( OA 1 ) ) ( − ln ( 1 − OT 1 ) ) a θ 1 / a θ , 1 − e − ( 1 + OT ( OA 1 ) ) ∑ i = 1 2 ( 1 + OT ( OA 1 ) ) ( − ln ( OI 1 ) ) a θ 1 / a θ , 1 − e − ( 1 + OT ( OA 1 ) ) ∑ i = 1 2 ( 1 + OT ( OA 1 ) ) ( − ln ( OF 1 ) ) a θ 1 / a θ ⊗ e − ( 1 + OT ( OA 2 ) ) ∑ i = 1 2 ( 1 + OT ( OA 2 ) ) ( − ln ( 1 − OT 2 ) ) a θ 1 / a θ , 1 − e − ( 1 + OT ( OA 2 ) ) ∑ i = 1 2 ( 1 + OT ( OA 2 ) ) ( − ln ( OI 2 ) ) a θ 1 / a θ , 1 − e − ( 1 + OT ( OA 2 ) ) ∑ i = 1 2 ( 1 + OT ( OA 2 ) ) ( − ln ( O F 2 ) ) a θ 1 / a θ

    = e − ∑ i = 1 2 ( 1 + O T ( O A i ) ) ∑ i = 1 n ( 1 + O T ( O A i ) ) ( − ln ( 1 − O T j ) ) a θ 1 / a θ , 1 − e − ∑ i = 1 2 ( 1 + O T ( O A i ) ) ∑ i = 1 n ( 1 + O T ( O A i ) ) ( − ln ( O I j ) ) a θ 1 / a θ , 1 − e − ∑ i = 1 2 ( 1 + O T ( O A i ) ) ∑ i = 1 n ( 1 + O T ( O A i ) ) ( − ln ( O F j ) ) a θ 1 / a θ

  2. If equation (9) holds for i = k , then

    SVNNAAPG ( OA 1 , OA 2 , … , OA k ) = ⊗ i = 1 k ( O A i ) ( 1 + OT ( OA i ) ) / ∑ i = 1 n ( 1 + OT ( OA i ) ) = e − ∑ i = 1 k ( 1 + OT ( OA i ) ) ∑ i = 1 k ( 1 + OT ( OA i ) ) ( − ln ( 1 − OT j ) ) a θ 1 / a θ , 1 − e − ∑ i = 1 k ( 1 + OT ( OA i ) ) ∑ i = 1 k ( 1 + OT ( OA i ) ) ( − ln ( OI j ) ) a θ 1 / a θ , 1 − e − ∑ i = 1 k ( 1 + OT ( OA i ) ) ∑ i = 1 k ( 1 + OT ( OA i ) ) ( − ln ( OF j ) ) a θ 1 / a θ .

  3. Set i = k + 1 . Based on Definition 5 and equation (9), we obtain

SVNNAAPG ( OA 1 , OA 2 , ⋯ , OA k , OA k + 1 ) = ⊗ i = 1 k ( OA i ) ( 1 + OT ( OA i ) ) / ∑ i = 1 n ( 1 + OT ( OA i ) ) ⊗ ( OA k + 1 ) ( 1 + OT ( OA k + 1 ) ) / ∑ i = 1 k + 1 ( 1 + OT ( OA i ) )

= e ‒ ∑ i = 1 k ( 1 + OT ( OA i ) ) ∑ i = 1 k ( 1 + OT ( OA i ) ) ( ‒ ln ( 1 ‒ OT j ) ) a θ 1 / a θ , 1 ‒ e ‒ ∑ i = 1 k ( 1 + OT ( OA i ) ) ∑ i = 1 k ( 1 + OT ( OA i ) ) ( ‒ ln ( OI j ) ) a θ 1 / a θ , 1 ‒ e ‒ ∑ i = 1 k ( 1 + OT ( OA i ) ) ∑ i = 1 k ( 1 + OT ( OA i ) ) ( ‒ ln ( OF j ) ) a θ 1 / a θ ⊗ e ‒ ( 1 + OT ( OA k + 1 ) ) ∑ i = 1 k + 1 ( 1 + OT ( OA i ) ) ( ‒ ln ( 1 ‒ OT k + 1 ) ) a θ 1 / a θ , 1 ‒ e ‒ ( 1 + OT ( OA k + 1 ) ) ∑ i = 1 k + 1 ( 1 + OT ( OA i ) ) ( ‒ ln ( OI k + 1 ) ) a θ 1 / a θ , 1 ‒ e ‒ ( 1 + OT ( OA k + 1 ) ) ∑ i = 1 k + 1 ( 1 + OT ( OA i ) ) ( ‒ ln ( OF k + 1 ) ) a θ 1 / a θ

