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Q-rung orthopair fuzzy multiple attribute group decision-making method based on normalized bidirectional projection model and generalized knowledge-based entropy measure

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Abstract

The q-rung orthopair fuzzy sets (q-ROFSs) can serve as a generalization of intuitionistic fuzzy sets (IFSs) and Pythagorean fuzzy sets (PFSs). q-ROFSs provide more freedom for decision makers in describing their opinions than other ordinary orthopair fuzzy sets. In this paper, a novel multiple attribute group decision making(MAGDM) method is constructed under q-rung orthopair fuzzy (q-ROF) environment. First, considering the projection measure provides the distance and the angle between two alternatives simultaneously, this work investigates a new normalized bidirectional projection model (NBPM) of q-ROFSs. By combining the proposed NBPM with Jaynes maximum entropy method, a nonlinear programming model is constructed to calculate the objective attribute weight information. Second, we present a new entropy measure based on the proposed generalized p-norm knowledge-based measure which takes into account both the membership and non-membership functions and the inherent fuzziness of q-ROFSs. Then the weights of decision makers are given by the proposed entropy measure. Furthermore, an integrated MAGDM framework is presented by using the weight determination methods of decision makers and attributes under q-ROF environment. Finally, an illustrative example is given to illustrate the operation process of the proposed decision-making method, sensitivity analysis and comparison analysis are also performed to show the effectiveness and superiority of the proposed method.

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References

  • Boran FE, Genç S, Kurt M, Akay D (2009) A multi-criteria intuitionistic fuzzy group decision making for supplier selection with topsis method. Expert Syst Appl 36(8):11363–11368

    Google Scholar 

  • Liu Z, Liu P (2017) Intuitionistic uncertain linguistic partitioned bonferroni means and their application to multiple attribute decision-making. Int J Syst Sci 48(5):1092–1105

    MathSciNet  MATH  Google Scholar 

  • Yu C, Shao Y, Wang K, Zhang L (2019) A group decision making sustainable supplier selection approach using extended topsis under interval-valued pythagorean fuzzy environment. Expert Syst Appl 121:1–17

    Google Scholar 

  • Shi H, Wang L, Li X-Y, Liu H-C (2020) A novel method for failure mode and effects analysis using fuzzy evidential reasoning and fuzzy petri nets. J Ambient Intell Humaniz Comput 11:2381–2395

    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

    Google Scholar 

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

    MATH  Google Scholar 

  • Bustince H, Barrenechea E, Pagola M, Fernandez J, Xu Z, Bedregal B, Montero J, Hagras H, Herrera F, De Baets B (2015) A historical account of types of fuzzy sets and their relationships. IEEE Trans Fuzzy Syst 24(1):179–194

    Google Scholar 

  • Atanassov KT (1999) Intuitionistic fuzzy sets. In: Intuitionistic fuzzy sets. Springer, New York, pp 1–137

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

    Google Scholar 

  • Torra V (2010) Hesitant fuzzy sets. Int J Intell Syst 25(6):529–539

    MATH  Google Scholar 

  • Yager RR (2016) Generalized orthopair fuzzy sets. IEEE Trans Fuzzy Syst 25(5):1222–1230

    Google Scholar 

  • Liu P, Wang P (2018) Some q-rung orthopair fuzzy aggregation operators and their applications to multiple-attribute decision making. Int J Intell Syst 33(2):259–280

    Google Scholar 

  • Wang P, Wei G, Wang J, Lin R, Wei Y (2019) Dual hesitant q-rung orthopair fuzzy hamacher aggregation operators and their applications in scheme selection of construction project. Symmetry 11(6):771

    Google Scholar 

  • Shu X, Ai Z, Xu Z, Ye J (2019) Integrations of q-rung orthopair fuzzy continuous information. IEEE Trans Fuzzy Syst 27(10):1974–1985

    Google Scholar 

  • Krishankumar R, Ravichandran K, Kar S, Cavallaro F, Zavadskas EK, Mardani A (2019) Scientific decision framework for evaluation of renewable energy sources under q-rung orthopair fuzzy set with partially known weight information. Sustainability 11(15):4202

