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A new decision analysis based on 2-tuple linguistic q-rung picture fuzzy ITARA–VIKOR method

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Abstract

The primary goal of the current work is to investigate and improve the ITARA (Indifference Threshold-Based Attribute Ratio Analysis) and VIKOR (VlseKriterijumska Optimizacija I Kompromisno Resenje) techniques using 2-tuple linguistic q-rung picture fuzzy sets (2TLq-RPFSs) as a backdrop. The terminology of VIKOR method to define the compromise solution is based on the key ideas of regret measure and group utility measure. The VIKOR technique uses ascending order to evaluate the options according to their potential for the highest group benefit and the least potential for individual opponent regret. The ITARA method is expanded for 2TLq-RPFSs. To create the innovative approach known as 2TLq-RPF-ITARA–VIKOR for 2TLq-RPFSs, we combine the ITARA method with VIKOR. Our motivation for using the concept of 2TLq-RPFSs is the capacity of q-RPFSs in order to support a broad range of information and the prominent properties of 2-tuple linguistic term sets to handle qualitative data. The proposed methodology accommodates the salient features of ITARA and VIKOR techniques. Moreover, the integration of two methods covers the weaknesses of each other. The expanded approach can contain significantly more data to represent information by increasing the powers of q. Additionally, utilization of linguistic factors provides the benefit to present the data with the aid of qualitative characteristics. In order to support the expanded approach, an example of choosing the best audit company is handled using the suggested methodology. In the end, a comparison analysis is conducted to validate the established approach. Therefore, we draw the conclusion that the methodology is general, simple to understand, easy to apply, and capable of capturing the linguistic multi-criteria group decision-making issues that are uncertain.

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References

  • Akram M, Khan A, Ahmad U (2023) Extended MULTIMOORA method based on \(2\)-tuple linguistic Pythagorean fuzzy sets for multi-attribute group decision-making. Granu Comput 8:311–332

    Article  Google Scholar 

  • Akram M, Khan A, Ahmad U, Alcantud JCR, Al-Shamiri MMA (2022) A new group decision-making framework based on \(2\)-tuple linguistic complex \(q\)-rung picture fuzzy sets. Math Biosci Eng 19(11):11281–11323

    Article  MathSciNet  MATH  Google Scholar 

  • Akram M, Khan A, Luqman A, Senapati T, Pamucar D (2023) An extended MARCOS method for MCGDM under \(2\)-tuple linguistic \(q\)-rung picture fuzzy environment. Eng Appl Artif Intell 120:105892

    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  MATH  Google Scholar 

  • Akram M, Niaz Z (2022) \(2\)-Tuple linguistic Fermatean fuzzy decision-making method based on COCOSO with CRITIC for drip irrigation system analysis. J Cogn Eng. https://doi.org/10.47852/bonviewJCCE2202356

  • Akram M, Noreen U, Al-Shamiri MMA, Pamucar D (2022) Integrated decision-making methods based on \(2\)-tuple linguistic \(m\)-polar fuzzy information. AIMS Math 7(8):14557–14594

    Article  MathSciNet  Google Scholar 

  • Akram M (2021) Multi-criteria decision-making methods based on \(q\)-rung picture fuzzy information. J Intell Fuzzy Syst 40(5):10017–10042

    Article  Google Scholar 

  • Akram M, Ramzan N, Deveci M (2023) Linguistic Pythagorean fuzzy CRITIC-EDAS method for multiple-attribute group decision analysis. Eng Appl Artif Intell 119:105777

    Article  Google Scholar 

  • Arya V, Kumar S (2021) Extended TODIM method based on VIKOR for \(q\)-rung orthopair fuzzy information measures and their application in MAGDM problem of medical consumption products. Int J Intell Syst 36(11):6837–6870

    Article  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  • Bellman RE, Zadeh LA (1970) Decision-making in a fuzzy environment. Manag Sci 4(17):141–164

    Article  MathSciNet  MATH  Google Scholar 

  • Benayoun R, Roy B, Sussman N (1966) Manual de reference du programme electre. Note Synth Form 25(79):79

  • Chang CL, Hsu CH (2011) Applying a modified VIKOR method to classify land subdivisions according to watershed vulnerability. Water Resour Manag 25(1):301–309

    Article  Google Scholar 

  • Chang TW, Pai CJ, Lo HW, Hu SK (2021) A hybrid decision-making model for sustainable supplier evaluation in electronics manufacturing. Comput Ind Eng 156:107283

