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Pythagorean fuzzy MCDM method based on CoCoSo and CRITIC with score function for 5G industry evaluation

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Abstract

The 5G industry is of great concern to countries to formulate a major national strategy for 5G planning, promote industrial upgrading, and accelerate their economic and technological modernization. When considering the 5G industry evaluation, the basic issues involve strong uncertainty. Pythagorean fuzzy sets, depicted by membership degree and non-membership degree, are a more resultful means for capturing uncertainty. In this paper, the comparison issue in Pythagorean fuzzy environment is disposed by proposing novel score function. Next, the \(\ominus \) and \(\oslash \) operations are defined and their properties are proved. Later, the objective weight is calculated by Criteria Importance Through Inter-criteria Correlation method. Meanwhile, the combined weight is determined by reflecting both subjective weight and the objective weight. Then, the Pythagorean fuzzy decision making algorithm based Combined Compromise Solution is developed. Lastly, the validity of algorithm is expounded by the 5G evaluation issue, along with their sensitivity analysis. The main advantages of proposed algorithm are: (1) have no counterintuitive phenomena; (2) without division or antilogarithm by zero problem; (3) own stronger ability to distinguish alternatives.

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References

  • Andrews JG, Buzzi S, Choi W, Hanly SV, Lozano A, Soong AC, Zhang JC (2014) What will 5G be? IEEE J Sel Area Commun 32:1065–1082

    Google Scholar 

  • Atanassov K (1986) Intuitionistic fuzzy sets. Fuzzy Set Syst 20:87–96

    MATH  Google Scholar 

  • Biswas A, Sarkar B (2019) Pythagorean fuzzy TOPSIS for multicriteria group decision-making with unknown weight information through entropy measure. Int J Intell Syst 34:1108–1128

    Google Scholar 

  • Bonferroni C (1950) Sulle medie multiple di potenze. Boll Mate Ital 5:267–270

    MathSciNet  MATH  Google Scholar 

  • Chen TY (2018a) A novel PROMETHEE-based outranking approach for multiple criteria decision analysis with Pythagorean fuzzy information. IEEE Access 6:54495–54506

    Google Scholar 

  • Chen TY (2018b) An effective correlation-based compromise approach for multiple criteria decision analysis with Pythagorean fuzzy information. J Intell Fuzzy Syst 35:3529–3541

    Google Scholar 

  • Chen TY (2019) Multiple criteria decision analysis under complex uncertainty: a Pearson-like correlation-based Pythagorean fuzzy compromise approach. Int J Intell Syst 34:114–151

    Google Scholar 

  • Diakoulaki D, Mavrotas G, Papayannakis L (1995) Determining objective weights in multiple criteria problems: the critic method. Comput Oper Res 22:763–770

    MATH  Google Scholar 

  • Gao H, Lu M, Wei G, Wei Y (2018) Some novel Pythagorean fuzzy interaction aggregation operators in multiple attribute decision making. Fund Inform 159:385–428

    MathSciNet  MATH  Google Scholar 

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

    Google Scholar 

  • Garg H (2016b) A novel correlation coefficients between Pythagorean fuzzy sets and its applications to decision-making processes. Int J Intell Syst 31:1234–1252

    Google Scholar 

  • Garg H (2017) Generalized Pythagorean fuzzy geometric aggregation operators using Einstein t-norm and t-conorm for multicriteria decision-making process. Int J Intell Syst 32:597–630

    Google Scholar 

  • Garg H (2018a) Generalised Pythagorean fuzzy geometric interactive aggregation operators using Einstein operations and their application to decision making. J Exp Theor Artif Intell 30:763–794

    Google Scholar 

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

    Google Scholar 

  • Garg H (2019) New logarithmic operational laws and their aggregation operators for Pythagorean fuzzy set and their applications. Int J Intell Syst 34:82–106

    Google Scholar 

  • Ghorabaee MK, Amiri M, Zavadskas EK, Antucheviciene J (2018) A new hybrid fuzzy MCDM approach for evaluation of construction equipment with sustainability considerations. Arch Civ Mech Eng 18:32–49

