Pythagorean fuzzy set: state of the art and future directions
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Alcantud JCR (2016) Some formal relationships among soft sets, fuzzy sets, and their extensions. Int J Approx Reason 68:45–53
Beg I, Rashid T (2016) An intuitionistic 2-tuple linguistic information model and aggregation operators. Int J Intell Syst 31(6):569–592
Beliakov G, James S (2014) Averaging aggregation functions for preferences expressed as pythagorean membership grades and fuzzy orthopairs. In: Proceedings of the IEEE international conference on fuzzy systems (FUZZ-IEEE), pp 298–305
Dick S, Yager R, Yazdanbakhsh O (2016) On pythagorean and complex fuzzy set operations. IEEE Trans Fuzzy Syst 24(5):1009–1021
Du YQ, Hou F, Zafar W, Yu Q, Zhai Y (2017) A novel method for multiattribute decision making with interval-valued pythagorean fuzzy linguistic information. Int J Intell Syst 32(10):1085–1112
Fodor J, Marichal J, Roubens M (1995) Characterization of the ordered weighted averaging operators. IEEE Trans Fuzzy Syst 3(2):236–240
Garg H (2016a) A new generalized pythagorean fuzzy information aggregation using einstein operations and its application to decision making. Int J Intell Syst 31(9):886–920
Garg H (2016b) A novel accuracy function under interval-valued pythagorean fuzzy environment for solving multicriteria decision making problem. J Intell Fuzzy Syst 31(1):529–540
Garg H (2016c) A novel correlation coefficients between pythagorean fuzzy sets and its applications to decision-making processes. Int J Intell Syst 31(12):1234–1252
Garg H (2017a) Confidence levels based pythagorean fuzzy aggregation operators and its application to decision-making process. Comput Math Organ Theory. https://doi.org/10.1007/s10588-017-9242-8
Garg H (2017b) Generalized pythagorean fuzzy geometric aggregation operators using einstein t-norm and t-conorm for multicriteria decision-making process. Int J Intell Syst 32(6):597–630
Garg H (2017c) A novel improved accuracy function for interval valued pythagorean fuzzy sets and its applications in the decision-making process. Int J Intell Syst. https://doi.org/10.1002/int.21898
Ghorabaee MK, Amiri M, Sadaghiani J, Goodarzi G (2014) Multiple criteria group decision-making for supplier selection based on copras method with interval type-2 fuzzy sets. Int J Adv Manuf Technol 75:1115–1130
Ghorabaee MK, Zavadskas EK, Olfat L, Turskis Z (2015) Multi-criteria inventory classification using a new method of evaluation based on distance from average solution (EDAS). Informatica 26:435–451
Ghorabaee MK, Zavadskas EK, Amiri M, Turskis Z (2016) Extended edas method for fuzzy multi-criteria decision-making: an application to supplier selection. Int J Comput Commun Control 11:358–371
Gou XJ, Xu ZS, Ren PJ (2016) The properties of continuous pythagorean fuzzy information. Int J Intell Syst 31(5):401–424
Hadi-Venchen A, Mirjaberi M (2014) Fuzzy inferior ratio method for multiple attribute decision making problems. Inf Sci 277:263–272
He X, Du Y, Liu W (2016) Pythagorean fuzzy power average operators. Fuzzy Syst Math 30(6):116–124
Herrera F, Herrera-Viedma E, Verdegay J (1996) A model of consensus in group decision making under linguistic assessments. Fuzzy Set Syst 79(1):73–87
Kang X, Li D, Wang S, Qu K (2013) Rough set model based on formal concept analysis. Inf Sci 222:611–625
Li D, Zhang B, Leung Y (2004) On knowledge reduction in inconsistent decision information systems. Int J Uncertain Fuzziness Knowl-Based Syst 12(5):651–672
Li M, Yu Y, Xu Y (2015) Knowledge checking service selection method in pythagorean fuzzy environment. In: International conference on logistics engineering. Management and Computer Science, pp 1438–1443
Liang DC, 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
Liang DC, Xu ZS, 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
Liang J, Wang F, Dang C, Qian Y (2012) An efficient rough feature selection algorithm with a multi-granulation view. Int J Approx Reason 53(6):912–926
Liang W, Zhang X, Liu M (2015) The maximizing deviation method based on interval-valued pythagorean fuzzy weighted aggregating operator for multiple criteria group decision analysis. Discrete Dyn Nat Soc 2015:1–15
Liao HC, Xu Z (2014) Intuitionistic fuzzy hybrid weighted aggregation operators. Int J Intell Syst 29(11):971–993
Liao HC, Xu Z (2015) Extended hesitant fuzzy hybrid weighted aggregation operators and their application in decision making. Soft Comput 19(9):2551–2564
Liao HC, Xu ZS, Zeng XJ (2015) Hesitant fuzzy linguistic vikor method and its application in qualitative multiple criteria decision making. IEEE Trans Fuzzy Syst 23(5):1343–1355
Liao HC, Gou XJ, Xu ZS (2017) A survey of decision making theory and methodologies of hesitant fuzzy linguistic term set. Syst Eng Theor Pract 37(1):35–48
Liou JJ, Tamosaitiene J, Zavadskas E, Tzeng G (2016) New hybrid copras-g madm model for improving and selecting suppliers in green supply chain management. Int J Prod Res 54:114–134
Liu C, Tang G, Liu P (2017) An approach to multi-criteria group decision making with unknown weight information based on pythagorean fuzzy uncertain linguistic aggregation operators. Math Probl Eng 2017:1–18
