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An intelligent decision methodology for triangular Pythagorean fuzzy MADM and applications to college English teaching quality evaluation

  • Liwei Li EMAIL logo
Published/Copyright: December 31, 2023
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Journal of Intelligent Systems
From the journal Journal of Intelligent Systems Volume 32 Issue 1

Abstract

The development of contemporary college English teaching methods and practice should respect the subjective will of college students; fully tap their wisdom and potential; constantly innovate college English teaching methods, teaching practice activities, classroom teaching, and teaching evaluation models; create a good teaching atmosphere; and establish the concept of developmental evaluation. Through the innovation of teaching methods, college students’ actual language communication ability is cultivated, the teaching objectives and teaching methods of college English reading are innovated, and interactive, body language, role play, situational teaching, communicative teaching, and other teaching methods are used. The College English teaching quality evaluation is a classical multiple attribute decision making (MADM). In this article, the triangular Pythagorean fuzzy sets (TPFSs) are introduced, and the MADM problem is investigated under TPFSs. Based on the traditional dual generalized weighted Bonferroni mean operator and power average operator, the triangular Pythagorean fuzzy dual generalized power Bonferroni mean (TPFDGPBM) operator is proposed. Accordingly, the TPFDGPBM operator is employed to construct the triangular Pythagorean fuzzy MADM method. Finally, a numerical example for College English teaching quality evaluation is constructed to verify the TPFDGPBM technique.

Keywords: multiple attribute decision making; triangular Pythagorean fuzzy sets; DGWBM operator; triangular Pythagorean fuzzy dual generalized power Bonferroni mean; teaching quality

1 Introduction

In blended English teaching, teachers can assist students in applying and practicing English language knowledge online and offline, integrating new and old knowledge [1,2]. In online teaching, students can acquire new knowledge by watching videos, listening to audio, and other means [3,4,5]. In offline teaching, teachers can help students consolidate old knowledge through oral practice, listening practice, and other methods. In blended English teaching, teachers need to present classroom content in various ways and construct a blended teaching model. Teachers should improve teaching resources on online teaching platforms, including text, audio, and video forms of content. For example, uploading classroom lecture notes, listening materials, and video courseware on the platform allows students to preview and learn before class, meeting the learning needs of different students, enabling them to more clearly grasp teaching and knowledge points, and facilitating students to review and consolidate after class. In blended English teaching, students’ existing English knowledge can be integrated, and online teaching platforms can be used for English testing and autonomous preview [6,7,8]. This method can enhance students’ learning effectiveness. On online teaching platforms, teachers can set test questions and types, allowing students to take English tests before class [9,10]. The test should cover the knowledge points and grammar rules already learned in the course to test students’ understanding and mastery of these contents. Through the test, students can evaluate their English proficiency, understand their strengths and weaknesses, and better learn and improve their English abilities [11,12,13]. Establishing a blended English teaching evaluation system requires teachers to comprehensively consider multiple aspects of content. First, in the course design, teachers should evaluate the degree of achievement of teaching objectives, the rationality and completeness of course content, and the adequacy of teaching resources. In terms of students’ learning situation, evaluation methods such as exam scores, homework quality, and classroom participation can be used to comprehensively understand students’ learning outcomes and attitudes. A combination of student evaluation and teacher self-evaluation is used to evaluate the quality of teacher teaching. Student evaluation can be conducted through anonymous questionnaires or group discussions to understand students’ evaluations of teacher teaching ability, attitude, and effectiveness. Teacher self-evaluation is conducted through regular teaching reflection and improvement plans, with the ultimate goal of optimizing teaching quality [14,15,16,17]. In the college English teaching system, the application of assessment methods in practical teaching reforms requires teachers to establish a multidimensional evaluation system, comprehensively understanding the performance of students and teachers from different perspectives, and providing reference for optimizing teaching effectiveness. In summary, blended English teaching is an inevitable trend in the reform of English education in universities [18,19]. Teachers can innovate teaching models, improve teaching effectiveness, and stimulate students’ learning interest and motivation through the use of modern technological means. Faced with the problems and challenges in practice, it is necessary for teachers and students to work together to overcome them, continue to explore the application of blended English teaching methods in college English teaching, and gradually improve relevant teaching models to promote the reform and development of college English education.

Multiple attribute decision making (MADM) exists here and there, and a MADM problem is to find the most desirable candidate from some feasible decision alternatives [20,21,22,23,24]. In real life, decision-makers often express their preferences on decision alternatives using uncertain information instead of numerical values owing to the fuzziness of the human thinking process, and MADM under an uncertain environment has been a focus in recent years [25,26,27,28,29,30]. In the process of MADM, the input arguments need to be fused by some proper decision approaches so that the decision makers can select the most desirable decision alternative [31,32,33,34,35,36]. As the evaluation information shows fuzziness [37,38,39,40], Zadeh [41] put up with a fuzzy sets (FSs). Atanassov [42] put up with the intuitionistic FSs (IFSs). Yager [43] put up with the Pythagorean fuzzy set (PFSs). In line with the literature [43,44,45], Du [46] connected PFSs with triangular fuzzy numbers (TFNs) and put up with the Pythagorean triangular fuzzy sets (PTFSs). Fan et al. [47] also put up with triangular Pythagorean fuzzy sets (TPFSs). The college English teaching quality evaluation is a MADM issue. Thus, in line with the advantages of the TPFSs and dual generalized weighted Bonferroni mean (DGWBM) operator [34] and power average (PA) technique [48], in this article, the traditional DGWBM [34] and PA [48] are employed to develop the triangular Pythagorean fuzzy dual generalized power Bonferroni mean (TPFDGPBM) operator. Then, we have utilized the TPFDGPBM operator to solve MADM with TPFSs. Finally, a numerical example for college English teaching quality evaluation is constructed to verify the constructed technique.

To do so, the framework of the article is constructed. TPFSs are presented in Section 2. In Section 3, the TPFDGPBM operator is presented. In Section 4, the MADM is discussed in line with the TPFDGPBM operator. Section 5 presents the numerical example for teaching quality evaluation. Section 6 presents conclusion.

2 Preliminaries

Van Laarhoven and Pedrycz [49] constructed TFNs.

Definition 1

[49] A TFN p a could be constructed through ( p a L , p a M , p a U ) . The membership function μ p a ( x ) is constructed as follows:

(1) μ p a ( θ ) = 0 , θ < p a L , θ − p a L p a M − p a L , p a L ≤ θ ≤ p a M , θ − p a U p a M − p a U , p a M ≤ θ ≤ p a U , 0 , θ ≥ p a U .

where 0 < p a L ≤ p a M ≤ p a U , p a L , and p a U are the lower and upper values p a and p a M for the modal value.

Definition 2

[49] The operational laws for TFNs are constructed:

p a ⊕ p b = [ p a L , p a M , p a U ] ⊕ [ p b L , p b M , p b U ] = [ p a L + p b L , p a M + p b M , p a U + p b U ]

p a ⊗ p b = [ p a L , p a M , p a U ] ⊗ [ p b L , p b M , p b U ] = [ p a L × p b L , p a M × p b M , p a U × p b U ]

λ ⊗ p a = λ ⊗ [ p a L , p a M , p a U ] = [ λ p a L , λ p a M , λ p a U ] , λ > 0 .

The TPFSs are constructed [46,47].