    Google Scholar 

  • Guan N, Liu T, Zhang Y, Tao D, Davis LS (2019) Truncated Cauchy non-negative matrix factorization. IEEE Trans Pattern Anal Mach Intell 41:246–259

    Google Scholar 

  • Hara T, Uchiyama M, Takahasi SE (1998) A refinement of various mean inequalities. J Inequal Appl 1998:387–395

    MathSciNet  MATH  Google Scholar 

  • Huang HH, Liang Y (2019) An integrative analysis system of gene expression usings self-paced learning and SCAD-Net. Expert Syst Appl 135:102–112

    Google Scholar 

  • Jia-hua D, Zhang H, He Y (2019) Possibility Pythagorean fuzzy soft set and its application. J Intell Fuzzy Syst 36:413–421

    Google Scholar 

  • Joshi BP (2019) Pythagorean fuzzy average aggregation operators based on generalized and group-generalized parameter with application in MCDM problems. Int J Intell Syst 34:895–919

    Google Scholar 

  • Khan AA, Ashraf S, Abdullah S, Qiyas M, Luo J, Khan SU (2019a) Pythagorean fuzzy Dombi aggregation operators and their application in decision support system. Symmetry 11:383

    MATH  Google Scholar 

  • Khan M, Abdullah S, Ali A (2019b) Multiattribute group decision-making based on Pythagorean fuzzy Einstein prioritized aggregation operators. Int J Intell Syst 34:1001–1033

    Google Scholar 

  • Lang G, Miao D, Fujita H (2019) Three-way group conflict analysis based on Pythagorean fuzzy set theory. IEEE Trans Fuzzy Syst. https://doi.org/10.1109/TFUZZ.2019.2908123

    Article  Google Scholar 

  • Laurin CM (1729) A second letter to Martin Folkes, Esq.; concerning the roots of equations, with demonstration of other rules of algebra. Philos Trans R Soc Lond A 36:59–96

    Google Scholar 

  • Li DQ, Zeng WY (2018) Distance measure of Pythagorean fuzzy sets. Int J Intell Syst 33:348–361

    Google Scholar 

  • Li Z, Wei G, Lu M (2018a) Pythagorean fuzzy hamy mean operators in multiple attribute group decision making and their application to supplier selection. Symmetry 10:505

    Google Scholar 

  • Li L, Zhang R, Wang J, Zhu X, Xing Y (2018b) Pythagorean fuzzy power Muirhead mean operators with their application to multi-attribute decision making. J Intell Fuzzy Syst 35:2035–2050

    Google Scholar 

  • Li YY, Wang JQ, Wang TL (2019) A linguistic neutrosophic multi-criteria group decision-making approach with EDAS method. Arab J Sci Eng 44:2737–2749

    Google Scholar 

  • Liang D, Xu Z (2017) The new extension of TOPSIS method for multiple criteria decision making with hesitant Pythagorean fuzzy sets. Appl Soft Comput 60:167–179

    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 32:966–987

    Google Scholar 

  • Liang D, Zhang Y, Xu Z, Darko AP (2018a) Pythagorean fuzzy Bonferroni mean aggregation operator and its accelerative calculating algorithm with the multithreading. Int J Intell Syst 33:615–633

    Google Scholar 

  • Liang D, Xu Z, Liu D, Wu Y (2018b) Method for three-way decisions using ideal TOPSIS solutions at Pythagorean fuzzy information. Inf Sci 435:282–295

    MathSciNet  Google Scholar 

  • Liang D, Darko AP, Xu Z (2019a) Pythagorean fuzzy partitioned geometric Bonferroni mean and its application to multi-criteria group decision making with grey relational analysis. Int J Fuzzy Syst 21:115–128

    MathSciNet  Google Scholar 

  • Liang D, Zhang Y, Xu Z, Jamaldeen A (2019b) Pythagorean fuzzy VIKOR approaches based on TODIM for evaluating internet banking website quality of Ghanaian banking industry. Appl Soft Comput 78:583–594

