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Extended MULTIMOORA method based on 2-tuple linguistic Pythagorean fuzzy sets for multi-attribute group decision-making

Granular Computing (2022)Cite this article

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.

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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

    Article  Google Scholar 

  • Akram M, Khan A (2021) Complex Pythagorean Dombi fuzzy graphs for decision making. Granul Comput 6(3):645–669

    MathSciNet  Article  Google Scholar 

  • 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

    Article  Google Scholar 

  • Akram M, Sattar A, Saeid AB (2022) Competition graphs with complex intuitionistic fuzzy information. Granul Comput 7:25–47

    Article  Google Scholar 

  • Akram M, Shahzadi G (2021) A hybrid decision making model under \(q\)-rung orthopair fuzzy Yager aggregation operators. Granul Comput 6(4):763–777

    Article  Google Scholar 

  • Akram M, Shahzadi G, Alcantud JCR (2022a) Multi-attribute decision-making with q-rung picture fuzzy information. Granul Comput 7:197–215

    Article  Google Scholar 

  • 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

    Article  Google Scholar 

  • Atanassov KT (1986) Intuitionistic fuzzy sets. Fuzzy Sets Syst 20(1):87–96

    Article  MATH  Google Scholar 

  • 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

    Google Scholar 

  • 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

    Article  Google Scholar 

  • 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

    Article  Google Scholar 

  • Brauers WKM, Zavadskas EK (2006) The MOORA method and its application to privatization in a transition economy. Control Cybern 35(2):445–469

    MathSciNet  MATH  Google Scholar 

  • Brauers WKM, Zavadskas EK (2010) Project management by MULTIMOORA as an instrument for transition economies. Technol Econ Dev Econ 16(1):5–24

    Article  Google Scholar 

  • 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

    Article  Google Scholar 

  • 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

    Article  Google Scholar 

  • 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

    MathSciNet  Google Scholar 

  • Chen SM (1997) Interval-valued fuzzy hypergraph and fuzzy partition. IEEE Trans Syst Man Cybern 27(4):725–733

    Article  Google Scholar 

  • Chen SM, Hsiao WH (2000) Bidirectional approximate reasoning for rule-based systems using interval-valued fuzzy sets. Fuzzy Set Syst 113(2):185–203

    MathSciNet  Article  MATH  Google Scholar 

  • Chen SM, Hsiao WH, Jong WT (1997) Bidirectional approximate reasoning based on interval-valued fuzzy sets. Fuzzy Sets Syst 91(3):339–353

    MathSciNet  Article  MATH  Google Scholar 

  • Chen SM, Jong WT (1997) Fuzzy query translation for relational database systems. IEEE Trans Syst Man Cybern 27(4):714–721

    Article  Google Scholar 

  • Chen SM, Niou SJ (2011) Fuzzy multiple-attributes group decision-making based on fuzzy preference relations. Expert Syst Appl 38(4):3865–3872

    Article  Google Scholar 

  • 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

    Article  MATH  Google Scholar 

  • 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

    Article  Google Scholar 

  • 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

    Article  MATH  Google Scholar 

  • 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

    Article  Google Scholar 

  • 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

    Article  Google Scholar 

  • 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

    Article  MATH  Google Scholar 

  • Garg H (2018) Linguistic Pythagorean fuzzy sets and its applications in multiattribute decision-making process. Int J Intell Syst 33(6):1234–1263

    Article  Google Scholar 

  • 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

    Article  Google Scholar 

  • Gündogdu FK (2020) A spherical fuzzy extension of MULTIMOORA method. J Intell Fuzzy Syst 38(1):963–978

    Article  Google Scholar 

  • Hafezalkotob A, Hafezalkotob A (2016) Fuzzy entropy weighted MULTIMOORA method for materials selection. J Intell Fuzzy Syst 31(3):1211–1226