Definition 3

[46,47]. The TPFSs P A are constructed as follows:

(2) P A = { 〈 θ , t P A ( θ ) , f P A ( θ ) 〉 ∣ θ ∈ Θ } ,

where t P A ( θ ) ⊂ [ 0 , 1 ] and f P A ( θ ) ⊂ [ 0 , 1 ] are TFNs, and t P A ( θ ) = ( p a ( θ ) , p b ( θ ) , p c ( θ ) ) : Θ → [ 0 , 1 ] , f P A ( θ ) = ( p l ( θ ) , p m ( θ ) , p n ( θ ) ) : Θ → [ 0 , 1 ] , 0 ≤ p c 2 ( θ ) + p n 2 ( θ ) ≤ 1 , ∀ θ ∈ Θ . For more convenience, let t P A ( θ ) = ( p a , p b , p c ) , f P A ( θ ) = ( p l , p m , p n ) , so the pair P A = 〈 ( p a , p b , p c ) , ( p l , p m , p n ) 〉 is the triangular Pythagorean fuzzy number (TPFN) and p c 2 + p n 2 ≤ 1 .

Definition 4

[46,47]. For P A 1 = 〈 ( p a 1 , p b 1 , p c 1 ) , ( p l 1 , p m 1 , p n 1 ) 〉 , P A 2 = 〈 ( p a 2 , p b 2 , p c 2 ) , ( p l 2 , p m 2 , p n 2 ) 〉 , and P A = 〈 ( p a , p b , p c ) , ( p l , p m , p n ) 〉 , the fundamental operational laws are constructed as follows:

( 1 ) P A 1 ⊕ P A 2 = ( p a 1 ) 2 + ( p a 2 ) 2 − ( p a 1 ) 2 ( p a 2 ) 2 , ( p b 1 ) 2 + ( p b 2 ) 2 − ( p b 1 ) 2 ( p b 2 ) 2 ( p c 1 ) 2 + ( p c 2 ) 2 − ( p c 1 ) 2 ( p c 2 ) 2 , ( p l 1 p l 2 , p m 1 p m 2 , p n 1 p n 2 ) ; ( 2 ) P A 1 ⊗ P A 2 = ( p a 1 p a 2 , p b 1 p b 2 , p c 1 p c 2 ) , ( p l 1 ) 2 + ( p l 2 ) 2 − ( p l 1 ) 2 ( p l 2 ) 2 , ( p m 1 ) 2 + ( p m 2 ) 2 − ( p m 1 ) 2 ( p m 2 ) 2 ( p n 1 ) 2 + ( p n 2 ) 2 − ( p n 1 ) 2 ( p n 2 ) 2 ; ( 3 ) λ P A = { ( 1 − ( 1 − p a 2 ) λ , 1 − ( 1 − p b 2 ) λ , 1 − ( 1 − p c 2 ) λ ) , ( p l λ , p m λ , p n λ ) } , λ > 0 ; ( 4 ) ( P A ) λ = { ( p a λ , p b λ , p c λ ) , ( 1 − ( 1 − p l 2 ) λ , 1 − ( 1 − p m 2 ) λ , 1 − ( 1 − p n 2 ) λ ) } , λ > 0 .

Theorem 1

[46,47]. Let P A 1 = 〈 ( p a 1 , p b 1 , p c 1 ) , ( p l 1 , p m 1 , p n 1 ) 〉 and P A 2 = 〈 ( p a 2 , p b 2 , p c 2 ) , ( p l 2 , p m 2 , p n 2 ) 〉 be two TPFNs, and let λ , λ 1 , λ 2 > 0 be three real numbers, then

( 1 ) P A 1 ⊕ P A 2 = P A 2 ⊕ P A 1 ; ( 2 ) P A 1 ⊗ P A 2 = P A 2 ⊗ P A 1 ; ( 3 ) λ ( P A 1 ⊕ P A 2 ) = λ P A 1 ⊕ λ P A 2 ; ( 4 ) ( P A 1 ⊗ P A 2 ) λ = ( P A 1 ) λ ⊗ ( P A 2 ) λ ; ( 5 ) λ 1 P A 1 ⊕ λ 2 P A 1 = ( λ 1 + λ 2 ) P A 1 ; ( 6 ) ( P A 1 ) λ 1 ⊗ ( P A 1 ) λ 2 = ( P A 1 ) ( λ 1 + λ 2 ) ; ( 7 ) ( ( P A 1 ) λ 1 ) λ 2 = ( P A 1 ) λ 1 λ 2 .

Definition 5

For an TPFN P A = 〈 ( p a , p b , p c ) , ( p l , p m , p n ) 〉 , the score and accuracy functions are constructed as S F ( P A ) = 1 3 p a 2 + 2 p b 2 + p c 2 − ( p l 2 + 2 p m 2 + p n 2 ) 4 + 2 and A F ( P A ) = p a 2 + 2 p b 2 + p c 2 + ( p l 2 + 2 p m 2 + p n 2 ) 4 . Moreover, the order relation is constructed:

  1. if S F ( P A 1 ) < S F ( P A 2 ) , then A 1 < A 2 ;

  2. if S F ( P A 1 ) = S F ( P A 2 ) , then if A F ( P A 1 ) = A F ( P A 2 ) , then P A 1 = P A 2 ; if A F ( P A 1 ) < A F ( P A 2 ) , then P A 1 < P A 2 .

3 TPFDGPBM operator

Al-Gharabally et al. [34] proposed the DGWBM operator.

Definition 6

[34]. Let p b i ( i = 1 , 2 , … , n ) be a set of nonnegative numbers with weight p w = ( p w 1 , p w 2 , … , p w n ) T , p w i ∈ [ 0 , 1 ] and ∑ i = 1 n p w i = 1 . If

(3) DGWBM p w R ( p b 1 , p b 2 , … , p b n ) = ∑ i 1 , i 2 , … , i n = 1 n ∏ j = 1 n p w i j p b i j r j 1 / ∑ j = 1 n r j ,

where R = ( r 1 , r 2 , … , r n ) T is the parameter vector with r i ≥ 0 ( i = 1 , 2 , … , n ) .

Yager [48] put forward the PA operator.

Definition 7

[48] The PA operator is listed as follows:

(4) PA ( p a 1 , p a 2 , ⋯ , p a n ) = ∑ j = 1 n ( 1 + T ( p a j ) ) p a j ∑ j = 1 n ( 1 + T ( p a j ) ) ,

where T ( p a j ) = ∑ i = 1 i ≠ j n Sup ( p a j , p a i ) , and Sup ( p a , p b ) is the support for p a from p b , which satisfies the three properties: (1) Sup ( p a , p b ) ∈ [ 0 , 1 ] ; (2) Sup ( p a , p b ) = Sup ( p b , p a ) ; (3) Sup ( p a , p b ) ≥ Sup ( p x , p y ) , if ∣ p a − p b ∣ < ∣ p x − p y ∣ . Obviously, the support (Sup) measure is essentially a similarity index.

