A Novel Method Based on Induced Aggregation Operator for Classroom Teaching Quality Evaluation with Probabilistic and Pythagorean Fuzzy Information

Shouzhen Zeng; Nan Wang; Chonghui Zhang; Weihua Su

doi:10.29333/ejmste/89518

Shouzhen Zeng ¹, Nan Wang ², Chonghui Zhang ², Weihua Su ² ^*

More Detail

¹ School of Business, Ningbo University, Ningbo, CHINA² College of Statistics and Mathematics, Zhejiang Gongshang University, Hangzhou, CHINA^* Corresponding Author

This article is retracted by request from the corresponding author. All authors agree to the retraction of the Article. Retraction Note: https://doi.org/10.29333/ejmste/96348

Abstract

The purpose of this study is to develop a novel method based on induced aggregation operator to evaluate classroom teaching quality with probabilistic and Pythagorean fuzzy (PF) information. Inspired by the induced ordered weighted averaging (IOWA) operator, a PF aggregation operator called the PF induced probabilistic ordered weighted average (PFIPOWA) operator is developed. This operator uses probabilities and order-induced variables in the same formulas to aggregate PF information. Some of key features and special cases of the PFIPOWA operator are also investigated. Finally, the practicality of the developed operator is tested by using realistic classroom teaching quality evaluation problems. Hopefully, the research of this paper is of great significance to the evaluation of classroom teaching quality problems.

Keywords

Pythagorean fuzzy set
induced aggregation operator
probabilistic information
classroom teaching quality evaluation
multi-attribute decision making

License

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.