    Article  MATH  Google Scholar 

  • 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

    Article  Google Scholar 

  • 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

    MathSciNet  Article  MATH  Google Scholar 

  • 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

    Article  Google Scholar 

  • Herrera F, Martínez L (2000a) A 2-tuple fuzzy linguistic representation model for computing with words. IEEE Tran Fuzzy Syst 8(6):746–752

    Article  Google Scholar 

  • 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

    MathSciNet  Article  MATH  Google Scholar 

  • 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

    Article  Google Scholar 

  • Lazauskas M, Kutut V, Zavadskas EK (2015a) Multicriteria assessment of unfinished construction projects. Gradevinar 67(04):319–328

    Google Scholar 

  • 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

    Google Scholar 

  • 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

    MathSciNet  Article  MATH  Google Scholar 

  • 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

    Article  Google Scholar 

  • 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

    Article  Google Scholar 

  • 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

    Article  Google Scholar 

  • 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

    Article  Google Scholar 

  • 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

    Article  Google Scholar 

  • 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

    Article  MATH  Google Scholar 

  • 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

    Article  Google Scholar 

  • 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

    Article  Google Scholar 

  • 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

    Article  Google Scholar 

  • 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

    Article  Google Scholar 

  • Peng X (2019) Neutrosophic reducible weighted maclaurin symmetric mean for undergraduate teaching audit and evaluation. IEEE Access 7:18634–18648

    Article  Google Scholar 

  • 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

    Article  Google Scholar 

  • Sarkar B, Biswas A (2022) A multi-criteria decision making approach for strategy formulation using Pythagorean fuzzy logic. Expert Syst 39(1):e12802

    Article  Google Scholar 

  • Stanujkic D, Zavadskas EK, Smarandache F, Brauers WKM, Karabasevic D (2017) A neutrosophic extension of the MULTIMOORA method. Informatica 28(1):181–192

    Article  Google Scholar 

  • Streimikiene D, Baležentis T, Krisciukaitienë I, Baležentis A (2012) Prioritizing sustainable electricity production technologies: MCDM approach. Renew Sust Energ Rev 16(5):3302–3311

    Article  Google Scholar 

  • Turksen IB (1986) Interval valued fuzzy sets based on normal forms. Fuzzy sets syst 20(2):191–210

    MathSciNet  Article  MATH  Google Scholar 

  • 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

    Article  Google Scholar 

  • Wei GW (2019) 2-tuple intuitionistic fuzzy linguistic aggregation operators in multiple attribute decision making. Iran J Fuzzy Syst 16(4):159–174

    MathSciNet  MATH  Google Scholar 

  • Wei Z, Baocun L (2018) The undergraduate teaching evaluation system in China: progress, problems and suggestions. Chin Educ Soc 51(4):248–259

    Article  Google Scholar 

  • 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

    Article  Google Scholar 

  • 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

    Article  Google Scholar 

  • 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

    Article  Google Scholar 

  • 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

    Article  Google Scholar 

  • 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

    Article  Google Scholar 

  • Zadeh LA (1965) Fuzzy sets. Inf. Control 8(3):338–353

    MathSciNet  Article  MATH  Google Scholar 

  • Zadeh LA (1975) The concept of a linguistic variable and its application to approximate reasoning part I. Inf Sci 8(3):199–249

    Article  MATH  Google Scholar 

  • 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

    Article  Google Scholar 

  • 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

    Google Scholar 

  • 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

    MathSciNet  Article  MATH  Google Scholar 

  • 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

    Article  Google Scholar 

  • 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

    Article  Google Scholar 

  • 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

    Google Scholar 

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  1. Department of Mathematics, University of the Punjab, New Campus, Lahore, Pakistan

    Muhammad Akram, Ayesha Khan & Uzma Ahmad

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  1. Muhammad Akram
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  2. Ayesha Khan
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  3. Uzma Ahmad
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Correspondence to Muhammad Akram.

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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. (2022). https://doi.org/10.1007/s41066-022-00330-5

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Keywords

  • MULTIMOORA method
  • 2-tuple linguistic Pythagorean fuzzy sets
  • teaching quality
  • MAGDM