    Google Scholar 

  • Luglio M, Romano SP, Roseti C, Zampognaro F (2019) Service delivery models for converged satellite-terrestrial 5G network deployment: a satellite-assisted CDN use-case. IEEE Netw 33:142–150

    Google Scholar 

  • Ma Z, Xu Z (2016) Symmetric Pythagorean fuzzy weighted geometric/averaging operators and their application in multicriteria decision-making problems. Int J Intell Syst 31:1198–1219

    Google Scholar 

  • Mozaffari M, Kasgari A, Saad W, Bennis M, Debbah M (2019) Beyond 5G with UAVs: foundations of a 3D wireless cellular network. IEEE Trans Wirel Commun 18:357–372

    Google Scholar 

  • Muirhead RF (1902) Some methods applicable to identities and inequalities of symmetric algebraic functions of n letters. Proc Edinb Math Soc 21:144–162

    Google Scholar 

  • Nguyen XT, Nguyen VH, Garg H (2019) Exponential similarity measures for Pythagorean fuzzy sets and their applications to pattern recognition and decision-making process. Complex Intell Syst 5:217–228

    Google Scholar 

  • Nie RX, Tian ZP, Wang JQ, Hu JH (2019) Pythagorean fuzzy multiple criteria decision analysis based on Shapley fuzzy measures and partitioned normalized weighted Bonferroni mean operator. Int J Intell Syst 34:297–324

    Google Scholar 

  • Ning Z, Wang X, Xia F, Rodrigues JJ (2019) Joint computation offloading, power allocation, and channel assignment for 5G-enabled traffic management systems. IEEE Trans Ind Inform 15:3058–3067

    Google Scholar 

  • Onar SC, Oztaysi B, Kahraman C (2018) Multicriteria evaluation of cloud service providers using Pythagorean fuzzy TOPSIS. J Mult Valued Log Soft Comput 30:263–283

    Google Scholar 

  • Ozdemir Y, Gul M (2019) Measuring development levels of NUTS-2 regions in Turkey based on capabilities approach and multi-criteria decision-making. Comput Ind Eng 128:150–169

    Google Scholar 

  • Peng X (2019a) Algorithm for Pythagorean fuzzy multi-criteria decision making based on WDBA with new score function. Fund Inform 165:99–137

    MathSciNet  MATH  Google Scholar 

  • Peng X (2019b) New multiparametric similarity measure and distance measure for interval neutrosophic set with IoT industry evaluation. IEEE Access 7:28258–28280

    Google Scholar 

  • Peng X, Dai J (2017) Approaches to Pythagorean fuzzy stochastic multi-criteria decision making based on prospect theory and regret theory with new distance measure and score function. Int J Intell Syst 32:1187–1214

    Google Scholar 

  • Peng XD, Garg H (2019a) Multiparametric similarity measures on Pythagorean fuzzy sets with applications to pattern recognition. Appl Intell. https://doi.org/10.1007/s10489-019-01445-0

    Article  Google Scholar 

  • Peng X, Selvachandran G (2019b) Pythagorean fuzzy set: state of the art and future directions. Artif Intell Rev 52:1873–1927

    Google Scholar 

  • Peng X, Smarandache F (2019c) New multiparametric similarity measure for neutrosophic set with big data industry evaluation. Artif Intell Rev. https://doi.org/10.1007/s10462-019-09756-x

    Article  Google Scholar 

  • Peng X, Smarandache F (2019d) Novel neutrosophic Dombi Bonferroni mean operators with mobile cloud computing industry evaluation. Expert Syst 36:e12411

    Google Scholar 

  • Peng X, Yang Y (2015) Some results for Pythagorean fuzzy sets. Int J Intell Syst 30:1133–1160

    Google Scholar 

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

    Google Scholar 

  • Peng X, Yang Y (2016b) Fundamental properties of interval-valued Pythagorean fuzzy aggregation operators. Int J Intell Syst 31:444–487