Article Type: Research Article

EURASIA J Math Sci Tech Ed, Volume 14, Issue 7, July 2018, 3205-3212

https://doi.org/10.29333/ejmste/89518

Publication date: 15 May 2018

Article Views: 2570

Article Downloads: 0

Open Access References How to cite this article

References

Aggarwal, M. (2015). A New Family of Induced OWA Operators. International Journal of Intelligent Systems, 30(2), 170–205. https://doi.org/10.1002/int.21693.
Atanassov, K. (1986). Intuitionistic fuzzy sets. Fuzzy Sets and Systems, 20(1), 87-96. https://doi.org/10.1007/978-3-7908-1870-3.
Chen, T. Y. (2018). Remoteness index-based Pythagorean fuzzy VIKOR methods with a generalized distance measure for multiple criteria decision analysis. Information Fusion, 41, 129–150. https://doi.org/10.1016/j.inffus.2017.09.003.
Merigó, J. M. (2010). Fuzzy decision making with immediate probabilities. Computers & Industrial Engineering, 58(4), 651–657. https://doi.org/10.1016/j.cie.2010.01.007.
Merigó, J. M. (2011a). Fuzzy multi-person decision making with fuzzy probabilistic aggregation operators. International Journal of Fuzzy Systems, 13(3), 163-173. http://doi.org/10.1016/j.eswa.2011.03.034.
Merigó, J. M. (2011b). A unified model between the weighted average and the induced OWA operator. Expert Systems with Applications, 38(9), 11560-11572. http://dx.doi.org/10.1016/j.eswa.2011.03.034.
Merigó, J. M., & Gil-Lafuente, A. M. (2013). Induced 2-tuple linguistic generalized aggregation operators and their application in decision-making. Information Sciences, 236, 1–16. https://doi.org/10.1016/j.ins.2013.02.039.
Peng, X. D., & Dai, J. G. (2017). Approaches to Pythagorean fuzzy stochastic multi-criteria decision making based on prospect theory and regret theory with new distance measure and score function. International Journal of Intelligent Systems, 32(11), 1187-1214. https://doi.org/10.1002/int.21896.
Peng, X. D., & Yang, Y. (2015). Some results for Pythagorean fuzzy sets. International Journal of Intelligent Systems, 30(11), 1133–1160. https://doi.org/10.1002/int.21738.
Peng, X. D., & Yang, Y. (2016). Pythagorean fuzzy Choquet integral based MABAC method for multiple attribute group decision making. International Journal of Intelligent Systems, 31(10), 989-1020. https://doi.org/10.1002/int.21814.
Shieh, C. J., & Yu, L. (2016). A study on information technology integrated guided discovery instruction towards students’ learning achievement and learning retention. EURASIA Journal of Mathematics, Science & Technology Education, 12(4), 833-842. https://doi.org/10.12973/eurasia.2015.1554a.
Wei, G. W. (2017). Pythagorean fuzzy interaction aggregation operators and their application to multiple attribute decision making. Journal of Intelligent and Fuzzy Systems, 33(4), 2119-2132. https://doi.org/10.3233/JIFS-162030.
Xia, M. M., Xu, Z. S., & Chen, N. (2011). Induced aggregation under confidence levels. International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, 19(2), 201-227. https://doi.org/10.1142/S0218488511006976.
Xian, S., Zhang, J., & Xue, W. (2016). Fuzzy linguistic induced generalized OWA operator and its application in fuzzy linguistic decision making. International Journal of Intelligent Systems, 31(8), 749-762. https://doi.org/10.1002/int.21801.
Yager, R. R. (1988). On ordered weighted averaging aggregation operators in multi-criteria decision making. IEEE Transactions on Systems, Man & Cybernetics B, 18(1), 183–190. https://doi.org/10.1109/21.87068.
Yager, R. R. (2014). Pythagorean membership grades in multi-criteria decision making. IEEE Transactions on Fuzzy Systems, 22(4), 958–965. https://doi.org/10.1109/TFUZZ.2013.2278989.
Yager, R. R., & Filev, D. P. (1999). Induced ordered weighted averaging operators. IEEE Transactions on Systems Man & Cybernetics Part B, 29(2), 141-150. https://doi.org/10.1109/3477.752789.
Yu, D. J. (2013). Prioritized information fusion method for triangular intuitionistic fuzzy set and its application to teaching quality evaluation. International Journal of Intelligent Systems, 28(5), 411-435. http://dx.doi.org/10.1002/int.21583.
Yu, D. J. (2014). Intuitionistic fuzzy information aggregation under confidence levels. Applied Soft Computing, 19(6), 147–160. https://doi.org/10.1016/j.asoc.2014.02.001.
Yu, L., & Lai, K. K. (2011). A distance-based group decision making methodology for multi-person multicriteria emergency decision support. Decision Support Systems, 51(2), 307-315. https://doi.org/10.1016/j.dss.2010.11.024.
Yu, L., Wang, S. Y., & Lai, K. K. (2009). An Intelligent-Agent-Based Fuzzy Group Decision Making Model for Financial Multicriteria Decision Support: The Case of Credit Scoring. European Journal of Operational Research, 195(3), 942-959. https://doi.org/10.1016/j.ejor.2007.11.025.
Zeng, S. Z. (2017). Pythagorean fuzzy multiattribute group decision making with probabilistic information and OWA approach. International Journal of Intelligent Systems, 32(11), 1136-1150. https://doi.org/10.1002/int.21886.
Zeng, S. Z., Chen, J. P., & Li, X. S. (2016a). A hybrid method for Pythagorean fuzzy multiple-criteria decision making. International Journal of Information Technology & Decision Making, 15(2), 403–422. https://doi.org/10.1142/S0219622016500012.
Zeng, S. Z., Merigó, J. M., Palacios-Marqués, D., Jin, H., & Gu, F. (2017). Intuitionistic fuzzy induced ordered weighted averaging distance operator and its application to decision making. Journal of Intelligent & Fuzzy Systems, 32(1), 11-22. https://doi.org/10.3233/JIFS-141219.
Zeng, S. Z., Su, W. H. S., & Zhang, C. H. (2016b). Intuitionistic fuzzy generalized probabilistic ordered weighted averaging operator and its application to group decision making. Technological and Economic Development of Economy, 22(2), 177-193. https://doi.org/10.3846/20294913.2014.984253.
Zhang, C. H., Su, W. H., & Zeng, S. Z. (2017a). Intuitionistic linguistic multiple attribute decision-making based on Heronian mean method and its application to evaluation of scientific research capacity. EURASIA Journal of Mathematics Science and Technology Education, 13(2), 8017-8025. https://doi.org/10.12973/ejmste/77933.
Zhang, X. L. (2016). A novel approach based on similarity measure for Pythagorean fuzzy multiple criteria group decision making. International Journal of Intelligent Systems, 31(6), 593-611. https://doi.org/10.1002/int.21796.
Zhang, X. L., & Xu, Z. S. (2014). Extension of TOPSIS to multiple criteria decision making with Pythagorean fuzzy sets. International Journal of Intelligent Systems, 29(12), 1061–1078. https://doi.org/10.1002/int.21676.
Zhang, X. Y., Wang, J. Q., Zhang, H. Y., & Hu, J. H. (2017b). A heterogeneous linguistic MAGDM framework to classroom teaching quality evaluation. EURASIA Journal of Mathematics Science and Technology Education, 13(8), 4929-4956. https://doi.org/10.12973/eurasia.2017.00966a.
Zhang, Z. M., Wang, C., Tian, D., & Li, K. (2014). Induced generalized hesitant fuzzy operators and their application to multiple attribute group decision making. Computers & Industrial Engineering, 67(1), 116–138. https://doi.org/10.1016/j.cie.2013.10.011.
Zhou, L. G., & Chen, H. Y. (2013). The induced linguistic continuous ordered weighted geometric operator and its application to group decision making. Computers & Industrial Engineering, 66(2), 222-232. https://doi.org/10.1016/j.cie.2013.07.021.

