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Group decision-making based on 2-tuple linguistic T-spherical fuzzy COPRAS method


Data mining is a thoroughly advanced method that evaluates and makes more sense of a variety in electronic commerce (e-commerce)-related knowledge, discovering useful ideas, predicting user actions, and assisting enterprises selection in modifying competitive strategy, minimizing cost, and attaining the finest results. Data mining has already become more popular in recent years. In this research paper, we propose a multi-attribute group decision-making (MAGDM) method under T-spherical fuzzy environment for selecting an optimal data mining strategy which is an important part of modern decision-making research. The information aggregation operators play an important role in solving MAGDM problems. Some point aggregation operators based on the 2-tuple linguistic T-spherical fuzzy numbers, including 2-tuple linguistic T-spherical fuzzy point weighted averaging (2TLT-SFPWA) operator, 2-tuple linguistic T-spherical fuzzy point weighted geometric (2TLT-SFPWG) operator, 2-tuple linguistic T-spherical fuzzy generalized point weighted averaging (2TLT-SFGPWA) operator and 2-tuple linguistic T-spherical fuzzy generalized point weighted geometric (2TLT-SFGPWG) operator, are proposed which competently capture all the aspects of human opinions expressible in terms of yes, no, cessation and denial with no limitation. The proposed aggregation operators are valid and have some basic properties which are keenly analyzed. Furthermore, the complex proportional assessment (COPRAS) method is developed on the basis of 2-tuple linguistic T-spherical fuzzy point aggregation operators. Finally, a numerical example is illustrated for demonstrating the effectiveness of the proposed work along with comparative analysis which verifies the reliability and efficacy of its outcomes. In the end, we conclude some results from the numerical analysis, i.e., to balance the long-term development of e-commerce, data mining can mine massive amounts of data which boosts the growth of e-commerce in future.

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  • Akram M, Khan A, Borumand Saeid A (2020a) Complex pythagorean Dombi fuzzy operators using aggregation operators and their decision-making. Expert Syst 38(2):e12626

  • Akram M, Alsulami S, Khan A, Karaaslan F (2020b) Multi-criteria group decision-making using spherical fuzzy prioritized weighted aggregation operators. Int J Comput Intell Syst 13(1):1429–1446

  • Akram M, Naz S, Edalatpanah SA, Mehreen R (2021a) Group decision-making framework under linguistic \(q\)-rung orthopair fuzzy Einstein models. Soft Comput 25(15):10309–10334

  • Akram M, Sattar A, Peng X (2021b) A new decision making model using complex intuitionistic fuzzy Hamacher aggregation operators. Soft Comput 25(10):7059–7086

  • Akram M, Kahraman C, Zahid K (2021c) Group decision-making based on complex spherical fuzzy VIKOR approach. Knowl Based Syst 216:106793

  • Akram M, Naz S, Feng F, Shafiq A (2022) Assessment of hydropower plants in Pakistan: Muirhead mean-based 2-tuple linguistic \(T\)-spherical fuzzy model combining SWARA with COPRAS. Arab J Sci Eng.

    Article  Google Scholar 

  • Akran M, Kahraman C, Zahid K (2021) Extension of TOPSIS model to the decision making under complex spherical fuzzy information. Soft Comput 25(16):10771–10795

    Article  Google Scholar 

  • Ashraf S, Abdullah S (2019) Spherical aggregation operators and their application in multiattribute group decision-making. Int J Intell Syst 34(3):493–523

    Article  Google Scholar 

  • Ashraf S, Abdullah S, Aslam M, Qiyas M, Kutbi MA (2019) Spherical fuzzy sets and its representation of spherical fuzzy t-norms and t-conorms. J Intell Fuzzy Syst 36(6):6089–6102

    Article  Google Scholar 

  • Ashraf S, Abdullah S, Mahmood T (2020) Spherical fuzzy Dombi aggregation operators and their application in group decision making problems. J Ambient Intell Humaniz Comput 11(7):2731–2749

    Article  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  • Buyukozkan G, Gocer F (2019) A novel approach integrating AHP and COPRAS under Pythagorean fuzzy sets for digital supply chain partner selection. IEEE Trans Eng Manage 68(5):1486–1503

    Article  Google Scholar 

  • Cuong BC, Kreinovich V (2014) Picture fuzzy sets. J Comput Sci Cybern 30(4):409–420

    Google Scholar 

  • Darko AP, Liang D (2020) Some \(q\)-rung orthopair fuzzy Hamacher aggregation operators and their application to multiple attribute group decision making with modified EDAS method. Eng Appl Artif Intell 87:103259

    Article  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 

  • Dorfeshan Y, Mousavi SM (2019) A group TOPSIS-COPRAS methodology with Pythagorean fuzzy sets considering weights of experts for project critical path problem. J Intell Fuzzy Syst 36(2):1375–1387

    Article  Google Scholar 

  • Gündogdu FK, Kahraman C (2019) Spherical fuzzy sets and spherical fuzzy TOPSIS method. J Intell Fuzzy Syst 36(1):337–352

    Article  MATH  Google Scholar 

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

  • Herrera F, Martinez 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 Knowl Based Syst 8(05):539–562

  • Ju Y, Wang A, Ma J, Gao H, Santibanez Gonzalez ED (2020) Some \(q\)-rung orthopair fuzzy 2-tuple linguistic Muirhead mean aggregation operators and their applications to multiple-attribute group decision making. Int J Intell Syst 35(1):184–213

    Article  Google Scholar 

  • Kahraman C, Gündogdu FK, (2018) From 1D to 3D membership: spherical fuzzy sets, BOS, SOR. Polish Operational and Systems Research Society, September 24th–26th 2018. Palais Staszic, Warsaw, Poland