    Article  Google Scholar 

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

    Google Scholar 

  • Deng X, Wang J, Wei G, 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 

  • Du P, Chen Z, Gong X (2020) Load response potential evaluation for distribution networks: A hybrid decision-making model with intuitionistic normal cloud and unknown weight information. Energy 192:116673

    Article  Google Scholar 

  • El-Santawy MF (2012) A VIKOR method for solving personnel training selection problem. Int J Comput Sci 1(2):9–12

    Google Scholar 

  • Elshaboury N, Attia T, Marzouk M (2020) Application of evolutionary optimization algorithms for rehabilitation of water distribution networks. J Constr Eng Manag 146(7):04020069

    Article  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 

  • Gou X, Xu Z, Liao H, Herrera F (2021) Probabilistic double hierarchy linguistic term set and its use in designing an improved VIKOR method: The application in smart healthcare. J Oper Res Soc 72(12):2611–2630

    Article  Google Scholar 

  • Gül S (2021) Fermatean fuzzy set extensions of SAW, ARAS, and VIKOR with applications in COVID-19 testing laboratory selection problem. Expert Syst 38(8):e12769

    Article  Google Scholar 

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

    Article  MATH  Google Scholar 

  • Hasheminasab H, Streimikiene D, Pishahang M (2023) A novel energy poverty evaluation: study of the European Union countries. Energy 264:126157

    Article  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 

  • He T, Wei G, Lu J, Wei C, Lin R (2019) Pythagorean \(2\)-tuple linguistic taxonomy method for supplier selection in medical instrument industries. Int J Environ Res Public Health 16:4875. https://doi.org/10.3390/ijerph16234875

    Article  Google Scholar 

  • He T, Wei G, Lu J, Wei C, Lin R (2019) Pythagorean \(2\)-tuple linguistic VIKOR method for evaluating human factors in construction project management. Mathematics 7(12):1149

    Article  Google Scholar 

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

    Article  Google Scholar 

  • Herrera F, Martínez L (2000) An approach for combining linguistic and numerical information based on the \(2\)-tuple fuzzy linguistic representation model in decision-making. Int J Uncertain Fuzziness Knowl-Based Syst 8(05):539–562

    Article  MathSciNet  MATH  Google Scholar 

  • Hwanga CL, Yoon K (1981) Multiple attributes decision making methods and applications. Springer, Berlin, Heidelberg

    Book  Google Scholar 

  • Jin H, Ashraf S, Abdullah S, Qiyas M, Bano M, Zeng S (2019) Linguistic spherical fuzzy aggregation operators and their applications in multi-attribute decision making problems. Mathematics 7(5):413

    Article  Google Scholar 

  • Ju Y, Wang A (2013) Extension of VIKOR method for multi-criteria group decision making problem with linguistic information. Appl Math Model 37(5):3112–3125

    Article  MathSciNet  MATH  Google Scholar 

  • Khan A, Akram M, Ahmad U, Al-Shamiri MMA (2023) A new multi-objective optimization ratio analysis plus full multiplication form method for the selection of an appropriate mining method based on \(2\)-tuple spherical fuzzy linguistic sets. Math Biosci Eng 20(1):456–488

    Article  Google Scholar 

  • Khan MJ, Ali MI, Kumam P, Kumam W, Al-Kenani AN (2021) \(q\)-Rung orthopair fuzzy modified dissimilarity measure based robust VIKOR method and its applications in mass vaccination campaigns in the context of COVID-19. IEEE Access 9:93497–93515

    Article  Google Scholar 

  • Li L, Zhang RT, Wang J, Shang XP, Bai KY (2018) A novel approach to multi-attribute group decision-making with \(q\)-rung picture linguistic information. Symmetry 10(5):172

    Article  Google Scholar 

  • Liao H, Xu Z, Zeng XJ (2014) Hesitant fuzzy linguistic VIKOR method and its application in qualitative multiple criteria decision making. IEEE Trans Fuzzy Syst 23(5):1343–1355

    Article  Google Scholar 

  • Lihong M, Yanping Z, Zhiwei Z (2008) Improved VIKOR algorithm based on AHP and Shannon entropy in the selection of thermal power enterprise’s coal suppliers. Int Conf Inf Manag Innov Manag Ind Eng 2:129–133

