[Retracted] Grey Relational Analysis Method for Probabilistic Double Hierarchy Linguistic Multiple Attribute Group Decision Making and Its Application to College Tennis Classroom Teaching Effect Evaluation

Wang, Lihua; Li, Huiming; Zhang, Jianpeng; Yang, Jin

doi:https://doi.org/10.1155/2022/7419496

Mathematical Problems in Engineering

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Abstract Introduction Preliminaries Numerical Example Conclusion Data Availability Conflicts of Interest References Copyright Related Articles

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Different Approaches in Treating Uncertainty in the Application of Multicriteria Decision Modeling

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Research Article | Open Access

Volume 2022 | Article ID 7419496 | https://doi.org/10.1155/2022/7419496

[Retracted] Grey Relational Analysis Method for Probabilistic Double Hierarchy Linguistic Multiple Attribute Group Decision Making and Its Application to College Tennis Classroom Teaching Effect Evaluation

Lihua Wang,¹Huiming Li,¹Jianpeng Zhang,¹and Jin Yang¹

Academic Editor: Darko Božanić

Received25 Feb 2022

Revised19 Apr 2022

Accepted20 Apr 2022

Published10 Jun 2022

Abstract

The college tennis classroom teaching effect evaluation is viewed as the multiattribute group decision making (MAGDM). The probabilistic double hierarchy linguistic term set (PDHLTS) not only conforms to people’s language expression habit of “adverb + adjective” but also can accurately depict its importance in real MAGDM. Therefore, this paper comes up with the probabilistic double hierarchy linguistic grey relational analysis (PDHL-GRA) method based on the grey relational analysis (GRA) process for MAGDM based on PDHLTS environment and applies it to the college tennis classroom teaching effect evaluation. Finally, a practical case for college tennis classroom teaching effect evaluation is presented to demonstrate the steps of our method, and a comparison analysis illustrates its feasibility and effectiveness.

1. Introduction

To better fuse decision information, MAGDM technology came into being [1–5]. After MAGDM theory came into being, it has been widely used in finance, engineering, corporate decision making, and many other aspects [6–10]. In view of the intricateness and fuzzification of decision circumstances [11–15], in many MAGDM issues, expert opinions are often stated as fuzzy data [16–18]. For this reason, Zadeh [19] raised concept of a linguistic variable for approximate reasoning. In many environments, the linguistic variable cannot exactly formulate proficient’s perspective. Hence, hesitant fuzzy LTS (HFLTS) was proposed by Rodriguez, Martinez and Herrera [20]. An idea about probabilistic linguistic term sets (PLTSs) was proposed by Pang et al. [21]. Soon afterwards, critical malfunction matters were finished off by the PLAMM and PLWAMM formulas derived by Liu and Teng [22]. The performance estimation system of college teachers was finished off by the PLPA and PLPWG formulas derived by Kobina et al. [23]. Wei et al. [24] built the EDAS method for PL-MAGDM. The extensive similarity measure based on probabilistic language circumstances was derived by Wei et al. [25]. Su et al. [26] defined the PT-TODIM method for PL-MAGDM. Lin et al. [27] defined the probabilistic uncertain linguistic term sets (PULTs). Wang et al. [28] developed the GRP and CRITIC methods for PUL-MAGDM. Wei et al. [29] built the generalized Dice similarity measures for PUL-MAGDM. Zhao et al. [30] built the PUL-TODIM method based on prospect theory. He et al. [31] built the taxonomy-based MAGDM method with probabilistic uncertain linguistic assessment information. He et al. [32] built the bidirectional projection method for PUL-MAGDM. Nevertheless, a few sophisticated proficient estimation perspectives cannot be remarked in existing language terms such as “only a tiny bit poor” or “only a tiny bit good.” Hence, Gou et al. [33] made a conceptual layout about double hierarchy linguistic term set (DHLTS) and double hierarchy hesitant fuzzy linguistic term set (DHHFLTS). Many research results have emerged one after another [34–41]. Soon afterwards, Gou et al. [42] made a project about probabilistic double hierarchy linguistic term set (PDHLTS). Lei et al. [43] built the PDHL-CODAS model to rank online shopping platform. Lei et al. [44] defined a sequence of probabilistic double hierarchy linguistic polymerization formulas. Lei et al. [45] defined the PDHL-EDAS method for MAGDM.

GRA was initially defined by Deng [46] to cope with real MAGDM. Compared with other real MAGDM methods [47–51], the GRA method could consider the shape similarity of every given alternative from PIS as well as NIS. Javanmardi et al. [52] explored grey system theory-based methods and applications in sustainability studies. Javanmardi and Liu [53] explored the human cognitive capacity in understanding systems: a grey system theory perspective. Zhang et al. [54] used the GRA method based on cumulative prospect theory for IF-MAGDM. Javanmardi et al. [55] explored the philosophical paradigm of grey system theory as a postmodern theory. With the purpose of discerning the carbon market, Zhu et al. [56] took advantage of the GRA process as well as EMD. Malek et al. [57] built a revised hybrid GRA for green supply. Kung and Wen [58] used the GRA process to solve grey MADM. Javanmardi and Liu [59] explored grey system theory-based methods and applications in analyzing socioeconomic systems. Javanmardi et al. [60] explored the philosophical foundations of grey system theory. Alptekin et al. [61] solved the low carbon development based on the GRA process. Zhang et al. [62] defined the SF-GRA method based on cumulative prospect theory for MAGDM.