Then, the TPFDGWBM operators are introduced as follows [50]:

3.1 TPFDGWBM operator

Definition 8

[50] Let P A j = { ( p a j , p b j , p c j ) , ( p l j , p m j , p n j ) } ( j = 1 , 2 , ⋯ , n ) be TPFNs, p w = ( p w 1 , p w 2 , ⋯ , p w n ) T is the weight of P A j , p w j > 0 , and ∑ j = 1 n p w j = 1 . The TPFDGWBM operator is constructed:

(5) T P F D G W B M p w R ( P A 1 , P A 2 , ⋯ , P A n ) = ⊕ i 1 , i 2 , … , i n = 1 n ⊗ j = 1 n p w i j P A i j r j 1 / ∑ i = 1 n r j = 1 − ∏ i 1 , i 2 , … , i n = 1 n 1 − ∏ j = 1 n ( 1 − ( 1 − p a i j 2 r j ) p w i j ) 1 / ∑ i = 1 n r j 1 − ∏ i 1 , i 2 , … , i n = 1 n 1 − ∏ j = 1 n ( 1 − ( 1 − p b i j 2 r j ) p w i j ) 1 / ∑ i = 1 n r j 1 − ∏ i 1 , i 2 , … , i n = 1 n 1 − ∏ j = 1 n ( 1 − ( 1 − p c i j 2 r j ) p w i j ) 1 / ∑ i = 1 n r j 1 − 1 − ∏ i 1 , i 2 , … , i n = 1 n 1 − ∏ j = 1 n ( 1 − ( 1 − ( 1 − p l i j 2 ) r j ) p w i j ) 1 / ∑ i = 1 n r j 1 − 1 − ∏ i 1 , i 2 , … , i n = 1 n 1 − ∏ j = 1 n ( 1 − ( 1 − ( 1 − p m i j 2 ) r j ) p w i j ) 1 / ∑ i = 1 n r j 1 − 1 − ∏ i 1 , i 2 , … , i n = 1 n 1 − ∏ j = 1 n ( 1 − ( 1 − ( 1 − p n i j 2 ) r j ) p w i j ) 1 / ∑ i = 1 n r j ,

where R = ( r 1 , r 2 , … , r n ) T is the parameter vector with r i ≥ 0 ( i = 1 , 2 , … , n ) .

It can be testified easily that the TPFDGWBM operator [50] has the properties as follows.

Property 1

(Idempotency). If all P A j ( j = 1 , 2 , ⋯ , n ) are equal, i.e., P A j = P A for all j , then

(6) TPFDGWBM p w R ( P A 1 , P A 2 , ⋯ , P A n ) = P A .

Proof:

TPFDGWBM p w R ( P A 1 , P A 2 , ⋯ , P A n ) = ⊕ i 1 , i 2 , … , i n = 1 n ⊗ j = 1 n p w i j P A i j r j 1 / ∑ i = 1 n r j = ⊕ i 1 , i 2 , … , i n = 1 n ⊗ j = 1 n p w i j P A r j 1 / ∑ i = 1 n r j = ⊗ j = 1 n P A r j 1 / ∑ i = 1 n r j = P A 1 / ∑ i = 1 n r j 1 / ∑ i = 1 n r j = P A

Property 2

(Boundedness). Let P A j ( j = 1 , 2 , ⋯ , n ) be a collection of TPFNs, and let

P A − = min j P A j , P A + = max j P A j

Then

(7) P A − ≤ TPFDGWBM p w R ( P A 1 , P A 2 , ⋯ , P A n ) ≤ P A + .

Property 3

(Monotonicity). Let P A j ( j = 1 , 2 , ⋯ , n ) and P A ′ j ( j = 1 , 2 , ⋯ , n ) be TPFNs, if P A j ≤ P A ′ j , for all j , then

(8) TPFDGWBM p w R ( P A 1 , P A 2 , ⋯ , P A n ) ≤ TPFDGWBM p w R ( P A ′ 1 , P A ′ 2 , ⋯ , P A ′ n ) .

3.2 TPFDGPBM operator

Then, the TPFDGPBM operator is built on TPFDGWBM operator [50] and PA [48].

Definition 9

Let P A j = { ( p a j , p b j , p c j ) , ( p l j , p m j , p n j ) } ( j = 1 , 2 , ⋯ , n ) be a set of TPFNs. The TPFDGPBM operator is constructed as follows:

(9) TPFDGPBM R ( P A 1 , P A 2 , ⋯ , P A n ) = ⊕ i 1 , i 2 , … , i n = 1 n ⊗ j = 1 n ( 1 + T ( P A i j ) ) ∑ i = 1 n ( 1 + T ( P A i j ) ) P A i j r j 1 / ∑ i = 1 n r j .

where R = ( r 1 , r 2 , … , r n ) T is the parameter vector with r i ≥ 0 ( i = 1 , 2 , … , n ) , T ( P A i j ) = ∑ j = 1 j ≠ t n Sup ( P A i j , P A i t ) , and Sup ( P A i j , P A i t ) is the support for P A i j from P A i t to meet the given conditions: (1) Sup ( P A i j , P A i t ) ∈ [ 0 , 1 ] ; (2) Sup ( P A i j , P A i t ) = Sup ( P A i t , P A i j ) ; (3) Sup ( P A i j , P A i t ) ≥ Sup ( P A i s , P A i k ) , if d ( P A i j , P A i t ) ≤ d ( P A i s , P A i k ) , where d is a distance measure.

From Definition 9, we have:

Theorem 2

The fused information with TPFDGPBM operator is the TPFN, where

(10) T P F D G P B M R ( P A 1 , P A 2 , ⋯ , P A n ) = ⊕ i 1 , i 2 , … , i n = 1 n ⊗ j = 1 n ( 1 + T ( P A i j ) ) ∑ i = 1 n ( 1 + T ( P A i j ) ) P A i j r j 1 / ∑ i = 1 n r j = 1 − ∏ i 1 , i 2 , … , i n = 1 n 1 − ∏ j = 1 n 1 − ( 1 − p a i j 2 r j ) ( 1 + T ( P A i j ) ) ∑ i = 1 n ( 1 + T ( P A i j ) ) 1 / ∑ i = 1 n r j 1 − ∏ i 1 , i 2 , … , i n = 1 n 1 − ∏ j = 1 n 1 − ( 1 − p b i j 2 r j ) ( 1 + T ( P A i j ) ) ∑ i = 1 n ( 1 + T ( P A i j ) ) 1 / ∑ i = 1 n r j 1 − ∏ i 1 , i 2 , … , i n = 1 n 1 − ∏ j = 1 n 1 − ( 1 − p c i j 2 r j ) ( 1 + T ( P A i j ) ) ∑ i = 1 n ( 1 + T ( P A i j ) ) 1 / ∑ i = 1 n r j 1 − 1 − ∏ i 1 , i 2 , … , i n = 1 n 1 − ∏ j = 1 n 1 − ( 1 − ( 1 − p l i j 2 ) r j ) ( 1 + T ( P A i j ) ) ∑ i = 1 n ( 1 + T ( P A i j ) ) 1 / ∑ i = 1 n r j 1 − 1 − ∏ i 1 , i 2 , … , i n = 1 n 1 − ∏ j = 1 n 1 − ( 1 − ( 1 − p m i j 2 ) r j ) ( 1 + T ( P A i j ) ) ∑ i = 1 n ( 1 + T ( P A i j ) ) 1 / ∑ i = 1 n r j 1 − 1 − ∏ i 1 , i 2 , … , i n = 1 n 1 − ∏ j = 1 n 1 − ( 1 − ( 1 − p n i j 2 ) r j ) ( 1 + T ( P A i j ) ) ∑ i = 1 n ( 1 + T ( P A i j ) ) 1 / ∑ i = 1 n r j .