How to cite this article

APA

Zeng, S., Wang, N., Zhang, C., & Su, W. (2018). A Novel Method Based on Induced Aggregation Operator for Classroom Teaching Quality Evaluation with Probabilistic and Pythagorean Fuzzy Information. Eurasia Journal of Mathematics, Science and Technology Education, 14(7), 3205-3212. https://doi.org/10.29333/ejmste/89518

Vancouver

Zeng S, Wang N, Zhang C, Su W. A Novel Method Based on Induced Aggregation Operator for Classroom Teaching Quality Evaluation with Probabilistic and Pythagorean Fuzzy Information. EURASIA J Math Sci Tech Ed. 2018;14(7):3205-12. https://doi.org/10.29333/ejmste/89518

AMA

Zeng S, Wang N, Zhang C, Su W. A Novel Method Based on Induced Aggregation Operator for Classroom Teaching Quality Evaluation with Probabilistic and Pythagorean Fuzzy Information. EURASIA J Math Sci Tech Ed. 2018;14(7), 3205-3212. https://doi.org/10.29333/ejmste/89518

Chicago

Zeng, Shouzhen, Nan Wang, Chonghui Zhang, and Weihua Su. "A Novel Method Based on Induced Aggregation Operator for Classroom Teaching Quality Evaluation with Probabilistic and Pythagorean Fuzzy Information". Eurasia Journal of Mathematics, Science and Technology Education 2018 14 no. 7 (2018): 3205-3212. https://doi.org/10.29333/ejmste/89518

Harvard

Zeng, S., Wang, N., Zhang, C., and Su, W. (2018). A Novel Method Based on Induced Aggregation Operator for Classroom Teaching Quality Evaluation with Probabilistic and Pythagorean Fuzzy Information. Eurasia Journal of Mathematics, Science and Technology Education, 14(7), pp. 3205-3212. https://doi.org/10.29333/ejmste/89518

MLA

Zeng, Shouzhen et al. "A Novel Method Based on Induced Aggregation Operator for Classroom Teaching Quality Evaluation with Probabilistic and Pythagorean Fuzzy Information". Eurasia Journal of Mathematics, Science and Technology Education, vol. 14, no. 7, 2018, pp. 3205-3212. https://doi.org/10.29333/ejmste/89518