= e − ∑ i = 1 k + 1 ( 1 + OT ( OA i ) ) ∑ i = 1 k + 1 ( 1 + OT ( OA i ) ) ( − ln ( 1 − OT j ) ) a θ 1 / a θ , 1 − e − ∑ i = 1 k + 1 ( 1 + OT ( OA i ) ) ∑ i = 1 k + 1 ( 1 + OT ( OA i ) ) ( − ln ( OI j ) ) a θ 1 / a θ , 1 − e − ∑ i = 1 k + 1 ( 1 + OT ( OA i ) ) ∑ i = 1 k + 1 ( 1 + OT ( OA i ) ) ( − ln ( OF j ) ) a θ 1 / a θ .

From (a), (b), and (c), it can be seen that equation (9) meets any given i.

The SVNNAAPG has three properties.

Property 4

(idempotency). If OA i = OA = ( OT , OI , OF ) ,

(10) SVNNAAPG ( OA 1 , OA 2 , … , OA n ) = OA .

Property 5

(Monotonicity). Let OA i = ( OT A i , OI A i , OF A i ) and OB i = ( OT B i , OI B i , OF B i ) . If OT A i ≤ OT B i , OI A i ≥ OI B i , OF A i ≥ OF B i holds for all i, then

(11) SVNNAAPG ( OA 1 , OA 2 , … , OA n ) ≤ SVNNAAPG ( OB 1 , OB 2 , ⋯ , OB n ) .

Property 6

(Boundedness). Let OA i = ( OT A i , OI A i , OF A i ) . If

(12) OA + = ( max i ( OT i ) , min i ( OI i ) , min i ( OF i ) ) , OA − = ( min i ( OT i ) , max i ( OI i ) , max i ( OF i ) ) , then OA − ≤ SVNNAAPG ( OA 1 , OA 2 , … , OA n ) ≤ OA + .

4 MADM technique based on SVNNAAPG under SVNNs

Then, the SVNNAAPG technique is implemented for MADM with SVNSs. Let OZ = { OZ 1 , OZ 2 , … , OZ n } be attributes. Let OP = { OP 1 , OP 2 , … , OP m } be alternatives. OQ = ( OQ i j ) m × n = ( OT i j , OI i j , OF i j ) m × n is the SVNN matrix. The SVNNAAPG technique for MADM will be structured.

Step 1. Structure SVNN matrix OQ = ( OQ i j ) m × n = ( OT i j , OI i j , OF i j ) m × n .

(13) OQ = [ OQ i j ] m × n = OQ 11 OQ 12 … OQ 1 n OQ 21 OQ 22 … OQ 2 n ⋮ ⋮ ⋮ ⋮ OQ m 1 OQ m 2 … OQ m n ,

(14) OQ = [ OQ i j ] m × n = ( OT i j , OI i j , OF i j ) m × n = ( OT 11 , OI 11 , OF 11 ) ( OT 12 , OI 1 , OF 12 ) … ( OT 1 n , OI 1 n , OF 1 n ) ( OT 21 , OI 21 , OF 21 ) ( OT 22 ,OI 22 ,OF 22 ) … ( OT 2 n , OI 2 n , OF 2 n ) ⋮ ⋮ ⋮ ⋮ ( OT m 1 , OI m 1 , OF m 1 ) ( OT m 2 , OI m 2 , OF m 2 ) … ( OT m n , OI m n , OF m n ) .

Step 2. Normalize the OQ = ( OQ i j ) m × n = ( OT i j , OI i j , OF i j ) m × n to NOQ = [ NOQ i j ] m × n = ( NOT i j , NOI i j , NOF i j ) m × n .

(15) NOQ i j = ( NOT i j , NOI i j , NOF i j ) = ( OT i j , OI i j , OF i j ) , OZ j is a benefit criterion ( OF i j , 1 − OI i j , OT i j ) , OZ j is a cost criterion .