Proof:

(11) P A i j r j = ( p a i j r j , p b i j r j , p c i j r j ) , ( 1 − ( 1 − p l i j 2 ) r j , 1 − ( 1 − p m i j 2 ) r j , 1 − ( 1 − p n i j 2 ) r j ) ,

(12) ( 1 + T ( P A i j ) ) ∑ i = 1 n ( 1 + T ( P A i j ) ) P A i j r j = 1 − ( 1 − ( p a i j 2 r j ) ) ( 1 + T ( P A i j ) ) ∑ i = 1 n ( 1 + T ( P A i j ) ) , 1 − ( 1 − ( p b i j 2 r j ) ) ( 1 + T ( P A i j ) ) ∑ i = 1 n ( 1 + T ( P A i j ) ) , 1 − ( 1 − ( p c i j 2 r j ) ) ( 1 + T ( P A i j ) ) ∑ i = 1 n ( 1 + T ( P A i j ) ) ( 1 − ( 1 − p l i j 2 ) r j ) ( 1 + T ( P A i j ) ) ∑ i = 1 n ( 1 + T ( P A i j ) ) , ( 1 − ( 1 − p m i j 2 ) r j ) ( 1 + T ( P A i j ) ) ∑ i = 1 n ( 1 + T ( P A i j ) ) , ( 1 − ( 1 − p n i j 2 ) r j ) ( 1 + T ( P A i j ) ) ∑ i = 1 n ( 1 + T ( P A i j ) ) .

Therefore,

(13) ⊗ j = 1 n ( 1 + T ( P A i j ) ) ∑ i = 1 n ( 1 + T ( P A i j ) ) P A i j r j = ∏ j = 1 n 1 − ( 1 − p a i j 2 r j ) ( 1 + T ( P A i j ) ) ∑ i = 1 n ( 1 + T ( P A i j ) ) ∏ j = 1 n 1 − ( 1 − p b i j 2 r j ) ( 1 + T ( P A i j ) ) ∑ i = 1 n ( 1 + T ( P A i j ) ) ∏ j = 1 n 1 − ( 1 − p c i j 2 r j ) ( 1 + T ( P A i j ) ) ∑ i = 1 n ( 1 + T ( P A i j ) ) 1 − ∏ j = 1 n 1 − ( 1 − ( 1 − p l i j 2 ) r j ) ( 1 + T ( P A i j ) ) ∑ i = 1 n ( 1 + T ( P A i j ) ) 1 − ∏ j = 1 n 1 − ( 1 − ( 1 − p m i j 2 ) r j ) ( 1 + T ( P A i j ) ) ∑ i = 1 n ( 1 + T ( P A i j ) ) 1 − ∏ j = 1 n 1 − ( 1 − ( 1 − p n i j 2 ) r j ) ( 1 + T ( P A i j ) ) ∑ i = 1 n ( 1 + T ( P A i j ) ) .

Furthermore,

(14) ⊕ i 1 , i 2 , … , i n = 1 n ⊗ j = 1 n ( 1 + T ( P A i j ) ) ∑ i = 1 n ( 1 + T ( P A i j ) ) P A i j r j = 1 − ∏ i 1 , i 2 , … , i n = 1 n 1 − ∏ j = 1 n 1 − ( 1 − p a i j 2 r j ) ( 1 + T ( P A i j ) ) ∑ i = 1 n ( 1 + T ( P A i j ) ) 1 − ∏ i 1 , i 2 , … , i n = 1 n 1 − ∏ j = 1 n 1 − ( 1 − p b i j 2 r j ) ( 1 + T ( P A i j ) ) ∑ i = 1 n ( 1 + T ( P A i j ) ) 1 − ∏ i 1 , i 2 , … , i n = 1 n 1 − ∏ j = 1 n 1 − ( 1 − p c i j 2 r j ) ( 1 + T ( P A i j ) ) ∑ i = 1 n ( 1 + T ( P A i j ) ) , ∏ i 1 , i 2 , … , i n = 1 n 1 − ∏ j = 1 n 1 − ( 1 − ( 1 − p l i j 2 ) r j ) ( 1 + T ( P A i j ) ) ∑ i = 1 n ( 1 + T ( P A i j ) ) ∏ i 1 , i 2 , … , i n = 1 n 1 − ∏ j = 1 n 1 − ( 1 − ( 1 − p l i j 2 ) r j ) ( 1 + T ( P A i j ) ) ∑ i = 1 n ( 1 + T ( P A i j ) ) ∏ i 1 , i 2 , … , i n = 1 n 1 − ∏ j = 1 n 1 − ( 1 − ( 1 − p n i j 2 ) r j ) ( 1 + T ( P A i j ) ) ∑ i = 1 n ( 1 + T ( P A i j ) ) .

Therefore,

(15) T P F D G P B M R ( P A 1 , P A 2 , ⋯ , P A n ) = ⊕ i 1 , i 2 , … , i n = 1 n ⊗ j = 1 n ( 1 + T ( P A i j ) ) ∑ i = 1 n ( 1 + T ( P A i j ) ) P A i j r j 1 / ∑ i = 1 n r j = 1 − ∏ i 1 , i 2 , … , i n = 1 n 1 − ∏ j = 1 n 1 − ( 1 − p a i j 2 r j ) ( 1 + T ( P A i j ) ) ∑ i = 1 n ( 1 + T ( P A i j ) ) 1 / ∑ i = 1 n r j 1 − ∏ i 1 , i 2 , … , i n = 1 n 1 − ∏ j = 1 n 1 − ( 1 − p b i j 2 r j ) ( 1 + T ( P A i j ) ) ∑ i = 1 n ( 1 + T ( P A i j ) ) 1 / ∑ i = 1 n r j 1 − ∏ i 1 , i 2 , … , i n = 1 n 1 − ∏ j = 1 n 1 − ( 1 − p c i j 2 r j ) ( 1 + T ( P A i j ) ) ∑ i = 1 n ( 1 + T ( P A i j ) ) 1 / ∑ i = 1 n r j 1 − 1 − ∏ i 1 , i 2 , … , i n = 1 n 1 − ∏ j = 1 n 1 − ( 1 − ( 1 − p l i j 2 ) r j ) ( 1 + T ( P A i j ) ) ∑ i = 1 n ( 1 + T ( P A i j ) ) 1 / ∑ i = 1 n r j 1 − 1 − ∏ i 1 , i 2 , … , i n = 1 n 1 − ∏ j = 1 n 1 − ( 1 − ( 1 − p m i j 2 ) r j ) ( 1 + T ( P A i j ) ) ∑ i = 1 n ( 1 + T ( P A i j ) ) 1 / ∑ i = 1 n r j 1 − 1 − ∏ i 1 , i 2 , … , i n = 1 n 1 − ∏ j = 1 n 1 − ( 1 − ( 1 − p n i j 2 ) r j ) ( 1 + T ( P A i j ) ) ∑ i = 1 n ( 1 + T ( P A i j ) ) 1 / ∑ i = 1 n r j .

Then, we complete the proof.

It can be testified easily that the TPFDGPBM operator has the properties as follows.

Property 4

(Idempotency). If all P A j ( j = 1 , 2 , ⋯ , n ) are equal, i.e., P A j = P A for all j , then

(16) TPFDGPBM R ( P A 1 , P A 2 , ⋯ , P A n ) = P A .

Property 5

(Boundedness). Let P A j ( j = 1 , 2 , ⋯ , n ) be a collection of TPFNs, and let

P A − = min j P A j , P A + = max j P A j .

Then

(17) P A − ≤ TPFDGPBM R ( P A 1 , P A 2 , ⋯ , P A n ) ≤ P A + .

