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Multi-attribute decision making for power Dombi operators under Pythagorean fuzzy information with MABAC method

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Abstract

Pythagorean fuzzy sets have a lot of applications in the field of engineering and scientific problems. Also, besides, the power averaging (PA) operator can reduce the influence of evaluating extreme data from some bias experts. Dombi operator has flexibility in working on parameter evaluation. Here, Dombi operations combined with PA operator are used to construct some Pythagorean fuzzy power Dombi operators, i.e. Pythagorean fuzzy power Dombi weighted averaging (PFPDWA), order weighted averaging and hybrid weighted averaging operators have been introduced. Further, Pythagorean fuzzy power Dombi weighted geometric (PFPDWG), order weighted geometric and hybrid weighted geometric operators have been considered. Meanwhile, some properties of these operators have been established in detail. To solve the Pythagorean fuzzy multiple attribute decision making problem by using PFPDWA and PFPDWG operators to design an algorithm for the proposed approach. At the same time, a novel approach is proposed to design multiple attribute border approximation area comparison approached with Pythagorean fuzzy numbers to justify the feasibility of the proposed approach. Finally, we compare the developed approach with some existing operators to show its efficiency.

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References

  • Atanassov KT (1999) On intuitionistic fuzzy sets theory. In: Studies in Fuzziness and Soft Computing. 283, Springer-Verlag, Berlin Heidelberg

  • Biswas P, Pramanik S, Giri BC (2019) Neutrosophic TOPSIS with Group Decision Making. In: Kahraman C, Otay İ (eds) Fuzzy Multi-criteria Decision-Making Using Neutrosophic Sets. Studies in Fuzziness and Soft Computing, vol 369. Springer, Cham

  • 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

    Google Scholar 

  • Dombi J (1982) A general class of fuzzy operators, the demorgan class of fuzzy operators and fuzziness measures induced by fuzzy operators. Fuzzy Sets Syst 8:149–163

    MathSciNet  MATH  Google Scholar 

  • Garg H (2016) A new generalized pythagorean fuzzy information aggregation using einstein operations and its application to decision making. Int J Intell Syst 31(9):886–920

    Google Scholar 

  • Garg H (2016) A novel accuracy function under interval-valued Pythagorean fuzzy environment for solving multicriteria decision making problem. J Intell Fuzzy Syst 31(1):529–540

    MATH  Google Scholar 

  • Garg H, Arora R (2018) Novel scaled prioritized intuitionistic fuzzy soft interaction averaging aggregation operators and their application to multi criteria decision making. Eng Appl Artif Intell 71:100–112

    Google Scholar 

  • Gebrehiwet T, Luo HB (2018) Risk level evaluation on construction project lifecycle using fuzzy comprehensive evaluation and TOPSIS. Symmetry 11(1):12

    Google Scholar 

  • Gou X, Xu Z, Ren P (2016) The properties of continuous pythagorean fuzzy information. Int J Intell Syst 31(5):401–424

    Google Scholar 

  • He X (2018) Typhoon disaster assessment based on Dombi hesitant fuzzy information aggregation operators. Nat Hazards 90(3):1153–1175

    Google Scholar 

  • Jana C, Pal M (2021) Multi-criteria decision making process based on some single-valued neutrosophic Dombi power aggregation operators. Soft Comput 25(7):5055–5072

    Google Scholar 

  • Jana C, Pal M (2021) A dynamical hybrid method to design decision making process based on GRA approach for multiple attributes problem. Engineering Applications of Artificial Intelligence 100:104203. https://doi.org/10.1016/j.engappai.2021.104203

    Article  Google Scholar 

  • Jana C, Pal M (2021) Some m-polar fuzzy operators and their application in multiple-attribute decision-making process. Sādhanā 46(2):1–15

    MathSciNet  Google Scholar 

  • Jana C, Muhiuddin M, Pal M (2019) Some Dombi aggregation of \(Q\)-rung orthopair fuzzy numbers in multiple attribute decision making. Int J Intell Syst 34(12):3220–3240

