Abstract
Multi-attribute group decision-making (MAGDM) can be considered as the most significant branch in decision sciences and the multi-objective optimization ratio analysis plus full multiplicative form (MULTIMOORA) is a useful MAGDM method which provides effectiveness in problem solving. To upgrade the quality assurance system and enhance the teaching quality, undergraduate teaching audit and evaluation (UTAE) play a very important role. UTAE is an emerging kind of judgment, which plays a vital role in evaluating the teaching quality of a university. Choosing the best university through UTAE can be considered a complicated MAGDM problem. In this study, our main objective is to present a new methodology based on the 2-tuple linguistic Pythagorean fuzzy sets and the MULTIMOORA method to solve the UTAE problem called 2-tuple linguistic Pythagorean fuzzy-MULTIMOORA (2TLPF-MULTIMOORA) method. Motivated by the linguistic evaluations of 2-tuple linguistic terms, the broader structure of Pythagorean fuzzy sets, and the efficiency of the MULTIMOORA method to manage the complex problems, we aim to build the 2TLPF-MULTIMOORA method. In this article, we successfully design a proficient MULTIMOORA method which is based on the 2-tuple linguistic Pythagorean fuzzy sets for dealing with the arising uncertainties in MAGDM problems. Based on the existing MULTIMOORA method, the proposed method includes three methods, namely the ratio analysis method, the reference point method and the fully multiplicative form method. Further, we exhibit the authenticity and applicability of the presented approach through an actual UTAE problem. Moreover, we illustrate a comparative analysis of the established approach with existing techniques to reveal the validity of the presented approach.
Similar content being viewed by others
Data availability
No data were used to support this study.
References
Akram M, Ali G (2020) Hybrid models for decision making based on rough Pythagorean fuzzy bipolar soft information. Granul Comput 5(1):1–15
Akram M, Khan A (2021) Complex Pythagorean Dombi fuzzy graphs for decision making. Granul Comput 6(3):645–669
Akram M, Naz S, Edalatpanah SA, Mehreen R (2021) Group decision-making framework under linguistic \(q\)-rung orthopair fuzzy Einstein models. Soft Comput 25:10309–10334
Akram M, Sattar A, Saeid AB (2022) Competition graphs with complex intuitionistic fuzzy information. Granul Comput 7:25–47
Akram M, Shahzadi G (2021) A hybrid decision making model under \(q\)-rung orthopair fuzzy Yager aggregation operators. Granul Comput 6(4):763–777
Akram M, Shahzadi G, Alcantud JCR (2022a) Multi-attribute decision-making with q-rung picture fuzzy information. Granul Comput 7:197–215
Akram M, Shahzadi G, Peng X (2021) Extension of Einstein geometric operators to multiattribute decision making under \(q\)-rung orthopair fuzzy information. Granul Comput 6(4):779–795
Atanassov KT (1986) Intuitionistic fuzzy sets. Fuzzy Sets Syst 20(1):87–96
Baležentis A, Baležentis T (2011) An innovative multi-criteria supplier selection based on two-tuple MULTIMOORA and hybrid data. Econ Comput Econ Cybern Stud Res 45(2):37–56
Baležentis T, Baležentis A (2014) A survey on development and applications of the multi-criteria decision making method MULTIMOORA. J Multi-Criteria Decis Anal 21(3–4):209–222
Baležentis T, Zeng S (2013) Group multi-criteria decision making based upon interval-valued fuzzy numbers: An extension of the MULTIMOORA method. Expert Syst Appl 40(2):543–550
Brauers WKM, Zavadskas EK (2006) The MOORA method and its application to privatization in a transition economy. Control Cybern 35(2):445–469