Property 6

(Monotonicity). Let P A j ( j = 1 , 2 , ⋯ , n ) and P A j ′ ( j = 1 , 2 , ⋯ , n ) be two set of TPFNs, if P A j ≤ P A j ′ , for all j , then

(18) TPFDGPBM R ( P A 1 , P A 2 , ⋯ , P A n ) ≤ TPFDGPBM R ( P A 1 ′ , P A 2 ′ , ⋯ , P A n ′ ) .

4 Model for MADM with TPFNs

We shall utilize the TPFDGPBM to solve the MADM with TPFNs. Let P O = { P O 1 , P O 2 , ⋯ , P O m } be alternatives, and P G = { P G 1 , P G 2 , ⋯ , P G n } be attributes. Suppose that the TPFN matrix is: P A i j = { ( p a i j , p b i j , p c i j ) , ( p l i j , p m i j , p n i j ) } , ( p a i j , p b i j , p c i j ) , and ( p l i j , p m i j , p n i j ) are TFNs, ( p c i j ) 2 + ( p n i j ) 2 ≤ 1 , i = 1 , 2 , ⋯ , m , j = 1 , 2 , ⋯ , n . Then, the TPFDGPBM operator is used to solve the MADM with TPFNs.

Step 1. Under attribute P G j to overall value P A i ( i = 1 , 2 , … , m ) , the different preferences P A i j ( j = 1 , 2 , … , n ) of the A i by TPFDGPBM operator is aggregated as follows:

(19) P A i = T P F D G P B M R ( P A i 1 , P A i 2 , ⋯ , P A i n ) = ⊕ i 1 , i 2 , … , i n = 1 n ⊗ j = 1 n 1 + T ( P A i i j ) ∑ i = 1 n ( 1 + T ( P A i i j ) ) P A i i j r j 1 / ∑ i = 1 n r j = 1 − ∏ i 1 , i 2 , … , i n = 1 n 1 − ∏ j = 1 n 1 − ( 1 − p a i i j 2 r j ) 1 + T ( P A i i j ) ∑ i = 1 n ( 1 + T ( P A i i j ) ) 1 / ∑ i = 1 n r j 1 − ∏ i 1 , i 2 , … , i n = 1 n 1 − ∏ j = 1 n 1 − ( 1 − p b i i j 2 r j ) 1 + T ( P A i i j ) ∑ i = 1 n ( 1 + T ( P A i i j ) ) 1 / ∑ i = 1 n r j 1 − ∏ i 1 , i 2 , … , i n = 1 n 1 − ∏ j = 1 n 1 − ( 1 − p c i i j 2 r j ) 1 + T ( P A i i j ) ∑ i = 1 n ( 1 + T ( P A i i j ) ) 1 / ∑ i = 1 n r j 1 − 1 − ∏ i 1 , i 2 , … , i n = 1 n 1 − ∏ j = 1 n 1 − ( 1 − ( 1 − p l i i j 2 ) r j ) 1 + T ( P A i i j ) ∑ i = 1 n ( 1 + T ( P A i i j ) ) 1 / ∑ i = 1 n r j 1 − 1 − ∏ i 1 , i 2 , … , i n = 1 n 1 − ∏ j = 1 n 1 − ( 1 − ( 1 − p m i i j 2 ) r j ) 1 + T ( P A i i j ) ∑ i = 1 n ( 1 + T ( P A i i j ) ) 1 / ∑ i = 1 n r j 1 − 1 − ∏ i 1 , i 2 , … , i n = 1 n 1 − ∏ j = 1 n 1 − ( 1 − ( 1 − p n i i j 2 ) r j ) 1 + T ( P A i i j ) ∑ i = 1 n ( 1 + T ( P A i i j ) ) 1 / ∑ i = 1 n r j , i = 1 , 2 , ⋯ , m .

Step 2. Compute the S F ( P A i ) and A F ( P A i ) through S ( P A i ) = 1 3 ( p a i ) 2 + 2 ( p b i ) 2 + ( p c i ) 2 − ( ( p l i ) 2 + 2 ( p m i ) 2 + ( p n i ) 2 ) 4 + 2 and and A F ( P A i ) = ( p a i ) 2 + 2 ( p b i ) 2 + ( p c i ) 2 + ( ( p l i ) 2 + 2 ( p m i ) 2 + ( p n i ) 2 ) 4 .

Step 3. Rank the alternatives P O i ( i = 1 , 2 , ⋯ , m ) and choose the best one(s).

5 Numerical example and comparative analysis

5.1 Numerical example for college English teaching quality evaluation

The College English teaching method refers to a teaching method that combines traditional offline face-to-face teaching and online teaching. In blended teaching, teachers can provide students with some online learning resources, which can be recorded videos, PPTs, e-books, etc., or related resources collected from the Internet. Classify such resources based on different learning objectives and content, making it convenient for students to choose and learn according to their own needs. Teachers can also use online classrooms, discussion areas, and other tools for interactive teaching to help students engage in self-directed learning at home or in school self-study rooms. In the classroom, teachers can showcase their carefully prepared PPTs or videos through screen sharing and projection, guiding students to gain a richer learning experience while deeply understanding the course content. Utilize online classroom tools, such as voice or text chat, to allow students to ask questions or express opinions at any time, promoting students’ thinking exchange and interactive learning. By utilizing the functions of online discussion areas and other tools, students can increase their participation, encourage them to help each other, share their learning experiences, and solve each other’s questions and confusions. Teachers can also use tools to recommend extracurricular learning resources, providing students with more learning resources and choice space. Traditional face-to-face teaching refers to an educational model in which students are taught and guided by teachers in classrooms on campus. Under this method, teachers directly communicate with students, guide them, and assist them in learning, which helps students better understand and master knowledge points. Flexible control of teaching progress and learning situation allows teachers to better control teaching progress and students’ learning situation, and timely identify and solve students’ problems. The learning atmosphere is good, and students can study together with their classmates, explore problems together, and enhance the learning atmosphere and interactive experience. It refers to a teaching method that combines traditional offline face-to-face teaching and online teaching. In blended teaching, teachers can provide students with some online learning resources, which can be recorded videos, PPTs, e-books, etc., or related resources collected from the Internet. Classify such resources based on different learning objectives and contents, making it convenient for students to choose and learn according to their own needs. Teachers can also use online classrooms, discussion areas, and other tools for interactive teaching to help students engage in self-directed learning at home or in school self-study rooms. In the classroom, teachers can showcase their carefully prepared PPTs or videos through screen sharing and projection, guiding students to gain a richer learning experience while deeply understanding the course content. Utilize online classroom tools, such as voice or text chat, to allow students to ask questions or express opinions at any time, promoting students’ thinking exchange and interactive learning. By utilizing the functions of online discussion areas and other tools, students can increase their participation, encourage them to help each other, share their learning experiences, and solve each other’s questions and confusions. Teachers can also use tools to recommend extracurricular learning resources, providing students with more learning resources and choice space. Traditional face-to-face teaching refers to an educational model in which students are taught and guided by teachers in classrooms on campus. Under this method, teachers directly communicate with students, guide them, and assist them in learning, which helps students better understand and master knowledge points. Flexible control of teaching progress and learning situation allows teachers to better control teaching progress and students’ learning situation, and timely identify and solve students’ problems. The learning atmosphere is good, and students can study together with their classmates, explore problems together, and enhance the learning atmosphere and interactive experience. The college English teaching quality evaluation is the MADM. There are five English colleges P O i ( i = 1 , 2 , 3 , 4 , 5 ) to select in line with four attributes: (1) PG1 is the college English teaching satisfaction; (2) PG2 is College English teaching achievements; (3) PG3 is college English teaching methods; and (4) PG4 is college English teaching contents. Five English colleges P O i ( i = 1 , 2 , 3 , 4 , 5 ) are to be assessed with TPFNs according to four attributes, as shown in Table 1.