    Google Scholar 

  • Jana C, Muhiuddin G, Pal M (2020) Multiple-attribute decision making problems based on SVTNH methods. J Ambient Intell Humaniz Comput 11(9):3717–3733

    Google Scholar 

  • Jana C, Muhiuddin G, Pal M (2021) Multi-criteria decision making approach based on SVTrN Dombi aggregation functions. Artif Intell Rev 54(5):3685–3723

    Google Scholar 

  • Jana C, Pal M, Wang JQ (2019) Bipolar fuzzy Dombi aggregation operators and its application in multiple attribute decision making process. J Ambient Intell Humaniz Comput 10(9):3533–3549

    Google Scholar 

  • Jana C, Pal M, Wang JQ (2020) Bipolar fuzzy Dombi prioritized aggregation operators in multiple attribute decision making. Soft Comput 24:3631–3646

    MATH  Google Scholar 

  • Jana C, Senapati T, Pal M (2019) Pythagorean fuzzy Dombi aggregation operators and its applications in multiple attribute decision-making. Int J Intell Syst 34(9):2019–2038

    Google Scholar 

  • Jana C, Senapati T, Pal M, Yager RR (2019) Picture fuzzy Dombi aggregation operators: application to MADM process. Appl Soft Comput 74(1):99–109

    Google Scholar 

  • Jia F, Liu Y, Wang X (2019) An extended MABAC method for multi-criteria group decision making based on intuitionistic fuzzy rough numbers. Expert Syst Appl 127:241–255

    Google Scholar 

  • Liu PD (2017) Multiple attribute group decision making method based on interval-valued intuitionistic fuzzy power Heronian aggregation operators. Comput Industr Eng 108:199–212

    Google Scholar 

  • Liu P, Li H, Wang P, Liu J (2016) ELECTRE Method and Its Application in Multiple Attribute Decision Making Based on INS. J Shandong Univ Financ Econ 28:80–87

    Google Scholar 

  • Liu PD, Liu JL, Chen SM (2017) Some intuitionistic fuzzy Dombi Bonferroni mean operators and their application to multi-attribute group decision making. J Oper Res Soc 69(1):1–24

    MathSciNet  Google Scholar 

  • Liu PD, Wang YM (2014) Multiple attribute group decision making methods based on intuitionistic linguistic power generalized aggregation operators. Appl Soft Comput 17(1):90–104

    Google Scholar 

  • Liu PD, Yu XC (2014) 2-dimension uncertain linguistic power generalized weighted aggregation operator and its application for multiple attribute group decision making. Knowl-Based Syst 57(1):69–80

    Google Scholar 

  • Lourenzutti R, Krohling RA (2013) A study of TODIM in a intuitionistic fuzzy and random environment. Expert Syst Appl 40(16):6459–6468

    Google Scholar 

  • Mishra AR, Chandel A, Motwani DJGC (2020) Extended MABAC method based on divergence measures for multi-criteria assessment of programming language with interval-valued intuitionistic fuzzy sets. Granul Comput 5:97–117

    Google Scholar 

  • Mishra AR, Rani P (2018) Biparametric information measures-based TODIM technique for interval-valued intuitionistic fuzzy environment. Arab J Sci Eng 43:3291–3309

    MATH  Google Scholar 

  • Pamučar D, Petrovic I, Ćirović G (2018) Modification of the Best-Worst and MABAC methods: a novel approach based on interval-valued fuzzy-rough numbers. Expert Syst Appl 91:89–106

    Google Scholar 

  • Pamučar D, StevićŹ Zavadskas EK (2018) Integration of interval rough AHP and interval rough MABAC methods for evaluating university web pages. Appl Soft Comput 67:141–163

    Google Scholar 

  • Pamučar D, Ćirović G (2015) The selection of transport and handling resources in logistics centers using Multi-Attributive Border Approximation area Comparison (MABAC). Expert Syst Appl 42:3016–3028