Step 3. According to NOQ = [ NOQ i j ] m × n = ( NOT i j , NOI i j , NOF i j ) m × n , we could conduct all SVNNs NOQ = [ NOQ i j ] m × n = ( NOT i j , NOI i j , NOF i j ) m × n through employing the SVNNAAPG technique to obtain the SVNNs: NOQ i = ( NOT i , NOI i , NOF i ) ( i = 1 , 2 , … , m ) :

(16) NOQ i = SVNNAAPG ( NOQ i 1 , NOQ i 2 , ⋯ , NOQ i n ) = ⊗ j = 1 n ( NOQ i j ) ( 1 + OT ( NOQ i j ) ) / ∑ j = 1 n ( 1 + T ( NOQ i j ) ) = e − ∑ i = 1 n ( 1 + OT ( NOQ i j ) ) ∑ j = 1 n ( 1 + OT ( NOQ i j ) ) ( − ln ( 1 − NOT i j ) ) a θ 1 / a θ , 1 − e − ∑ j = 1 n ( 1 + OT ( NOQ i j ) ) ∑ j = 1 n ( 1 + OT ( NOQ i j ) ) ( − ln ( NOI i j ) ) a θ 1 / a θ , 1 − e − ∑ j = 1 n ( 1 + OT ( NOQ i j ) ) ∑ j = 1 n ( 1 + OT ( NOQ i j ) ) ( − ln ( NOF i j ) ) a θ 1 / a θ .

Step 4. Construct the OSV ( NOQ i ) , OAV ( NOQ i ) ( i = 1 , 2 , … , m ) .

(17) OSV ( NOQ i ) = ( 2 + NOT i − NOI i − NOF i ) 3 , OAV ( NOQ i ) = NOT i − NOF i .

Step 5. Rank the OP i ( i = 1 , 2 , … , m ) through OSV ( NOQ i ) and OAV ( NOQ i ) .

5 Numerical example and comparative studies

5.1 Numerical example

With the development of internet technology, education and teaching work needs to keep up with the times to adapt to the development of today’s society and meet the learning needs of students. The traditional teaching model usually consists of five parts: stimulating learning motivation, reviewing the previous lesson, teaching new lessons, consolidating knowledge, and taking examinations. This model is teacher-centered, and students passively learn. It emphasizes students’ digestion and understanding of the lecture content, treating students as receivers and recipients of previous knowledge and experience, and neglecting that students are people with creative thinking and subjective initiative. College English course is a public basic compulsory course for non-English major students, which includes content in different fields such as history, technology, economy, culture, and society. The teaching goal is to cultivate students’ English listening, speaking, reading, and writing skills, so that they can communicate information in English in the future, improve their cultural literacy, cultivate their self-learning ability, and adapt it to the needs of international exchange and future social development. Students will learn many articles related to history, culture, technology, and other aspects, and improve their English application skills through the conversion between English and Chinese. Nowadays, more and more teaching researchers advocate blended teaching models. Under the background of “Internet plus,” many colleges and universities have carried out educational informatization reform based on Internet technology, aiming to find a teaching mode that meets the current social development trend and students’ learning needs. The information-based teaching technique fully utilizes online teaching platforms, mobilizes teaching media and information resources, and creates a high-quality learning environment, and students actively and effectively learn under the guidance of teachers. The blended teaching mode integrates the advantages of information technology teaching and traditional teaching, and teachers and students need to play new roles in teaching. At present, open teaching platforms such as Rain Classroom, Ding-Talk, Superstar Learning Connect, and China University MOOC have been widely applied to college English teaching, and major universities are actively carrying out various attempts. The English-blended teaching quality evaluation is MADM. In this article, an example of English-blended teaching quality evaluation is implemented through SVNNAAPG technique. There are five English blended teaching colleges are evaluated in line with four defined attributes: ① OZ1 is student feedback; ② OZ2 is blended teaching costs; ③ OZ3 is blended teaching attitude; ④ OZ4 is invited peer expert recognition. Evidently, only OZ2 is the cost. Then, the SVNNAAPG technique is implemented to MADM for English-blended teaching quality evaluation under SVNNs.

Step 1. Implement the SVNN matrix OQ = ( OQ i j ) 5 × 4 as in Table 1.