    Google Scholar 

  • Peng X, Yang Y (2016c) Multiple attribute group decision making methods based on Pythagorean fuzzy linguistic set. Comput Eng Appl 52:50–54

    Google Scholar 

  • Peng X, Yuan H (2016) Fundamental properties of Pythagorean fuzzy aggregation operators. Fund Inform 147:415–446

    MathSciNet  MATH  Google Scholar 

  • Peng X, Yuan H, Yang Y (2017) Pythagorean fuzzy information measures and their applications. Int J Intell Syst 32:991–1029

    Google Scholar 

  • Pérez-Domínguez L, Rodríguez-Picón LA, Alvarado-Iniesta A, Luviano-Cruz D, Xu Z (2018) MOORA under Pythagorean fuzzy set for multiple criteria decision making. Complexity. https://doi.org/10.1155/2018/2602376

    Article  MATH  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 

  • Rostamzadeh R, Ghorabaee MK, Govindan K, Esmaeili A, Nobar H (2018) Evaluation of sustainable supply chain risk management using an integrated fuzzy TOPSIS-CRITIC approach. J Clean Prod 175:651–669

    Google Scholar 

  • Shakeel M, Abduulah S, Shahzad M, Mahmood T, Siddiqui N (2019) Averaging aggregation operators with Pythagorean trapezoidal fuzzy numbers and their application to group decision making. J Intell Fuzzy Syst 36:1899–1915

    Google Scholar 

  • Shen X, Zhang X, Lan L, Liao Q, Luo Z (2019) Another robust NMF: rethinking the hyperbolic tangent function and locality constraint. IEEE Access 7:31089–31102

    Google Scholar 

  • Taleb T, Afolabi I, Bagaa M (2019) Orchestrating 5G network slices to support industrial internet and to shape next-generation smart factories. IEEE Netw 33:146–154

    Google Scholar 

  • Tus A, Adali EA (2019) The new combination with CRITIC and WASPAS methods for the time and attendance software selection problem. OPSEARCH 56:528–538

    MATH  Google Scholar 

  • Wan SP, Li SQ, Dong JY (2018) A three-phase method for Pythagorean fuzzy multi-attribute group decision making and application to haze management. Comput Ind Eng 123:348–363

    Google Scholar 

  • Wang J, Gao H, Wei G (2019a) The generalized Dice similarity measures for Pythagorean fuzzy multiple attribute group decision making. Int J Intell Syst 34:1158–1183

    Google Scholar 

  • Wang L, Che YL, Long J, Duan L, Wu K (2019b) Multiple access mmwave design for UAV-aided 5G communications. IEEE Wirel Commun 26:64–71

    Google Scholar 

  • Wei GW (2019a) Pythagorean fuzzy Hamacher power aggregation operators in multiple attribute decision making. Fund Inform 166:57–85

    MathSciNet  MATH  Google Scholar 

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

    Google Scholar 

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

    Google Scholar 

  • Wei G, Wei Y (2018c) Similarity measures of pythagorean fuzzy sets based on the cosine function and their applications. Int J Intell Syst 33:634–652

    Google Scholar 

  • Wu SJ, Wei GW (2017) Pythagorean fuzzy Hamacher aggregation operators and their application to multiple attribute decision making. Int J Knowl Intell Eng Syst 21:189–201

    Google Scholar 

  • Wu P, Zhou L, Chen H, Tao Z (2019) Additive consistency of hesitant fuzzy linguistic preference relation with a new expansion principle for hesitant fuzzy linguistic term sets. IEEE Trans Fuzzy Syst 27:716–730

    Google Scholar 

  • Xiao F, Ding W (2019) Divergence measure of Pythagorean fuzzy sets and its application in medical diagnosis. Appl Soft Comput 79:254–267