    Google Scholar 

  • Peng X, Dai J (2018) Approaches to single-valued neutrosophic MADM based on MABAC, TOPSIS and new similarity measure with score function. Neural Comput Appl 29:939–954

    Google Scholar 

  • Peng XD, Yang Y (2016) Pythagorean fuzzy choquet integral based MABAC method for multiple attribute group decision making. Int J Intell Syst 31:989–1020

    Google Scholar 

  • Reformat M, Yager RR (2014) Suggesting recommendations using pythagorean fuzzy sets illustrated using netflix movie data. Inf Process Manag Uncertainity Knowl-Based Syst 2014:546–556

    Google Scholar 

  • Ren P, Xu Z, Gou X (2016) Pythagorean fuzzy TODIM approach to multi-criteria decision making. Appl Soft Comput 42:246–259

    Google Scholar 

  • Roy J, Chatterjee K, Bandhopadhyay A, Kar S (2016) Expert Syst. Evaluation and selection of Medical Tourism sites: a rough AHP based MABAC approach. https://doi.org/10.1111/exsy.12232

    Article  Google Scholar 

  • Roy J, Das S, Kar S, Pamucar D (2019) An extension of the CODAS approach using interval-valued intuitionistic fuzzy set for sustainable material selection in construction projects with incomplete weight information. Symmetry 11(3):393

    Google Scholar 

  • Shen KW, Wang JQ (2018) Z-VIKOR method based on a new comprehensive weighted distance measure of Z-number and its application. IEEE Trans Fuzzy Syst 26(6):3232–3245

    Google Scholar 

  • Sun R, Hu J, Zhou J, Chen X (2017) A Hesitant fuzzy linguistic projection-based MABAC method for patients’s prioritization. Int J Fuzzy Syst 20:1–17

    Google Scholar 

  • Tian C, Peng JJ, Zhang S, Zhang WY, Wang JQ (2019) Weighted picture fuzzy aggregation operators and their applications to multi-criteria decision-making problems. Comput Industr Eng 137:106037

    Google Scholar 

  • Wang J, Wei GW, Wei C, Wei Y (2020) MABAC method for multiple attribute group decision making under q-rung orthopair fuzzy environment. Defence Technol 16:208–216

    Google Scholar 

  • Wei GW (2017) Pythagorean fuzzy interaction aggregation operators and their application to multiple attribute decision making. J Intell Fuzzy Syst 33(4):2119–2132

    MATH  Google Scholar 

  • Wei GW (2019) Pythagorean Fuzzy Hamacher Power Aggregation Operators in Multiple Attribute Decision Making. Fundamenta Informaticae 166(1):57–85

    MathSciNet  MATH  Google Scholar 

  • Wei Y, Liu J, Lai X, Hu Y (2017) Which determinant is the most informative in forecasting crude oil market volatility: fundamental, speculation, or uncertainty? Energy Econ 68:141–50

    Google Scholar 

  • Wei GW, Lu M (2018) Pythagorean fuzzy maclaurin symmetric mean operators in multiple attribute decision making. Int J Intell Syst 33(5):1043–1070

    MathSciNet  Google Scholar 

  • Wei GW, Lu M (2018) Pythagorean fuzzy power aggregation operators in multiple attribute decision making. Int J Intell Syst 33(1):169–186

    MathSciNet  Google Scholar 

  • Wei Y, Qin S, Li X, Zhu S, Wei GW (2019) Oil price fluctuation, stock market and macroeconomic fundamentals: evidence from China before and after the financial crisis. Financ Res Lett 30:23–9

    Google Scholar 

  • Wu XL, Liao HC (2019) A consensus-based probabilistic linguistic gained and lost dominance score method. Eur J Oper Res 272:1017–1027

    MathSciNet  MATH  Google Scholar 

  • Xiao F (2019) EFMCDM: evidential fuzzy multicriteria decision making based on belief entropy. IEEE Trans Fuzzy Syst. https://doi.org/10.1109/TFUZZ.2019.2936368