The main contributions of this paper are to utilize the GRA algorithm to build the MAGDM matters on the strength of PDHLTSs. The main research work of this paper is arranged as follows: (1) the GRA is constructed on account of PDHLTSs; (2) the PDHL-GRA method is applied to finish off the MAGDM issue under PDHLTSs; (3) a practical case for college tennis classroom teaching effect evaluation is presented to demonstrate the steps of our method; and (4) a comparison analysis illustrates its feasibility and effectiveness. The framework of this article is as follows. Section 2 reviews some concepts of PDHLTSs. Section 3 designs a PDHL-GRA method for MAGDM with entropy weight. Section 4 provides a practical example to illustrate the method and a comparison analysis illustrates its effectiveness. Finally, Section 5 summarizes this study.

2. Preliminaries

First, let us learn some basics about PDHLTS.

Definition 1. (see [33]). Let us say is a DHLTS, and the definition of the DHLTS iswhere , the double hierarchy linguistic element (DHLE) is narrated as , the quantity of all DHLEs is , and all DHLEs are sorted in ascending sequence.

Definition 2 (see [42]). Let us say is a DHLTS, and the PDHLTS is created aswhere , the probabilistic double hierarchy linguistic element (PDHLE) is narrated as , the quantities of all PDHLEs are denoted as , and according to PDHLE is sorted in ascending order; the function is determined by formula (3).

Definition 3 (see [42]). Let be a DHLTS, and be a PDHLTS. The above conversion function for PDHLE is designed as follows:Because the probability sum of all PDHLEs in PDHLTS may be less than 1, we had to standardize PDHLTS, and the specific measures are as follows:where are all integers.

Definition 4. (see [43]). Let be a DHLTS and and be two different PDHLTSs, where , are the lengths of all PDHLEs in and , respectively. Especially, if , then the lengths of DHLEs are raised to . The added PDHLEs should not be greater than any of the elements in the , and the probability should be set to 0.

Definition 5. (see [42]). Let be a PDHLTS, and the expected values and deviation degree of are built as :

Definition 6. (see [43]). Let be a DHLTS, and and are two PDHLTSs, where ; then, Hamming distance is determined.

3. PDHL-GRA Method for MAGDM with Entropy Weight

Now, GRA mean in the context of PDHLTSs is proposed to deal with MAGDM matters. Also, a complete MAGDM issue is narrated as follows. Whole alternatives is shown as , is denoted a sequence of attributes, and the weight vector is , where , , , and are experts, and is weight vector of all experts. Suppose that q-th expert is evaluated alternative under attribute as .

Furthermore, PDHL-GRA mean is created to dispose of MAGDM issue with entropy weight. Step 1. Establish all decision makers’ decision matrixes PDHLTS . Step 2. Convert cost index into benefit index. Let be a PDHLTS; if is an evaluation on cost, we need to translate it into the benefit evaluation . Step 3. Compute the normalized decision matrix Step 4. The proportion of each attribute is calculated depending on the entropy formula. Entropy [63] is one of the important tools to ascertain the proportion of each attribute. The first thing to do is ascertaining the normalized decision matrix : Secondly, the Shannon entropy is obtained by the following formula: and is defined as 0, if . Finally, the attribute weights are computed: Step 5. Confirm the probabilistic double hierarchy linguistic positive ideal scheme more than zero (PDHLPIS) and probabilistic double hierarchy linguistic negative ideal scheme less than zero (PDHLNIS): where Step 6. Compute the grey rational coefficients of every given attribute of every given alternative from the PDHLPIS and PDHLNIS. Step 7. Figure out the degree of GRC of all given alternatives from PDHLPIS as well as PDHLNIS: Step 8. Compute each alternative’s PDHL relative relational degree (PDHLRRD) of all given alternatives from PDHLPIS: Step 9. According to . The highest value of , the optimal choice is.