    Google Scholar 

  • Xu Z, Hu H (2010) Projection models for intuitionistic fuzzy multiple attribute decision making. Int J Inf Technol Decis Making 9(02):267–280

    MATH  Google Scholar 

  • Liang D, Xu Z, Darko AP (2017) Projection model for fusing the information of pythagorean fuzzy multicriteria group decision making based on geometric bonferroni mean. Int J Intell Syst 32(9):966–987

    Google Scholar 

  • Huang J, Xu D-H, Liu H-C, Song M-S. A new model for failure mode and effect analysis integrating linguistic z-numbers and projection method. IEEE Trans Fuzzy Syst. https://doi.org/10.1109/tfuzz.2019.2955916

  • Peng D, Wang J, Liu D, Liu Z (2019) The similarity measures for linguistic q-rung orthopair fuzzy multi-criteria group decision making using projection method. IEEE Access 7:176732–176745

    Google Scholar 

  • Yue C (2017) Two normalized projection models and application to group decision-making. J Intell Fuzzy Syst 32(6):4389–4402

    MATH  Google Scholar 

  • Liu P, You X (2019) Bidirectional projection measure of linguistic neutrosophic numbers and their application to multi-criteria group decision making. Comput Ind Eng 128:447–457

    Google Scholar 

  • Ji P, Zhang H-Y, Wang J-Q (2018) A projection-based outranking method with multi-hesitant fuzzy linguistic term sets for hotel location selection. Cogn Comput 10(5):737–751

    Google Scholar 

  • Wang L, Zhang H-Y, Wang J-Q, Li L (2018) Picture fuzzy normalized projection-based Vikor method for the risk evaluation of construction project. Appl Soft Comput 64:216–226

    Google Scholar 

  • Sun R, Hu J, Zhou J, Chen X (2018) A hesitant fuzzy linguistic projection-based mabac method for patients prioritization. Int J Fuzzy Syst 20(7):2144–2160

    Google Scholar 

  • Yue C (2019) A normalized projection-based group decision-making method with heterogeneous decision information and application to software development effort assessment. Appl Intell 49(10):3587–3605

    Google Scholar 

  • Koksalmis E, Kabak Ö (2019) Deriving decision makers weights in group decision making: An overview of objective methods. Inf Fusion 49:146–160

    Google Scholar 

  • Shannon CE (1948) A mathematical theory of communication. Bell Syst Tech J 27(3):379–423

    MathSciNet  MATH  Google Scholar 

  • De Luca A, Termini S (1972) A definition of a nonprobabilistic entropy in the setting of fuzzy sets theory. Inf Control 20(4):301–312

    MathSciNet  MATH  Google Scholar 

  • Szmidt E, Kacprzyk J (2001) Entropy for intuitionistic fuzzy sets. Fuzzy Sets Syst 118(3):467–477

    MathSciNet  MATH  Google Scholar 

  • Szmidt E, Kacprzyk J, Bujnowski P (2014) How to measure the amount of knowledge conveyed by Atanassovs intuitionistic fuzzy sets. Inf Sci 257:276–285

    MathSciNet  MATH  Google Scholar 

  • Guo K (2015) Knowledge measure for Atanassov’s intuitionistic fuzzy sets. IEEE Trans Fuzzy Syst 24(5):1072–1078

    Google Scholar 

  • Peng X, Liu L (2019) Information measures for q-rung orthopair fuzzy sets. Int J Intell Syst 34(8):1795–1834

    Google Scholar 

  • Nguyen H (2015) A new knowledge-based measure for intuitionistic fuzzy sets and its application in multiple attribute group decision making. Expert Syst Appl 42(22):8766–8774

    Google Scholar 

  • Nguyen H (2020) A generalized p-norm knowledge-based score function for interval-valued intuitionistic fuzzy set in decision making. IEEE Trans Fuzzy Syst 28(3):409–423