Brauers WKM, Zavadskas EK (2010) Project management by MULTIMOORA as an instrument for transition economies. Technol Econ Dev Econ 16(1):5–24
Brauers WKM, Zavadskas EK (2011) MULTIMOORA optimization used to decide on a bank loan to buy property. Technol Econ Dev Econ 17(2):259–290
Brauers WKM, Zavadskas EK, Kildiene S (2014) Was the construction sector in 20 European countries anti-cyclical during the recession years 2008–2009 as measured by multicriteria analysis (MULTIMOORA)? Procedia Comput Sci 31:949–956
Chang TC, Wang H (2016) A multi-criteria group decision-making model for teacher evaluation in higher education based on cloud model and decision tree. Eurasia J Math Sci Technol Educ 12(5):1243–1262
Chen SM (1997) Interval-valued fuzzy hypergraph and fuzzy partition. IEEE Trans Syst Man Cybern 27(4):725–733
Chen SM, Hsiao WH (2000) Bidirectional approximate reasoning for rule-based systems using interval-valued fuzzy sets. Fuzzy Set Syst 113(2):185–203
Chen SM, Hsiao WH, Jong WT (1997) Bidirectional approximate reasoning based on interval-valued fuzzy sets. Fuzzy Sets Syst 91(3):339–353
Chen SM, Jong WT (1997) Fuzzy query translation for relational database systems. IEEE Trans Syst Man Cybern 27(4):714–721
Chen SM, Niou SJ (2011) Fuzzy multiple-attributes group decision-making based on fuzzy preference relations. Expert Syst Appl 38(4):3865–3872
Chen X, Zhao L, Liang H (2018) A novel multi-attribute group decision-making method based on the MULTIMOORA with linguistic evaluations. Soft Comput 22(16):5347–5361
Deng X, Wang J, Wei G (2019) Some 2-tuple linguistic Pythagorean Heronian mean operators and their application to multiple attribute decision-making. J Exp Theor Artif Intell 31(4):555–574
Deng X, Wang J, Wei W, Lu M (2018) Models for multiple attribute decision making with some 2-tuple linguistic Pythagorean fuzzy Hamy mean operators. Mathematics 6(11):236
Fattahi R, Khalilzadeh M (2018) Risk evaluation using a novel hybrid method based on FMEA, extended MULTIMOORA, and AHP methods under fuzzy environment. Saf Sci 102:290–300
Feng F, Zheng Y, Sun B, Akram A (2021) Novel score functions of generalized orthopair fuzzy membership grades with application to multiple attribute decision making. Granul Comput 7:95–111
Gao Y, Du Y, Liang H, Sun B (2018) Large group decision-making approach based on stochastic MULTIMOORA: An application of doctor evaluation in healthcare service. Complexity. https://doi.org/10.1155/2018/540940
Garg H (2018) Linguistic Pythagorean fuzzy sets and its applications in multiattribute decision-making process. Int J Intell Syst 33(6):1234–1263
Gong JW, Li Q, Yin L, Liu HC (2020) Undergraduate teaching audit and evaluation using an extended MABAC method under \(q\)-rung orthopair fuzzy environment. Int J Intell Syst 35(12):1912–1933
Gündogdu FK (2020) A spherical fuzzy extension of MULTIMOORA method. J Intell Fuzzy Syst 38(1):963–978
Hafezalkotob A, Hafezalkotob A (2016) Fuzzy entropy weighted MULTIMOORA method for materials selection. J Intell Fuzzy Syst 31(3):1211–1226
Hafezalkotob A, Hafezalkotob A, Liao H, Herrera F (2018) An overview of MULTIMOORA for multi-criteria decision-making: theory, developments, applications, and challenges. Inf Fusion 51:145–177
Hafezalkotob A, Hafezalkotob A, Sayadi MK (2016) Extension of MULTIMOORA method with interval numbers: An application in materials selection. Appl Math Model 40(2):1372–1386
Hatefi MA (2019) Indifference threshold based attribute ratio analysis: A method for assigning the weights to the attributes in multiple attribute decision making. Appl Soft Comput 74:643–651
Herrera F, Martínez L (2000a) A 2-tuple fuzzy linguistic representation model for computing with words. IEEE Tran Fuzzy Syst 8(6):746–752