4. Numerical Example and Comparative Analysis

4.1. Numerical Example

Based on the research on the development of tennis teachers in colleges and universities and the evaluation requirements of the new round of basic education curriculum reform, it is of great significance to measure whether tennis teaching meets the expected goals. The core courses in the curriculum reform were implemented, and the fundamental way is to implement curriculum classroom. Curriculum reform embodies an important issue that every school and teacher is thinking about. Classroom evaluation reform to carry out scientific and effective evaluation of classroom teaching and establish an effective evaluation system mechanism should be the core of the curriculum reform. According to the current and future period of teaching reform and development, classroom evaluation should be “developmental classroom evaluation.” Classroom evaluation helps to overcome the limitations and deficiencies of current evaluation. Classroom evaluation reflects the latest trend of current teacher evaluation, evaluation of advanced ideas, and evaluation functions. Classroom evaluation conducts reflection and analysis on teachers, evaluates teachers' development potential, teachers' classroom status and the process of value judgment. However, the evaluation of teaching in the field of teaching is a worldwide problem, but also the key to promoting quality education process. There is a clear gap between the current evaluation theories, methods and systems, and quality education. Similar problems exist in teacher teaching evaluation. These serious constraints restricted the promotion of quality education. Therefore, the establishment of the quality of classroom education development of the concept of evaluation system is the full implementation of the objective of quality education, and at the same time, it also pushes the design and implementation of teaching activities to a new stage. However, these problems can be attributed to the MAGDM problem. This paper analyzes college tennis classroom teaching effect evaluation problems based on the proposed PDHL-GRA method. There are five given latent college tennis teachers , who may be the best. For the sake of assessing the college tennis classroom teaching effect fairly, three experts (expert’s weight ) are invited. All experts depict their assessment information through four subsequent attributes: ① is teaching attitude; ② represents the teaching methods; ③ is student feedback; and ④ is teaching quality. Obviously, all attributes are benefit, and is the weight of four attributes where , , Suppose that expert evaluated alternative under attribute as where the double linguistic hierarchy evaluation information tables are given as follows:

Then, the decision matrixes of each invited expert are expressed in Tables 1–3.

Now, the built PDHL-GRA method is used to select the optimal latent college tennis teacher. Step 1. Standardize the evaluation matrix of the three experts (Tables 4–6). Step 2. According to the weighted average operator, the evaluation of three experts is aggregated into a total decision matrix, which has been converted to the PDHLTSs (see Table 7). Step 3. Calculate the weight of the decision attribute. Step 4. The PDHLPIS and the PDHLNIS are determined according to the global decision matrix, which has been converted to the PDHLTSs (see Tables 8 and 9). Step 5. Figure out the GRC of every alternative from PDHLPIS as well as PDHLNIS (Tables 10 and 11). Step 6. Figure out the degree of GRC of all alternatives from PDHLPIS as well as PDHLNIS (Table 12). Step 7. Calculate the of each given alternative from PDHLPIS (Table 13). Step 8. According to the , all given alternatives are ranked, the higher the , the better the alternative selected. Evidently, the order is and is the best one.

4.2. Comparative Analysis

Finally, we compared it with the PDHL-VIKOR method [64], PDHL-CODAS method [43], PDHLWA operator, PDHLWG operator, PDHLPWA operator, and PDHLPWG operator. The results and analysis are as follows (see Table 14). It can be seen from Table 14 that although the six methods are different, the optimal scheme obtained is the same. Only schemes 3 and 4 have slight differences between the PDHLWA operator and other methods. Therefore, the PDHL-GRA method proposed by us can scientifically and effectively solve the investment decision problem.

5. Conclusion

Life changes and people’s ideas and educational expectation have brought great challenges to contemporary school education, especially to college tennis education. With the gradual development of social needs, schools seem hard to meet the more and more advanced and complex education needs of the society. In order to promote whole-person education to students, family-school cooperation has become one of the effective ways to collect common effort and establish collaboration for education. Family and school cooperation not only provides an opportunity for in-depth development by prioritizing education environment and exploring potentiality of education resources but also is a booster for the development of students’ physical and mental health. However, while there are achievements in family-school cooperative management, there are still difficulties and problems. Also, the theoretical basis and teaching practices need further exploration. Affordance theory proposed by Gibson [65] claims that there is an interaction between humans (individuals) and the environment (the nature). There is potentiality of potential act in the affordance environment. Its existence is closely related to actors’ capability and understanding of the environment. That is to say, affordance is characterized not only by the environment but also by the individuals and emerges only when the two factors interact. Generally, we may put our focus on the affordance of language, the affordance of social culture, and the affordance of situations. Although focal difference exists between these types of affordances, there are similarities. Classroom management can be considered as an environment created together by the child, the teacher, and the parents, as compared with the traditional classroom management, which put emphasis on the interactive rule of the teacher and the student and the environment managed by the teacher. However, parents’ participation in college tennis class management provides a possible route for affordable learning environment. This paper defines an useful method for this kind of issue, since it builds the PDHL-GRA method for college tennis classroom teaching effect evaluation. And then a numerical example is used to evaluate the College tennis classroom teaching effect. Furthermore, to check on the feasibility as well as availability of the new proposed method, useful comparative analysis is also designed. In the near future, we shall pay attention to the consensus reaching process [66–71], influence of DMs’ psychological factors [72–77], and how to deal with the situations when criteria weights are incompletely known [78–83].

Data Availability

The data used to support the findings of this study are included within the article.

Conflicts of Interest

The authors declare that they have no conflicts of interest.

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Copyright © 2022 Lihua Wang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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