    Google Scholar 

  • Lin M, Li X, Chen L (2020) Linguistic \(q\)-rung orthopair fuzzy sets and their interactional partitioned Heronian mean aggregation operators. Int J Intell Syst 35:217–249

    Article  Google Scholar 

  • Lin M, Wei J, Xu Z, Chen R (2018) Multiattribute group decision-making based on linguistic Pythagorean fuzzy interaction partitioned Bonferroni mean aggregation operators. Complexity. https://doi.org/10.1155/2018/9531064

    Article  MATH  Google Scholar 

  • Liu HC, Liu L, Wu J (2013) Material selection using an interval \(2\)-tuple linguistic VIKOR method considering subjective and objective weights. Mater Des 1980–2015(52):158–167

    Article  Google Scholar 

  • Liu HC, Qin JT, Mao LX, Zhang ZY (2015) Personnel selection using interval \(2\)-tuple linguistic VIKOR method. Hum Factors Ergon Manuf Service Indus 25(3):370–384

    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(4):883–906

    Article  Google Scholar 

  • Liu P, Shahzadi G, Akram M (2020) Specific types of \(q\)-rung picture fuzzy Yager aggregation operators for decision-making. Int J Comput Intell Syst 13(1):1072–1091

    Article  Google Scholar 

  • Liu P, Wu Y, Li Y (2022) Probabilistic hesitant fuzzy taxonomy method based on best-worst-method (BWM) and indifference threshold-based attribute ratio analysis (ITARA) for multi-attributes decision-making. Int J Fuzzy Syst 24(3):1301–1317

    Article  Google Scholar 

  • Liu HC, You JX, Fan XJ, Chen YZ (2014) Site selection in waste management by the VIKOR method using linguistic assessment. Appl Soft Comput 21:453–461

    Article  Google Scholar 

  • Lo HW, Hsu CC, Huang CN, Liou JJ (2021) An ITARA-TOPSIS based integrated assessment model to identify potential product and system risks. Mathematics 9(3):239

    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 

  • Mi X, Li J, Liao H, Zavadskas EK, Al-Barakati A, Barnawi A, Viedma EH (2019) Hospitality brand management by a score-based \(q\)-rung ortho pair fuzzy VIKOR method integrated with the best worst method. Econ Res-Ekon Istraz 32(1):3266–3295

    Google Scholar 

  • Naz S, Akram M, Muhiuddin G, Shafiq A (2022) Modified EDAS method for MAGDM based on MSM operators with \(2\)-tuple linguistic \(T\)-Spherical fuzzy sets. Math Probl Eng 2021:5075998

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

    Article  Google Scholar 

  • Naz S, Akram M, Saeid AB, Saadat A (2022) Models for MAGDM with dual hesitant \(q\)-rung orthopair fuzzy \(2\)-tuple linguistic MSM operators and their application to COVID-19 pandemic. Expert Syst. https://doi.org/10.1111/exsy.13005

    Article  Google Scholar 

  • Opricovic S (1998) Multicriteria optimization of civil engineering systems. Fac Civ Eng Belgrade 2(1):5–21

    MathSciNet  Google Scholar 

  • Opricovic S (2009) A compromise solution in water resources planning. Water Resour Manag 23(8):1549–1561

    Article  Google Scholar 

  • Opricovic S, Tzeng GH (2004) Compromise solution by MCDM methods: a comparative analysis of VIKOR and TOPSIS. Eur J Oper Res 156(2):445–455

    Article  MATH  Google Scholar 

  • Opricovic S, Tzeng GH (2007) Extended VIKOR method in comparison with outranking methods. Eur J Oper Res 178(2):514–529

    Article  MATH  Google Scholar 

  • Sanayei A, Mousavi SF, Yazdankhah A (2010) Group decision-making process for supplier selection with VIKOR under fuzzy environment. Expert Syst Appl 37(1):24–30

    Article  Google Scholar 

  • Senapati T, Yager RR (2020) Fermatean fuzzy sets. Ambient Intell Humaniz Comput 11(2):663–674

    Article  Google Scholar 

  • Shemshadi A, Shirazi H, Toreihi M, Tarokh MJ (2011) A fuzzy VIKOR method for supplier selection based on entropy measure for objective weighting. Expert Syst Appl 38(10):12160–12167

    Article  Google Scholar 

  • Shumaiza Akram M, Al-Kenani AN, Alcantud JCR (2019) Group decision-making based on the VIKOR method with trapezoidal bipolar fuzzy information. Symmetry 11(10):1–21