Table 1

SVNN matrix

OZ1 OZ2 OZ3 OZ4
OP1 (0.55, 0.51, 0.35) (0.58, 0.34, 0.47) (0.59, 0.24, 0.53) (0.53, 0.36, 0.34)
OP2 (0.52, 0.27, 0.56) (0.37, 0.26, 0.42) (0.54, 0.28, 0.59) (0.58, 0.27, 0.54)
OP3 (0.34, 0.52, 0.38) (0.28, 0.39, 0.45) (0.36, 0.23, 0.37) (0.35, 0.24, 0.36)
OP4 (0.39, 0.32, 0.63) (0.32, 0.43, 0.38) (0.34, 0.15, 0.52) (0.52, 0.23, 0.28)
OP5 (0.41, 0.26, 0.54) (0.57, 0.16, 0.35) (0.51, 0.36, 0.54) (0.56, 0.29, 0.61)

Step 2. Normalize OQ = ( OQ i j ) 5 × 4 to NOQ = [ NOQ i j ] 5 × 4 (Table 2).

Table 2

NQ matrix

OZ1 OZ2 OZ3 OZ4
OP1 (0.55, 0.51, 0.35) (0.47, 0.66, 0.58) (0.59, 0.24, 0.53) (0.53, 0.36, 0.34)
OP2 (0.52, 0.27, 0.56) (0.42, 0.74, 0.37) (0.54, 0.28, 0.59) (0.58, 0.27, 0.54)
OP3 (0.34, 0.52, 0.38) (0.45, 0.61, 0.28) (0.36, 0.23, 0.37) (0.35, 0.24, 0.36)
OP4 (0.39, 0.32, 0.63) (0.38, 0.57, 0.32) (0.34, 0.15, 0.52) (0.52, 0.23, 0.28)
OP5 (0.41, 0.26, 0.54) (0.35, 0.84, 0.57) (0.51, 0.36, 0.54) (0.56, 0.29, 0.61)

Step 3. Obtain the NOQ i ( i = 1 , 2 , 3 , 4 , 5 ) by utilizing SVNNAAPG technique (Table 3).

Table 3

NOQ i ( i = 1 , 2 , 3 , 4 , 5 ) by SVNNAAPG operator ( θ = 2 )

Alternatives NOQ i ( i = 1 , 2 , 3 , 4 , 5 )
OP1 (0.4126,0.3435,0.3072)
OP2 (0.7276,0.2324,0.3769)
OP3 (0.4756,0.5142,0.3443)
OP4 (0.5325,0.4436,0.3212)
OP5 (0.6164,0.6438,0.3096)

Step 4. Obtain the OSV ( NOQ i ) ( i = 1 , 2 , 3 , 4 , 5 ) (Table 4).

Table 4

OSV ( NOQ i ) ( i = 1 , 2 , 3 , 4 , 5 )

Alternatives OSV ( NOQ i ) ( i = 1 , 2 , 3 , 4 , 5 ) Order
OP1 0.7443 5
OP2 0.8367 1
OP3 0.7719 4
OP4 0.7679 3
OP5 0.7723 2

Step 5. In line with Table 4, the decision order is OP 2 > OP 5 > OP 3 > OP 4 > OP 1 , and the best choice is XP2.

5.2 Influence analysis

To implement the effects on the final results in line with different parameters of SVNNAAPG technique, the final results are implemented in Tables 5 and 6.

Table 5

Different parameters for SVNNAAPG technique

θ OSV ( OP 1 ) OSV ( OP 2 ) OSV ( OP 3 ) OSV ( OP 4 ) OSV ( OP 5 )
1 0.5261 0.6626 0.5548 0.5658 0.5791
2 0.7443 0.8367 0.7719 0.7679 0.7723
3 0.8043 0.8687 0.8272 0.8100 0.8300
4 0.8272 0.8774 0.8481 0.8228 0.8549
5 0.8383 0.8809 0.8588 0.8281 0.8684
6 0.8448 0.8826 0.8657 0.8310 0.8767
7 0.8490 0.8839 0.8705 0.8329 0.8822
8 0.8521 0.8850 0.8742 0.8345 0.8862
9 0.8543 0.8859 0.8772 0.8358 0.8893
10 0.8563 0.8869 0.8798 0.8368 0.8917
Table 6

Different order for SVNNAAPWG

θ Order
1 OP 2 > OP 5 > OP 4 > OP 3 > OP 1
2 OP 2 > OP 5 > OP 3 > OP 4 > OP 1
3 OP 2 > OP 5 > OP 3 > OP 4 > OP 1
4 OP 2 > OP 5 > OP 3 > OP 1 > OP 4
5 OP 2 > OP 5 > OP 3 > OP 1 > OP 4
6 OP 2 > OP 5 > OP 3 > OP 1 > OP 4
7 OP 2 > OP 5 > OP 3 > OP 1 > OP 4
8 OP 2 > OP 5 > OP 3 > OP 1 > OP 4
9 OP 2 > OP 5 > OP 3 > OP 1 > OP 4
10 OP 2 > OP 5 > OP 3 > OP 1 > OP 4

It could be seen from Tables 5 and 6 that when different decision parameter is implemented, the priority is slightly different.