Table 1

The TPFNs matrix

PG1 PG2 PG 3 PG 4
PO1 ((0.42, 0.53, 0.67),  (0.18, 0.34, 0.82)) ((0.25, 0.61, 0.78),  (0.27.0.31, 0.72)) ((0.44, 0.53, 0.65),  (0.18, 0.24, 0.37)) ((0.39, 0.43, 0.56),  (0.17, 0.21, 0.34))
PO2 ((0.27, 0.56, 0.72),  (0.45, 0.56, 0.73)) ((0.35, 0.51, 0.63),  (0.26, 0.51, 0.65)) ((0.39, 0.45, 0.53),  (0.48, 0.56, 0.64)) ((0.16, 0.21, 0.34),  (0.26, 0.34, 0.42))
PO3 ((0.39, 0.45, 0.51),  (0.24,  0.38,  0.42)) ((0.43, 0.57, 0.73),  (0.15, 0.43, 0.57)) ((0.29, 0.34, 0.45),  (0.41, 0.46, 0.56)) ((0.46, 0.46, 0.73),  (0.17, 0.26, 0.38))
PO4 ((0.23, 0.36, 0.65),  (0.21, 027, 0.43)) ((0.19, 0.36, 0.64),  (0.26, 0.56, 0.73)) ((0.37, 0.43, 0.52),  (0.57, 0.65, 0.72)) ((0.17, 0.24, 0.36),  (0.48, 0.54, 0.69))
PO5 ((0.28, 0.46, 0.85),  (0.18, 0.44, 0.52)) ((0.31, 0.54, 0.75),  (0.37, 0.63, 0.78)) ((0.24, 0.32, 0.45),  (0.36, 0.42, 0.51)) ((0.57, 0.68, 0.73),  (0.12, 0.15, 0.26))

Then, the TPFDGPBM operator is employed to manage the college English teaching quality evaluation.

Step 1. According to the Table 1 and TPFDGPBM operator, the TPFNs p ˜ i ( i = 1 , 2 , 3 , 4 , 5 ) of the P O i is derived (Table 2). Suppose that R = ( 3 , 3 , 3 ) .

Table 2

The TPFNs of English colleges through TPFDGPBM operator

TPFDGPBM
PO1 ((0.2327, 0.2658, 0.5545), (0.3663, 0.4654, 0.5436))
PO2 ((0.3367, 0.4769, 0.4014), (0.3536, 0.4987, 0.3209))
PO3 ((0.1579, 0.3437, 0.4215), (0.2986, 0.3332, 0.4214))
PO4 ((0.2874, 0.4421, 0.6671), (0.3557, 0.4414, 0.5512))
PO5 ((0.3185, 0.3715, 0.4057), (0.4802, 0.5326, 0.5513))

Step 2. In line with Table 2, the score is presented in Table 3.

Table 3

The score functions

TPFDGPBM
PO1 0.3793
PO2 0.4815
PO3 0.4646
PO4 0.4529
PO5 0.3518

Step 3. In line with Table 3, the order is constructed in Table 4. The most ideal English colleges is PO2.

Table 4

Order of the English colleges

Order
TPFDGPBM PO2 > PO3 > PO4 > PO1 > PO5

5.2 Influence analysis

The parameter R plays a pivotal role. By portioning different R , we may deduce a different order result. The scores are shown in Table 5. Table 6 shows that some different orders can be constructed through different values in the parameter vector R . Hence, by taking advantage of a parameter vector, the TPFDGPBM operator is fairly flexible.

Table 5

The score for TPFDGPBM operators

R = (1,1,1) R = (2,2,2) R = (3,3,3) R = (4,4,4) R = (5,5,5)
PO 1 0.3791 0.3886 0.3964 0.3439 0.3661
PO 2 0.4815 0.4919 0.4996 0.4425 0.4666
PO 3 0.4640 0.4699 0.4743 0.4382 0.4553
PO 4 0.4533 0.4639 0.4722 0.4142 0.4385
PO 5 0.3529 0.3663 0.3772 0.3071 0.3355
R = (6,6,6) R = (7,7,7) R = (8,8,8) R = (9,9,9) R = (10,10,10)
ZO 1 0.4141 0.4188 0.4231 0.4030 0.4089
ZO 2 0.5144 0.5179 0.5210 0.5056 0.5104
ZO 3 0.4831 0.4852 0.4869 0.4777 0.4807
ZO 4 0.4897 0.4942 0.4980 0.4790 0.4848
ZO 5 0.4003 0.4056 0.4102 0.3863 0.3939
Table 6

Order for TPFDGPBM operator

Order
R = (1,1,1) PO2 > PO3 > PO4 > PO1 > PO5
R = (2,2,2) PO2 > PO3 > PO4 > PO1 > PO5
R = (3,3,3) PO2 > PO3 > PO4 > PO1 > PO5
R = (4,4,4) PO2 > PO3 > PO4 > PO1 > PO5
R = (5,5,5) PO2 > PO3 > PO4 > PO1 > PO5
R = (6,6,6) PO2 > PO3 > PO4 > PO1 > PO5
R = (7,7,7) PO2 > PO3 > PO4 > PO1 > PO5
R = (8,8,8) PO2 > PO3 > PO4 > PO1 > PO5
R = (9,9,9) PO2 > PO3 > PO4 > PO1 > PO5
R = (10,10,10) PO2 > PO3 > PO4 > PO1 > PO5

5.3 Comparative analysis

The TPFWA operator [46], TPFWG operator [46], GTPFWA operator [47], and GTPFWG operator [47] are employed to compare with the proposed TPFDGPBM operator.

From Table 7, it could be known that these different methods have the same optimal choices, and the order of these methods is slightly different. This validates the reasonableness and effectiveness of the TPFDGPBM operator. The TPFDGPBM operator, as one of the efficient aggregation operators, can take into account the interrelationship between any number of arguments and can eliminate the influence of unfairly evaluated information on the decision outcome. The main advantages of the TPFDGPBM operator are outlined as follows: the TPFDGPBM operator could overcome some effects of awkward data information; the TPFDGPBM operator could consider the interrelationship of the fused arguments.

Table 7

Order for different techniques

Order
TPFWA operator [46] PO2 > PO3 > PO4 > PO1 > PO5
TPFWG operator [46] PO2 > PO3 > PO1 > PO4 > PO5
GTPFWA operator [47] PO2 > PO3 > PO4 > PO1 > PO5
GTPFWG operator [47] PO2 > PO3 > PO1 > PO4 > PO5
TPFDGPBM operator PO2 > PO3 > PO4 > PO1 > PO5

6 Conclusion

With the development of information technology and the advancement of educational reform, blended English teaching methods are gradually receiving attention in college English teaching. Blended English teaching methods integrate traditional teaching and modern technological means, aiming to improve students’ language abilities. College English teachers should incorporate the concept of blended English teaching into their classroom teaching activities to improve teaching quality. College English education is currently a hot topic in the field of education, and traditional English teaching methods are no longer able to meet the needs of students. It is necessary for educators to innovate teaching models and improve teaching effectiveness. The blended English teaching method is a relatively new teaching method, which combines traditional teaching and modern technology, changes the problem of solidification and simplification of college English teaching mode under a single mode, and can effectively improve students’ learning effect. The College English teaching quality evaluation is MADM. In this article, based on the DGWBM operator and PA operator, the TPFDGPBM operator is proposed. Accordingly, we have taken advantage of the TPFDGPBM operator to develop the MADM method to cope with the triangular Pythagorean fuzzy MADM. Ultimately, a practical example of College English teaching quality evaluation is taking advantage to validate the developed approach, and an influence analysis of the parameter on the final results has been presented to attest its availability and validity.