    Google Scholar 

  • Simic V, Milovanovic B, Pantelic S, Pamucar D, Tirkolaee EB (2023) Sustainable route selection of petroleum transportation using a type-2 neutrosophic number based ITARA-EDAS model. Inf Sci 622:732–754

  • Simic V, Torkayesh AE, Maghsoodi AI (2022) Locating a disinfection facility for hazardous healthcare waste in the COVID-19 era: a novel approach based on Fermatean fuzzy ITARA-MARCOS and random forest recursive feature elimination algorithm. Ann Oper Res. https://doi.org/10.1007/s10479-022-04822-0

    Article  Google Scholar 

  • Sofuoğlu MA (2019) Development of an ITARA-based hybrid multi-criteria decision-making model for material selection. Soft Comput 23(15):6715–6725

    Article  Google Scholar 

  • Ulutaş A, Karabasevic D, Popovic G, Stanujkic D, Nguyen PT, Karaköy Ç (2020) Development of a novel integrated CCSD-ITARA-MARCOS decision-making approach for stackers selection in a logistics system. Mathematics 8(10):1672

    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 G, Wang J, Lu J, Wu J, Wei C, Alsaadi FD, Hayat T (2020) VIKOR method for multiple criteria group decision making under \(2\)-tuple linguistic neutrosophic environment. Econ Res-Ekon Istraz 33(1):3209–3237

    Google Scholar 

  • Wen TC, Chang KH, Lai HH (2020) Integrating the 2-tuple linguistic representation and soft set to solve supplier selection problems with incomplete information. Eng Appl Artif Intell 87:103248

    Article  Google Scholar 

  • Xiong SH, Chen ZS, Chiclana F, Chin KS, Skibniewski MJ (2022) Proportional hesitant \(2\)-tuple linguistic distance measurements and extended VIKOR method: Case study of evaluation and selection of green airport plans. Int J Intell Syst 37(7):4113–4162

    Article  Google Scholar 

  • Xu Z (2012) Linguistic decision making: theory and methods. Springer. https://doi.org/10.1007/978-3-642-29440-2

    Article  MATH  Google Scholar 

  • Yager RR (2013) Pythagorean fuzzy subsets. Joint IFSA world congress and NAFIPS annual meeting (IFSA/NAFIPS), Edmonton, AB, Canada, pp 57-61

  • Yager RR (2013) Pythagorean membership grades in multi-criteria decision making. IEEE Trans Fuzzy Syst 22(4):958–965

    Article  Google Scholar 

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

    Article  Google Scholar 

  • Yang K, Duan T, Feng J, Mishra AR (2022) Internet of things challenges of sustainable supply chain management in the manufacturing sector using an integrated \(q\)-rung orthopair fuzzy-CRITIC-VIKOR method. J Enterp Inf Manag 35(4/5):1011–1039

    Article  Google Scholar 

  • Yang W, Pang Y (2019) Hesitant interval-valued Pythagorean fuzzy VIKOR method. Int J Intell Syst 34(5):754–789

    Article  Google Scholar 

  • You XY, You JX, Liu HC, Zhen L (2015) Group multi-criteria supplier selection using an extended VIKOR method with interval 2-tuple linguistic information. Expert Syst Appl 42(4):1906–1916

    Article  Google Scholar 

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

    Article  MathSciNet  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 

  • Zhang H (2014) Linguistic intuitionistic fuzzy sets and application in MAGDM. J Appl Math. https://doi.org/10.1155/2014/432092

    Article  MATH  Google Scholar 

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Authors and Affiliations

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

    Ayesha Khan & Uzma Ahmad

  2. Division of Science and Technology, Department of Mathematics, University of Education, Lahore, Pakistan

    Sundas Shahzadi

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  1. Ayesha Khan
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  2. Uzma Ahmad
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  3. Sundas Shahzadi
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Ayesha Khan, Uzma Ahmad and Sundas Shahzadi conceptualized and designed the study, analyzed the data, and wrote the manuscript.

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Correspondence to Sundas Shahzadi.

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Khan, A., Ahmad, U. & Shahzadi, S. A new decision analysis based on 2-tuple linguistic q-rung picture fuzzy ITARA–VIKOR method. Soft Comput (2023). https://doi.org/10.1007/s00500-023-08263-0

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