    Google Scholar 

  • Liu Z, Liu P, Liang X (2018) Multiple attribute decision-making method for dealing with heterogeneous relationship among attributes and unknown attribute weight information under q-rung orthopair fuzzy environment. Int J Intell Syst 33(9):1900–1928

    Google Scholar 

  • Yager RR (2017) Generalized orthopair fuzzy sets. IEEE Trans Fuzzy Syst 25(5):1222–1230

    Google Scholar 

  • Ji P, Zhang H-Y, Wang J-Q (2018) A projection-based Todim method under multi-valued neutrosophic environments and its application in personnel selection. Neural Comput Appl 29(1):221–234

    Google Scholar 

  • Huang G, Liu Y (2005) The fuzzy entropy of vague sets based on non-fuzzy sets. Comput Appl Softw 22(6):16–17

    Google Scholar 

  • Szmidt E, Kacprzyk J (2005) New measures of entropy for intuitionistic fuzzy sets. In: Ninth Int Conf IFSs Sofia, vol 11, pp 12–20

  • Li J, Deng G, Li H, Zeng W (2012) The relationship between similarity measure and entropy of intuitionistic fuzzy sets. Inf Sci 188:314–321

    MathSciNet  MATH  Google Scholar 

  • Szmidt E, Kacprzyk J (2005) A new measure of entropy and its connection with a similarity measure for intuitionistic fuzzy sets. In: EUSFLAT Conf., pp 461–466

  • Vlachos IK, Sergiadis GD (2007) Intuitionistic fuzzy information-applications to pattern recognition. Pattern Recogn Lett 28(2):197–206

    Google Scholar 

  • Zhang Q-S, Jiang S-Y (2008) A note on information entropy measures for vague sets and its applications. Inf Sci 178(21):4184–4191

    MathSciNet  MATH  Google Scholar 

  • Liang X, Wei C, Xia M (2013) New entropy, similarity measure of intuitionistic fuzzy sets and their applications in group decision making. Int J Comput Intell Syst 6(5):987–1001

    Google Scholar 

  • Liang D, Zhang Y, Cao W (2019) q-rung orthopair fuzzy Choquet integral aggregation and its application in heterogeneous multicriteria two-sided matching decision making. Int J Intell Syst 34(12):3275–3301

    Google Scholar 

  • Liu Z, Wang S, Liu P (2018) Multiple attribute group decision making based on q-rung orthopair fuzzy heronian mean operators. Int J Intell Syst 33(12):2341–2363

    Google Scholar 

  • Wang P, Wang J, Wei G, Wei C (2019) Similarity measures of q-rung orthopair fuzzy sets based on cosine function and their applications. Mathematics 7(4):340

    Google Scholar 

  • Zhang X, Xu Z (2014) Extension of topsis to multiple criteria decision making with pythagorean fuzzy sets. Int J Intell Syst 29(12):1061–1078

    Google Scholar 

Download references

Acknowledgements

This study was funded by the Social Sciences Research Project of Ministry of Education of China (No. 17YJA630065), the Shandong Provincial Natural Science Foundation (No. ZR2017MG007), the Humanities, the Science and Technology Project of Colleges and Universities of Shandong Province (NO. J16LN25), the Special Funds of Taishan Scholars Project of Shandong Province (No. Ts201511045).

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  1. School of Management Science and Engineering, Shandong University of Finance and Economics, Jinan, 250014, China

    Zhengmin Liu, Xinya Wang, Lin Li, Xiaolan Zhao & Peide Liu

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  1. Zhengmin Liu
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  2. Xinya Wang
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  3. Lin Li
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  4. Xiaolan Zhao
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  5. Peide Liu
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Correspondence to Zhengmin Liu.

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Liu, Z., Wang, X., Li, L. et al. Q-rung orthopair fuzzy multiple attribute group decision-making method based on normalized bidirectional projection model and generalized knowledge-based entropy measure. J Ambient Intell Human Comput 12, 2715–2730 (2021). https://doi.org/10.1007/s12652-020-02433-w

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