  1. Funding information: The work was supported by the Anhui Province Quality Engineering Project: Curriculum thought & Politics Research and Relevant Construction of College English Teaching-Based on Cross-Cultural theory (Project No.: 2022jyxm1431) and Province Quality Engineering Project of Anhui Universities: Virtual Teaching and Research Office for English Major (2021xnjys030).

  2. Author contributions: This article was independently finished by myself.

  3. Conflict of interest: The authors declare 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: 2023-06-15
Revised: 2023-11-06
Accepted: 2023-11-06
Published Online: 2023-12-31

© 2023 the author(s), published by De Gruyter

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

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  5. A novel deep learning-based brain tumor detection using the Bagging ensemble with K-nearest neighbor
  6. Detecting biased user-product ratings for online products using opinion mining
  7. Evaluation and analysis of teaching quality of university teachers using machine learning algorithms
  8. Efficient mutual authentication using Kerberos for resource constraint smart meter in advanced metering infrastructure
  9. Recognition of English speech – using a deep learning algorithm
  10. A new method for writer identification based on historical documents
  11. Intelligent gloves: An IT intervention for deaf-mute people
  12. Reinforcement learning with Gaussian process regression using variational free energy
  13. Anti-leakage method of network sensitive information data based on homomorphic encryption
  14. An intelligent algorithm for fast machine translation of long English sentences
  15. A lattice-transformer-graph deep learning model for Chinese named entity recognition
  16. Robot indoor navigation point cloud map generation algorithm based on visual sensing
  17. Towards a better similarity algorithm for host-based intrusion detection system
  18. A multiorder feature tracking and explanation strategy for explainable deep learning
  19. Application study of ant colony algorithm for network data transmission path scheduling optimization
  20. Data analysis with performance and privacy enhanced classification
  21. Motion vector steganography algorithm of sports training video integrating with artificial bee colony algorithm and human-centered AI for web applications
  22. Multi-sensor remote sensing image alignment based on fast algorithms
  23. Replay attack detection based on deformable convolutional neural network and temporal-frequency attention model
  24. Validation of machine learning ridge regression models using Monte Carlo, bootstrap, and variations in cross-validation
  25. Computer technology of multisensor data fusion based on FWA–BP network
  26. Application of adaptive improved DE algorithm based on multi-angle search rotation crossover strategy in multi-circuit testing optimization
  27. HWCD: A hybrid approach for image compression using wavelet, encryption using confusion, and decryption using diffusion scheme
  28. Environmental landscape design and planning system based on computer vision and deep learning
  29. Wireless sensor node localization algorithm combined with PSO-DFP
  30. Development of a digital employee rating evaluation system (DERES) based on machine learning algorithms and 360-degree method
  31. A BiLSTM-attention-based point-of-interest recommendation algorithm
  32. Development and research of deep neural network fusion computer vision technology
  33. Face recognition of remote monitoring under the Ipv6 protocol technology of Internet of Things architecture
  34. Research on the center extraction algorithm of structured light fringe based on an improved gray gravity center method
  35. Anomaly detection for maritime navigation based on probability density function of error of reconstruction
  36. A novel hybrid CNN-LSTM approach for assessing StackOverflow post quality
  37. Integrating k-means clustering algorithm for the symbiotic relationship of aesthetic community spatial science
  38. Improved kernel density peaks clustering for plant image segmentation applications
  39. Biomedical event extraction using pre-trained SciBERT
  40. Sentiment analysis method of consumer comment text based on BERT and hierarchical attention in e-commerce big data environment
  41. An intelligent decision methodology for triangular Pythagorean fuzzy MADM and applications to college English teaching quality evaluation
  42. Ensemble of explainable artificial intelligence predictions through discriminate regions: A model to identify COVID-19 from chest X-ray images
  43. Image feature extraction algorithm based on visual information
  44. Optimizing genetic prediction: Define-by-run DL approach in DNA sequencing
  45. Study on recognition and classification of English accents using deep learning algorithms
  46. Review Articles
  47. Dimensions of artificial intelligence techniques, blockchain, and cyber security in the Internet of medical things: Opportunities, challenges, and future directions
  48. A systematic literature review of undiscovered vulnerabilities and tools in smart contract technology
  49. Special Issue: Trustworthy Artificial Intelligence for Big Data-Driven Research Applications based on Internet of Everythings
  50. Deep learning for content-based image retrieval in FHE algorithms
  51. Improving binary crow search algorithm for feature selection
  52. Enhancement of K-means clustering in big data based on equilibrium optimizer algorithm
  53. A study on predicting crime rates through machine learning and data mining using text
  54. Deep learning models for multilabel ECG abnormalities classification: A comparative study using TPE optimization
  55. Predicting medicine demand using deep learning techniques: A review
  56. A novel distance vector hop localization method for wireless sensor networks
  57. Development of an intelligent controller for sports training system based on FPGA
  58. Analyzing SQL payloads using logistic regression in a big data environment
  59. Classifying cuneiform symbols using machine learning algorithms with unigram features on a balanced dataset
  60. Waste material classification using performance evaluation of deep learning models
  61. A deep neural network model for paternity testing based on 15-loci STR for Iraqi families
  62. AttentionPose: Attention-driven end-to-end model for precise 6D pose estimation
  63. The impact of innovation and digitalization on the quality of higher education: A study of selected universities in Uzbekistan
  64. A transfer learning approach for the classification of liver cancer
  65. Review of iris segmentation and recognition using deep learning to improve biometric application
  66. Special Issue: Intelligent Robotics for Smart Cities
  67. Accurate and real-time object detection in crowded indoor spaces based on the fusion of DBSCAN algorithm and improved YOLOv4-tiny network
  68. CMOR motion planning and accuracy control for heavy-duty robots
  69. Smart robots’ virus defense using data mining technology
  70. Broadcast speech recognition and control system based on Internet of Things sensors for smart cities
  71. Special Issue on International Conference on Computing Communication & Informatics 2022
  72. Intelligent control system for industrial robots based on multi-source data fusion
  73. Construction pit deformation measurement technology based on neural network algorithm
  74. Intelligent financial decision support system based on big data
  75. Design model-free adaptive PID controller based on lazy learning algorithm
  76. Intelligent medical IoT health monitoring system based on VR and wearable devices
  77. Feature extraction algorithm of anti-jamming cyclic frequency of electronic communication signal
  78. Intelligent auditing techniques for enterprise finance
  79. Improvement of predictive control algorithm based on fuzzy fractional order PID
  80. Multilevel thresholding image segmentation algorithm based on Mumford–Shah model
  81. Special Issue: Current IoT Trends, Issues, and Future Potential Using AI & Machine Learning Techniques
  82. Automatic adaptive weighted fusion of features-based approach for plant disease identification
  83. A multi-crop disease identification approach based on residual attention learning
  84. Aspect-based sentiment analysis on multi-domain reviews through word embedding
  85. RES-KELM fusion model based on non-iterative deterministic learning classifier for classification of Covid19 chest X-ray images
  86. A review of small object and movement detection based loss function and optimized technique
https://doi.org/10.1515/jisys-2023-0074
Keywords for this article
multiple attribute decision making; triangular Pythagorean fuzzy sets; DGWBM operator; triangular Pythagorean fuzzy dual generalized power Bonferroni mean; teaching quality
Creative Commons
BY 4.0