Herrera F, Martínez L (2000b) An approach for combining linguistic and numerical information based on the 2-tuple fuzzy linguistic representation model in decision-making. Int J Uncertain Fuzz 8(05):539–562
Jiang Y, Zhang J, Chen C (2018) Research on a new teaching quality evaluation method based on improved fuzzy neural network for college english. Int J Contin Eng Educ Life Long Learn. 28(3–4):293–309
Lazauskas M, Kutut V, Zavadskas EK (2015a) Multicriteria assessment of unfinished construction projects. Gradevinar 67(04):319–328
Lazauskas M, Zavadskas EK, Šaparauskas J (2015b) Ranking of priorities among the baltic capital cities for the development of sustainable construction. Econ Manag 18(2):15–24
Li C, Zeng S, Pan T, Zheng L (2014) A method based on induced aggregation operators and distance measures to multiple attribute decision making under 2-tuple linguistic environment. J Comput Syst Sci 80(7):1339–1349
Liang W, Zhao G, Hong C (2019) Selecting the optimal mining method with extended multi-objective optimization by ratio analysis plus the full multiplicative form (MULTIMOORA) approach. Neural Comput Appl 31(10):5871–5886
Liu HC, Fan XJ, Li P, Chen YZ (2014) Evaluating the risk of failure modes with extended MULTIMOORA method under fuzzy environment. Eng Appl Artif Intell 34:168–177
Liu P, Naz S, Akram M, Muzammal M (2022) Group decision-making analysis based on linguistic \(q\)-rung orthopair fuzzy generalized point weighted aggregation operators. Int J Mach Learn Cybern 13:883–906
Liu Y, Qin Y, Liu F, Rong Y (2021) GIBWM-MABAC approach for MAGDM under multi-granularity intuitionistic 2-tuple linguistic information model. J Ambient Intell Humaniz Comput: https://doi.org/10.1007/s12652-021-03476-3
Liu HC, You JX, Lu C, Shan MM (2014) Application of interval 2-tuple linguistic MULTIMOORA method for health-care waste treatment technology evaluation and selection. Waste Manage 34(11):2355–2364
Lu M, Wei G, Alsaadi FE, Hayat T, Alsaedi A (2017) Bipolar 2-tuple linguistic aggregation operators in multiple attribute decision making. J Intell Fuzzy Syst 33(2):1197–1207
Mahmood T, Warraich MS, Ali Z, Pamucar D (2021) Generalized MULTIMOORA method and Dombi prioritized weighted aggregation operators based on T-spherical fuzzy sets and their applications. Int J Int Syst 36(9):4659–4692
Mora H, Signes-Pont MT, Fuster-Guilló A, Pertegal-Felices ML (2020) A collaborative working model for enhancing the learning process of science and engineering students. Comput Hum Behav 103:140–150
Naz S, Akram M, Al-Shamiri MMA, Khalaf MM, Yousaf G (2022) A new MAGDM method with 2-tuple linguistic bipolar fuzzy Heronian mean operators. Math Biosci Eng 19(4):3843–3878
Park JH, Park JM, Kwun YC (2013) 2-Tuple linguistic harmonic operators and their applications in group decision making. Knowl Based Syst 44:10–19
Peng X (2019) Neutrosophic reducible weighted maclaurin symmetric mean for undergraduate teaching audit and evaluation. IEEE Access 7:18634–18648
Qin Y, Liu Y, Abdullah S, Wei G (2021) Group decision support methodology based upon the multigranular generalized orthopair 2-tuple linguistic information model. Int J Intell Syst 36:3367–3400
Sarkar B, Biswas A (2022) A multi-criteria decision making approach for strategy formulation using Pythagorean fuzzy logic. Expert Syst 39(1):e12802
Stanujkic D, Zavadskas EK, Smarandache F, Brauers WKM, Karabasevic D (2017) A neutrosophic extension of the MULTIMOORA method. Informatica 28(1):181–192
Streimikiene D, Baležentis T, Krisciukaitienë I, Baležentis A (2012) Prioritizing sustainable electricity production technologies: MCDM approach. Renew Sust Energ Rev 16(5):3302–3311