5.3 Comparative analysis

The SVNNAAPG operator is compared with SVNNWA technique and SVNNWG technique [39], single-valued neutrosophic number CODAS (SVNN-CODAS) technique [40], and single-valued neutrosophic number EDAS (SVNN-EDAS) technique [41]. The results are implemented in Table 7.

Table 7

Results for different techniques

Techniques Order
SVNNWA technique [39] OP 2 > OP 5 > OP 4 > OP 3 > OP 1
SVNNWG technique [39] OP 2 > OP 5 > OP 3 > OP 4 > OP 1
SVNN-CODAS technique [40] OP 2 > OP 5 > OP 3 > OP 4 > OP 1
SVNN-EDAS technique [41] OP 2 > OP 5 > OP 3 > OP 4 > OP 1
SVNNAAPG technique OP 2 > OP 5 > OP 3 > OP 4 > OP 1

From Table 7, it is obvious that the ordering results of these five models are slightly different; however, the optimal decision choice is OP2, while the worst decision choice is OP1. The proposed SVNNAAPG operator has several advantages: (1) the built SVNNAAPG operator considers decision information with relationship between aggregated information and (2) the built SVNNAAPG could effectively portray the intrinsic relationship between aggregated attributes during the MADM issues.

6 Conclusion

In summary, in the context of educational reform and information technology application, in order to ensure the expected results of college English teaching, it is necessary to attach importance to the application of blended learning. For teachers, the application of blended teaching mode is a double-edged sword, which puts higher requirements on their comprehensive abilities. Therefore, it is suggested that teachers should seize the opportunities of the times and take the path of specialization. In the actual teaching stage, the differences and styles among individual students are considered, and on this basis, the most suitable teaching techniques are selected to fully meet the learning needs of students. Only in this way can the quality of talent cultivation be improved and the national development of English majors be met. The English-blended teaching quality evaluation is MADM. In such an article, the SVNNAAPG operator is implemented based on the Aczel–Alsina technique and PG technique under SVNSs. The SVNNAAPG technique is built for MADM. Eventually, an example about English-blended teaching quality evaluation and some selected comparative analysis was used to depict the SVNNAAPG technique. However, due to changes in existing research techniques and decision-making environments, there are many issues that need further improvement in this article: (1) in the future works, the Aczel–Alsina operations shall be applied to other fuzzy and uncertain decision settings [42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57] and (2) in the future, we can also study MADM techniques under SVNSs that consider the psychological behavior of decision makers [58–62].

  1. Funding information: This study did not receive any funding in any form.

  2. Author contributions: Zhiqiang Miao: Writing-original draft, Methodology, Data curation.

  3. Conflict of interest: The author declares that they have no conflict of interest.

  4. Ethical approval: This article does not contain any studies with human participants or animals performed by any of the authors.

  5. Data availability statement: The data used to support the findings of this study are included within the article.

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Received: 2023-07-04
Revised: 2023-12-06
Accepted: 2023-12-13
Published Online: 2024-04-23

© 2024 the author(s), published by De Gruyter

This work is licensed under the Creative Commons Attribution 4.0 International License.

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https://doi.org/10.1515/jisys-2023-0091
Keywords for this article
multiple-attribute decision-making; single-valued neutrosophic sets; power geometric; English-blended teaching quality evaluation
Creative Commons
BY 4.0