    Google Scholar 

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

    MathSciNet  MATH  Google Scholar 

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

    Google Scholar 

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

    Google Scholar 

  • Yalcin N, Unlu U (2018) A multi-criteria performance analysis of Initial Public Offering (IPO) firms using CRITIC and VIKOR methods. Technol Econ Dev Econ 24:534–560

    Google Scholar 

  • Yang W, Pang Y (2018) New pythagorean fuzzy interaction Maclaurin symmetric mean operators and their application in multiple attribute decision making. IEEE Access 6:39241–39260

    Google Scholar 

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

    Google Scholar 

  • Yang Y, Chin KS, Ding H, Lv HX, Li YL (2019) Pythagorean fuzzy Bonferroni means based on T-norm and its dual T-conorm. Int J Intell Syst 34:1303–1336

    Google Scholar 

  • Yazdani M, Chatterjee P (2018) Intelligent decision making tools in manufacturing technology selection. Futuristic composites. Springer, Singapore, pp 113–126

    Google Scholar 

  • Yazdani M, Zarate P, Zavadskas K, Turskis Z (2018) A Combined Compromise Solution (CoCoSo) method for multi-criteria decision-making problems. Manag Decis. https://doi.org/10.1108/MD-05-2017-0458

    Article  Google Scholar 

  • Yu L, Zeng S, Merigó JM, Zhang C (2019) A new distance measure based on the weighted induced method and its application to Pythagorean fuzzy multiple attribute group decision making. Int J Intell Syst 34:1440–1454

    Google Scholar 

  • Yucesan M, Kahraman G (2019) Risk evaluation and prevention in hydropower plant operations: a model based on Pythagorean fuzzy AHP. Energy Policy 126:343–351

    Google Scholar 

  • Zeng W, Li D, Yin Q (2018) Distance and similarity measures of Pythagorean fuzzy sets and their applications to multiple criteria group decision making. Int J Intell Syst 33:2236–2254

    Google Scholar 

  • Zhan J, Alcantud JCR (2019) A novel type of soft rough covering and its application to multicriteria group decision making. Artif Intell Rev 52:2381–2410

    Google Scholar 

  • Zhang X (2016) A novel approach based on similarity measure for Pythagorean fuzzy multiple criteria group decision making. Int J Intell Syst 31:593–611

    Google Scholar 

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

    MathSciNet  Google Scholar 

  • Zhu J, Li Y (2018) Pythagorean fuzzy Muirhead mean operators and their application in multiple-criteria group decision-making. Information 9:142

    Google Scholar 

  • Zhu L, Liang X, Wang L, Wu X (2018) Generalized pythagorean fuzzy point operators and their application in multi-attributes decision making. J Intell Fuzzy Syst 35:1407–1418

    Google Scholar 

  • Zolfani SH, Chatterjee P, Yazdani M (2019) A structured framework for sustainable supplier selection using a combined BWM-CoCoSo model. In: International scientific conference in business, management and economics engineering. Vilnius, Lithuania, pp 797–804

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Acknowledgements

The authors are very appreciative to the reviewers for their precious comments which enormously ameliorated the quality of this paper. Our work is sponsored by the National Natural Science Foundation of China (Nos. 61462019, 61806213), MOE (Ministry of Education in China) Project of Humanities and Social Sciences (No. 18YJCZH054), Natural Science Foundation of Guangdong Province (Nos. 2018A030307033, 2018A0303130274), Social Science Foundation of Guangdong Province (No. GD18CFX06) and Special Innovation Projects of Universities in Guangdong Province (No. KTSCX205).

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  1. College of Computer, National University of Defense Technology, Changsha, 410073, China

    Xindong Peng, Xiang Zhang & Zhigang Luo

  2. School of Information Science and Engineering, Shaoguan University, Shaoguan, 512005, China

    Xindong Peng

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Peng, X., Zhang, X. & Luo, Z. Pythagorean fuzzy MCDM method based on CoCoSo and CRITIC with score function for 5G industry evaluation. Artif Intell Rev 53, 3813–3847 (2020). https://doi.org/10.1007/s10462-019-09780-x

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