  • Kahraman C, Gündogdu FK, Onar SC, Oztaysi B (2019) Hospital location selection using spherical fuzzy TOPSIS. In: In 11th Conference of the European society for fuzzy logic and technology (EUSFLAT 2019), Atlantis Press

  • Liu P, Zhu B, Wang P, Shen M (2020) An approach based on linguistic spherical fuzzy sets for public evaluation of shared bicycles in China. Eng Appl Artif Intell 87:103295

    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 

  • Mahmood T, Ullah K, Khan Q, Jan N (2019) An approach toward decision-making and medical diagnosis problems using the concept of spherical fuzzy sets. Neural Comput Appl 31(11):7041–7053

    Article  Google Scholar 

  • Mishra AR, Rani P, Pardasani KR (2019) Multiple-criteria decision-making for service quality selection based on Shapley COPRAS method under hesitant fuzzy sets. Granul Comput 4(3):435–449

    Article  Google Scholar 

  • Mo J, Huang HL (2020) Archimedean geometric Heronian mean aggregation operators based on dual hesitant fuzzy set and their application to multiple attribute decision making. Soft Comput 24(19):14721–14733

    Article  MATH  Google Scholar 

  • Naz S, Akram M, Muhiuddin G, Shafiq A (2022a) Modified EDAS method for MAGDM based on MSM operators with 2-tuple linguistic-spherical fuzzy sets. Math Probl Eng 2022:1–34

  • Naz S, Akram M, Saeid AB, Saadat A (2022b) Models for MAGDM with dual hesitant q-rung orthopair fuzzy 2-tuple linguistic MSM operators and their application to COVID-19 pandemic. Expert Syst 39(8):e13005

  • Naz S, Akram M, Al-Shamiri MA, Khalaf MM, Yousaf G (2022c) A new MAGDM method with 2-tuple linguistic bipolar fuzzy Heronian mean operators. Math Biosci Eng 19:3843–3878

  • Rong Y, Liu Y, Pei Z (2020a) Complex \(q\)-rung orthopair fuzzy 2-tuple linguistic Maclaurin symmetric mean operators and its application to emergency program selection. Int J Intell Syst 35(11):1749–1790

  • Rong Y, Pei Z, Liu Y (2020b) Hesitant fuzzy linguistic Hamy mean aggregation operators and their application to linguistic multiple attribute decision-making. Math Probl Eng 2020:1–22

  • Ullah K, Mahmood T, Garg H (2020) Evaluation of the performance of search and rescue robots using \(T\)-spherical fuzzy Hamacher aggregation operators. Int J Fuzzy Syst 22(2):570–582

  • Wang L, Garg H, Li N (2019a) Interval-valued q-rung orthopair 2-tuple linguistic aggregation operators and their applications to decision making process. IEEE Access 7:131962–131977

  • Wang J, Zhang R, Zhu X, Zhou Z, Shang X, Li W (2019b) Some \(q\)-rung orthopair fuzzy Muirhead means with their application to multi-attribute group decision making. J Intell Fuzzy Syst 36(2):1599–1614

  • Xing Y, Zhang R, Zhou Z, Wang J (2019) Some \(q\)-rung orthopair fuzzy point weighted aggregation operators for multi-attribute decision making. Soft Comput 23(22):11627–11649

    Article  MATH  Google Scholar 

  • Xu ZS, Yager RR (2006) Some geometric aggregation operators based on intuitionistic fuzzy sets. Int J Intell Syst 35:417–433

    MathSciNet  MATH  Google Scholar 

  • Yager RR (1988) On ordered weighted averaging aggregation operators in multi-criteria decision making. IEEE Trans Syst Man Cybern 18:183–190

    Article  MATH  Google Scholar 

  • Yager RR (2014) Pythagorean membership grades in multi-criteria decision-making. IEEE Trans Fuzzy Syst 22:958–965

    Article  Google Scholar 

  • Yager RR (2016) Generalized orthopair fuzzy sets. IEEE Trans Fuzzy Syst 26(5):1222–1230

    Article  Google Scholar 

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

    Article  MATH  Google Scholar 

  • Zahid K, Akram M, Kahraman C (2022) A new ELECTRE-based method for group decision-making with complex spherical fuzzy information. Knowl Based Syst 243:108525

    Article  Google Scholar 

  • Zavadskas EK, Kaklauskas A, Sarka V (1994) The new method of multicriteria complex proportional assessment of projects. Technol Econ Dev Econ 1(3):131–139

    Google Scholar 

  • Zeng S, Munir M, Mahmood T, Naeem M (2020) Some \(T\)-Spherical fuzzy Einstein interactive aggregation operators and their application to selection of photovoltaic cells. Math Probl Eng 2020:1–16

    MathSciNet  Google Scholar 

  • Zheng Y, Xu Z, He Y, Liao H (2018) Severity assessment of chronic obstructive pulmonary disease based on hesitant fuzzy linguistic COPRAS method. Appl Soft Comput 69:60–71

    Article  Google Scholar 

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SN, MA and MM contributed to investigation; SN, MA and MM contributed to writing-original draft; MA contributed to writing-review and editing.

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Correspondence to Muhammad Akram.

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Naz, S., Akram, M. & Muzammal, M. Group decision-making based on 2-tuple linguistic T-spherical fuzzy COPRAS method. Soft Comput 27, 2873–2902 (2023).

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  • 2-Tuple linguistic T-spherical fuzzy set
  • Point weighted averaging operator
  • Point weighted geometric operator
  • COPRAS method