Turksen IB (1986) Interval valued fuzzy sets based on normal forms. Fuzzy sets syst 20(2):191–210
Wei GW (2011) Some generalized aggregating operators with linguistic information and their application to multiple attribute group decision making. Comput Ind Eng 61(1):32–38
Wei GW (2019) 2-tuple intuitionistic fuzzy linguistic aggregation operators in multiple attribute decision making. Iran J Fuzzy Syst 16(4):159–174
Wei Z, Baocun L (2018) The undergraduate teaching evaluation system in China: progress, problems and suggestions. Chin Educ Soc 51(4):248–259
Xian S, Liu Z, Gou X, Wan W (2020) Interval 2-tuple Pythagorean fuzzy linguistic MULTIMOORA method with CIA and their application to MCGDM. Int J Intell Syst 35(4):650–681
Xu Y, Wang H (2011) Approaches based on 2-tuple linguistic power aggregation operators for multiple attribute group decision making under linguistic environment. Appl Soft Comput 11(5):3988–3997
Yager RR (2013) Pythagorean fuzzy subsets. IEEE :57-61
Yager RR (2013) Pythagorean membership grades in multi-criteria decision making. IEEE Trans Fuzzy Syst 22(4):958–965
Yang J, Shen L, Jin X, Hou L, Shang S, Zhang Y (2019) Evaluating the quality of simulation teaching in fundamental nursing curriculum: AHP-fuzzy comprehensive evaluation. Nurse Educ Today 77:77–82
Yildirim B, Topkaya EZ (2020) Clarificative evaluation of elementary level grammar program of a tertiary level preparatory class in Turkey. Stud Educ Eval 65:100862
Zadeh LA (1965) Fuzzy sets. Inf. Control 8(3):338–353
Zadeh LA (1975) The concept of a linguistic variable and its application to approximate reasoning part I. Inf Sci 8(3):199–249
Zavadskas EK, Antucheviciene J, Hajiagha R, Hossein S, Hashemi SS (2015) The interval-valued intuitionistic fuzzy MULTIMOORA method for group decision making in engineering. Math Probl Eng. https://doi.org/10.1155/2015/560690
Zavadskas EK, Bausys R, Juodagalviene B, Garnyte-Sapranaviciene I (2017) Model for residential house element and material selection by neutrosophic MULTIMOORA method. Eng Appl Artif Intell 64:315–324
Zhang H (2014) Linguistic intuitionistic fuzzy sets and application in MAGDM. J Appl Math. https://doi.org/10.1155/2014/432092
Zhang X, Wang J, Zhang H, Hu J (2017) A heterogeneous linguistic MAGDM framework to classroom teaching quality evaluation. Eurasia J Math Sci Technol Educ 13(8):4929–4956
Zhao X (2014) TOPSIS method for interval valued intuitionistic fuzzy multiple attribute decision making and its application to teaching quality evaluation. J Intell Fuzzy Syst 26(6):3049–3055
Zhao H, You JX, Liu HC (2017) Failure mode and effect analysis using MULTIMOORA method with continuous weighted entropy under interval-valued intuitionistic fuzzy environment. Soft Comput 21(18):5355–5367
Zhou F, Chen TY (2020) An integrated multicriteria group decision-making approach for green supplier selection under Pythagorean fuzzy scenarios. IEEE Access 8:165216–165231
Zhou WY, You XY, Zhao H, Liu HC (2018) Robot evaluation and selection using the hesitant fuzzy linguistic MULTIMOORA method. J Test Eval 47(2):1405–1426
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
Ethical approval
This article does not contain any studies with human participants or animals performed by any of the authors.
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Akram, M., Khan, A. & Ahmad, U. Extended MULTIMOORA method based on 2-tuple linguistic Pythagorean fuzzy sets for multi-attribute group decision-making. Granul. Comput. 8, 311–332 (2023). https://doi.org/10.1007/s41066-022-00330-5
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s41066-022-00330-5