Articles in the same Issue

  1. Research Articles
  2. Salp swarm and gray wolf optimizer for improving the efficiency of power supply network in radial distribution systems
  3. Deep learning in distributed denial-of-service attacks detection method for Internet of Things networks
  4. On numerical characterizations of the topological reduction of incomplete information systems based on evidence theory
  5. A novel deep learning-based brain tumor detection using the Bagging ensemble with K-nearest neighbor
  6. Detecting biased user-product ratings for online products using opinion mining
  7. Evaluation and analysis of teaching quality of university teachers using machine learning algorithms
  8. Efficient mutual authentication using Kerberos for resource constraint smart meter in advanced metering infrastructure
  9. Recognition of English speech – using a deep learning algorithm
  10. A new method for writer identification based on historical documents
  11. Intelligent gloves: An IT intervention for deaf-mute people
  12. Reinforcement learning with Gaussian process regression using variational free energy
  13. Anti-leakage method of network sensitive information data based on homomorphic encryption
  14. An intelligent algorithm for fast machine translation of long English sentences
  15. A lattice-transformer-graph deep learning model for Chinese named entity recognition
  16. Robot indoor navigation point cloud map generation algorithm based on visual sensing
  17. Towards a better similarity algorithm for host-based intrusion detection system
  18. A multiorder feature tracking and explanation strategy for explainable deep learning
  19. Application study of ant colony algorithm for network data transmission path scheduling optimization
  20. Data analysis with performance and privacy enhanced classification
  21. Motion vector steganography algorithm of sports training video integrating with artificial bee colony algorithm and human-centered AI for web applications
  22. Multi-sensor remote sensing image alignment based on fast algorithms
  23. Replay attack detection based on deformable convolutional neural network and temporal-frequency attention model
  24. Validation of machine learning ridge regression models using Monte Carlo, bootstrap, and variations in cross-validation
  25. Computer technology of multisensor data fusion based on FWA–BP network
  26. Application of adaptive improved DE algorithm based on multi-angle search rotation crossover strategy in multi-circuit testing optimization
  27. HWCD: A hybrid approach for image compression using wavelet, encryption using confusion, and decryption using diffusion scheme
  28. Environmental landscape design and planning system based on computer vision and deep learning
  29. Wireless sensor node localization algorithm combined with PSO-DFP
  30. Development of a digital employee rating evaluation system (DERES) based on machine learning algorithms and 360-degree method
  31. A BiLSTM-attention-based point-of-interest recommendation algorithm
  32. Development and research of deep neural network fusion computer vision technology
  33. Face recognition of remote monitoring under the Ipv6 protocol technology of Internet of Things architecture
  34. Research on the center extraction algorithm of structured light fringe based on an improved gray gravity center method
  35. Anomaly detection for maritime navigation based on probability density function of error of reconstruction
  36. A novel hybrid CNN-LSTM approach for assessing StackOverflow post quality
  37. Integrating k-means clustering algorithm for the symbiotic relationship of aesthetic community spatial science
  38. Improved kernel density peaks clustering for plant image segmentation applications
  39. Biomedical event extraction using pre-trained SciBERT
  40. Sentiment analysis method of consumer comment text based on BERT and hierarchical attention in e-commerce big data environment
  41. An intelligent decision methodology for triangular Pythagorean fuzzy MADM and applications to college English teaching quality evaluation
  42. Ensemble of explainable artificial intelligence predictions through discriminate regions: A model to identify COVID-19 from chest X-ray images
  43. Image feature extraction algorithm based on visual information
  44. Optimizing genetic prediction: Define-by-run DL approach in DNA sequencing
  45. Study on recognition and classification of English accents using deep learning algorithms
  46. Review Articles
  47. Dimensions of artificial intelligence techniques, blockchain, and cyber security in the Internet of medical things: Opportunities, challenges, and future directions
  48. A systematic literature review of undiscovered vulnerabilities and tools in smart contract technology
  49. Special Issue: Trustworthy Artificial Intelligence for Big Data-Driven Research Applications based on Internet of Everythings
  50. Deep learning for content-based image retrieval in FHE algorithms
  51. Improving binary crow search algorithm for feature selection
  52. Enhancement of K-means clustering in big data based on equilibrium optimizer algorithm
  53. A study on predicting crime rates through machine learning and data mining using text
  54. Deep learning models for multilabel ECG abnormalities classification: A comparative study using TPE optimization
  55. Predicting medicine demand using deep learning techniques: A review
  56. A novel distance vector hop localization method for wireless sensor networks
  57. Development of an intelligent controller for sports training system based on FPGA
  58. Analyzing SQL payloads using logistic regression in a big data environment
  59. Classifying cuneiform symbols using machine learning algorithms with unigram features on a balanced dataset
  60. Waste material classification using performance evaluation of deep learning models
  61. A deep neural network model for paternity testing based on 15-loci STR for Iraqi families
  62. AttentionPose: Attention-driven end-to-end model for precise 6D pose estimation
  63. The impact of innovation and digitalization on the quality of higher education: A study of selected universities in Uzbekistan
  64. A transfer learning approach for the classification of liver cancer
  65. Review of iris segmentation and recognition using deep learning to improve biometric application
  66. Special Issue: Intelligent Robotics for Smart Cities
  67. Accurate and real-time object detection in crowded indoor spaces based on the fusion of DBSCAN algorithm and improved YOLOv4-tiny network
  68. CMOR motion planning and accuracy control for heavy-duty robots
  69. Smart robots’ virus defense using data mining technology
  70. Broadcast speech recognition and control system based on Internet of Things sensors for smart cities
  71. Special Issue on International Conference on Computing Communication & Informatics 2022
  72. Intelligent control system for industrial robots based on multi-source data fusion
  73. Construction pit deformation measurement technology based on neural network algorithm
  74. Intelligent financial decision support system based on big data
  75. Design model-free adaptive PID controller based on lazy learning algorithm
  76. Intelligent medical IoT health monitoring system based on VR and wearable devices
  77. Feature extraction algorithm of anti-jamming cyclic frequency of electronic communication signal
  78. Intelligent auditing techniques for enterprise finance
  79. Improvement of predictive control algorithm based on fuzzy fractional order PID
  80. Multilevel thresholding image segmentation algorithm based on Mumford–Shah model
  81. Special Issue: Current IoT Trends, Issues, and Future Potential Using AI & Machine Learning Techniques
  82. Automatic adaptive weighted fusion of features-based approach for plant disease identification
  83. A multi-crop disease identification approach based on residual attention learning
  84. Aspect-based sentiment analysis on multi-domain reviews through word embedding
  85. RES-KELM fusion model based on non-iterative deterministic learning classifier for classification of Covid19 chest X-ray images
  86. A review of small object and movement detection based loss function and optimized technique
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