    Article  Google Scholar 

  • Xu ZS (2007) Intuitionistic fuzzy aggregation operators. IEEE Trans Fuzzy Syst 15(6):1179–1187

    Google Scholar 

  • Xu ZS (2011) Approaches to multiple attribute group decision making based on intuitionistic fuzzy power aggregation operators. Knowledge-Based Syst 24:749–760

    Google Scholar 

  • Xu ZS, Da QL (2003) An overview of operators for aggregating information. Int J Intell Syst 18(9):953–969

    MATH  Google Scholar 

  • Xu Y, Merigo JM, Wang H (2012) Linguistic power aggregation operators and their application to multiple attribute group decision making. Appl Math Modell 36:5427–5444

    MathSciNet  MATH  Google Scholar 

  • Xu ZS, Yager RR (2006) Some geometric aggregation operators based on intuitionistic fuzzy sets. Int J General Syst 35(4):417–433

    MathSciNet  MATH  Google Scholar 

  • Xu ZS, Yager RR (2010) Power-Geometric operators and their use in group decision making. IEEE Trans Fuzzy Syst 18(1):94–105

    Google Scholar 

  • Xue YX, You JX, Lai XD, Liu HC (2016) An interval-valued intuitionistic fuzzy MABAC approach for material selection with incomplete weight information. Appl Soft Comput 38:703–713

    Google Scholar 

  • Yager RR (1998) On Ordered Weighted averaging aggregation operators in multicriteria decision making. IEEE Trans Syst Man Cybern 18(1):183–190

    MATH  Google Scholar 

  • Yager RR (2001) The power average operator. IEEE Trans Syst Man Cybern Part A 31:724–731

    Google Scholar 

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

    Google Scholar 

  • Yager RR, Abbasov AM (2013) Pythagorean membership grades, complex numbers, and decision making. Int J Intell Syst 28(5):436–452

    Google Scholar 

  • Yager RR, Kacprzyk J (1997) The ordered weighted averaging operators: theory and applications. Kluwer, Boston, M.A.

    MATH  Google Scholar 

  • Yu SM, Wang J, Wang JQ (2017) An interval type-2 fuzzy likelihood-based MABAC approach and its application in selecting hotels on a tourism website. Int J Fuzzy Syst 19:47–61

    MathSciNet  Google Scholar 

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

    Google Scholar 

  • Zadeh LA (1996) Fuzzy Sets. World Scientific Press, Fuzzy Systems, Fuzzy Logic

    MATH  Google Scholar 

  • Zavadskas EK, Bausys R, Juodagalviene B, Sapranavicence IG (2017) Model for residential house element and material selection by neutrosophic MULTIMOORA methods. Eng Appl Artif Intell 64:315–324

    Google Scholar 

  • Zeng S, Chen J, Li X (2016) A hybrid method for pythagorean fuzzy multiple-criteria decision making. Int J Inf Technol Decis Mak 15(2):403–422

    Google Scholar 

  • Zhou L, Chen H, Liu J (2012) Generalized power aggregation operators and their applications in group decision making. Comput Industr Eng 62(4):989–999

    Google Scholar 

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Acknowledgements

The authors wish to thank the anonymous reviewers for their valuable comments and helpful suggestions which greatly improved the quality of this paper.

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Authors and Affiliations

  1. Department of Applied Mathematics with Oceanology and Computer Programming, Vidyasagar University, Midnapore, 721102, India

    Chiranjibe Jana & Madhumangal Pal

  2. School of Mathematics, Thapar Institute of Engineering and Technology (Deemed University), Patiala, 147004, Punjab, India

    Harish Garg

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  1. Chiranjibe Jana
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Correspondence to Chiranjibe Jana.

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Jana, C., Garg, H. & Pal, M. Multi-attribute decision making for power Dombi operators under Pythagorean fuzzy information with MABAC method. J Ambient Intell Human Comput 14, 10761–10778 (2023). https://doi.org/10.1007/s12652-022-04348-0

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