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  2. A study on intelligent translation of English sentences by a semantic feature extractor
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  44. Employment management system for universities based on improved decision tree
  45. English grammar intelligent error correction technology based on the n-gram language model
  46. Speech recognition and intelligent translation under multimodal human–computer interaction system
  47. Enhancing data security using Laplacian of Gaussian and Chacha20 encryption algorithm
  48. Construction of GCNN-based intelligent recommendation model for answering teachers in online learning system
  49. Neural network big data fusion in remote sensing image processing technology
  50. Research on the construction and reform path of online and offline mixed English teaching model in the internet era
  51. Real-time semantic segmentation based on BiSeNetV2 for wild road
  52. Online English writing teaching method that enhances teacher–student interaction
  53. Construction of a painting image classification model based on AI stroke feature extraction
  54. Big data analysis technology in regional economic market planning and enterprise market value prediction
  55. Location strategy for logistics distribution centers utilizing improved whale optimization algorithm
  56. Research on agricultural environmental monitoring Internet of Things based on edge computing and deep learning
  57. The application of curriculum recommendation algorithm in the driving mechanism of industry–teaching integration in colleges and universities under the background of education reform
  58. Application of online teaching-based classroom behavior capture and analysis system in student management
  59. Evaluation of online teaching quality in colleges and universities based on digital monitoring technology
  60. Face detection method based on improved YOLO-v4 network and attention mechanism
  61. Study on the current situation and influencing factors of corn import trade in China – based on the trade gravity model
  62. Research on business English grammar detection system based on LSTM model
  63. Multi-source auxiliary information tourist attraction and route recommendation algorithm based on graph attention network
  64. Multi-attribute perceptual fuzzy information decision-making technology in investment risk assessment of green finance Projects
  65. Research on image compression technology based on improved SPIHT compression algorithm for power grid data
  66. Optimal design of linear and nonlinear PID controllers for speed control of an electric vehicle
  67. Traditional landscape painting and art image restoration methods based on structural information guidance
  68. Traceability and analysis method for measurement laboratory testing data based on intelligent Internet of Things and deep belief network
  69. A speech-based convolutional neural network for human body posture classification
  70. The role of the O2O blended teaching model in improving the teaching effectiveness of physical education classes
  71. Genetic algorithm-assisted fuzzy clustering framework to solve resource-constrained project problems
  72. Behavior recognition algorithm based on a dual-stream residual convolutional neural network
  73. Ensemble learning and deep learning-based defect detection in power generation plants
  74. Optimal design of neural network-based fuzzy predictive control model for recommending educational resources in the context of information technology
  75. An artificial intelligence-enabled consumables tracking system for medical laboratories
  76. Utilization of deep learning in ideological and political education
  77. Detection of abnormal tourist behavior in scenic spots based on optimized Gaussian model for background modeling
  78. RGB-to-hyperspectral conversion for accessible melanoma detection: A CNN-based approach
  79. Optimization of the road bump and pothole detection technology using convolutional neural network
  80. Comparative analysis of impact of classification algorithms on security and performance bug reports
  81. Cross-dataset micro-expression identification based on facial ROIs contribution quantification
  82. Demystifying multiple sclerosis diagnosis using interpretable and understandable artificial intelligence
  83. Unifying optimization forces: Harnessing the fine-structure constant in an electromagnetic-gravity optimization framework
  84. E-commerce big data processing based on an improved RBF model
  85. Analysis of youth sports physical health data based on cloud computing and gait awareness
  86. CCLCap-AE-AVSS: Cycle consistency loss based capsule autoencoders for audio–visual speech synthesis
  87. An efficient node selection algorithm in the context of IoT-based vehicular ad hoc network for emergency service
  88. Computer aided diagnoses for detecting the severity of Keratoconus
  89. Improved rapidly exploring random tree using salp swarm algorithm
  90. Network security framework for Internet of medical things applications: A survey
  91. Predicting DoS and DDoS attacks in network security scenarios using a hybrid deep learning model
  92. Enhancing 5G communication in business networks with an innovative secured narrowband IoT framework
  93. Quokka swarm optimization: A new nature-inspired metaheuristic optimization algorithm
  94. Digital forensics architecture for real-time automated evidence collection and centralization: Leveraging security lake and modern data architecture
  95. Image modeling algorithm for environment design based on augmented and virtual reality technologies
  96. Enhancing IoT device security: CNN-SVM hybrid approach for real-time detection of DoS and DDoS attacks
  97. High-resolution image processing and entity recognition algorithm based on artificial intelligence
  98. Review Articles
  99. Transformative insights: Image-based breast cancer detection and severity assessment through advanced AI techniques
  100. Network and cybersecurity applications of defense in adversarial attacks: A state-of-the-art using machine learning and deep learning methods
  101. Applications of integrating artificial intelligence and big data: A comprehensive analysis
  102. A systematic review of symbiotic organisms search algorithm for data clustering and predictive analysis
  103. Modelling Bitcoin networks in terms of anonymity and privacy in the metaverse application within Industry 5.0: Comprehensive taxonomy, unsolved issues and suggested solution
  104. Systematic literature review on intrusion detection systems: Research trends, algorithms, methods, datasets, and limitations
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