Liu W, Chang J, He X (2016) Generalized pythagorean fuzzy aggregation operators and applications in decision making. Control Decis 31(12):2280–2286
Liu W, Du Y, Chang J (2017b) Pythagorean fuzzy interaction aggregation operators and applications in decision making. Control Decis. https://doi.org/10.13195/j.kzyjc.2016.0431
Liu ZM, Liu PD, Liu WL, Pang JY (2017c) Pythagorean uncertain linguistic partitioned bonferroni mean operators and their application in multi-attribute decision making. J Intell Fuzzy Syst 32(3):2779–2790
Luca AD, Termini S (1972) A definition of non-probabilistic entropy in the setting of fuzzy sets theory. Inf Control 20:301–312
Ma ZM, Xu ZS (2016) Symmetric pythagorean fuzzy weighted geometric/averaging operators and their application in multicriteria decision-making problems. Int J Intell Syst 31(12):1198–1219
Maji PK, Biswas R, Roy A (2001a) Intuitionistic fuzzy soft sets. J Fuzzy Math 9:677–692
Maji PK, Biswas R, Roy AR (2001b) Fuzzy soft sets. J Fuzzy Math 9:589–602
Merigó JM (2011) A unified model between the weighted average and the induced owa operator. Expert Syst Appl 38(9):11,560–11,572
Pamucar D, Cirovic G (2015) The selection of transport and handling resources in logistics centers using multi-attributive border approximation area comparison (mabac). Expert Syst Appl 42(6):3016–3028
Peng DH, Gao C, Gao Z (2013) Generalized hesitant fuzzy synergetic weighted distance measures and their application to multiple criteria decision-making. Appl Math Model 37:5837–5850
Peng XD, Dai J (2016) Approaches to single-valued neutrosophic madm based on mabac, topsis and new similarity measure with score function. Neural Comput Appl. https://doi.org/10.1007/s00521-016-2607-y
Peng XD, 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(11):1187–1214
Peng XD, Liu C (2017) Algorithms for neutrosophic soft decision making based on EDAS, new similarity measure and level soft set. J Intell Fuzzy Syst 32(1):955–968
Peng XD, Yang Y (2016a) Fundamental properties of interval-valued pythagorean fuzzy aggregation operators. Int J Intell Syst 31(5):444–487
Peng XD, Yang Y (2016b) Multiple attribute group decision making methods based on pythagorean fuzzy linguistic set. Comput Eng Appl 52(23):50–54
Peng XD, Yang Y (2016c) Pythagorean fuzzy choquet integral based mabac method for multiple attribute group decision making. Int J Intell Syst 31(10):989–1020
Peng XD, Yuan H (2016) Fundamental properties of pythagorean fuzzy aggregation operators. Fund Inform 147(4):415–446
Peng XD, Yang Y, Song J, Jiang Y (2015a) Pythagorean fuzzy soft set and its application. Comput Eng 41(7):224–229
Peng XD, Yang Y, Zhu YL (2015b) Similarity measure and its application based on multi-parametric intuitionistic fuzzy sets. Comput Eng Appl 51(13):122–125
Peng XD, Dai J, Yuan H (2017a) Interval-valued fuzzy soft decision making methods based on MABAC, similarity measure and EDAS. Fund Inform 152:1–24
Peng XD, Yuan H, Yang Y (2017b) Pythagorean fuzzy information measures and their applications. Int J Intell Syst 32(10):991–1029
Phong PH, Son L (2017) Linguistic vector similarity measures and applications to linguistic information classification. Int J Intell Syst 32(1):67–81
Qian Y, Liang J, Dang C (2010a) Incomplete multigranulation rough set. IEEE Trans Syst Man Cybern A 40(2):420–431
Rahman K, Abdullah S, Ahmed R, Ullah M (2017a) Pythagorean fuzzy einstein weighted geometric aggregation operator and their application to multiple attribute group decision making. J Intell Fuzzy Syst 33(1):635–647
Rahman K, Khan MS, Ullah M, Fahmi A (2017b) Multiple attribute group decision making for plant location selection with pythagorean fuzzy weighted geometric aggregation operator. The Nucleus 54(1):66–74
Reformat MZ, Yager RR (2014) Suggesting recommendations using pythagorean fuzzy sets illustrated using netflix movie data. In: Proceedings of the information processing and management of uncertainty in knowledge-based systems, pp 546–556
Ren PJ, Xu ZS, Gou XJ (2016) Pythagorean fuzzy todim approach to multi-criteria decision making. Appl Soft Comput 42:246–259
Wang JQ, Li JJ (2009) The multi-criteria group decision making method based on multi-granularity intuitionistic two semantics. Sci Tech Inf 33:8–9
Wang P (1983) Fuzzy sets and its applications. Shanghai Science and Technology Press, Shanghai
Wei CP, Liao H (2016) A multigranularity linguistic group decision-making method based on hesitant 2-tuple sets. Int J Intell Syst 31(6):612–634
Wei GW, Lu M (2017) Pythagorean fuzzy maclaurin symmetric mean operators in multiple attribute decision making. Int J Intell Syst. https://doi.org/10.1002/int.21911
Wei GW, Wang H, Lin R (2011) Application of correlation coefficient to interval-valued intuitionistic fuzzy multiple attribute decision-making with incomplete weight information. Knowl Inf Syst 26(2):337–349
Xia MM, Xu ZS (2011) Hesitant fuzzy information aggregation in decision making. Int J Approx Reason 52(3):395–407
Xu ZS (2016) Additive intuitionistic fuzzy aggregation operators based on fuzzy measure. Int J Uncertain Fuzz Based Syst 24(1):1–12
Xu ZS, Da Q (2004) Linguistic approaches to multiple attribute decision making in uncertain linguistic setting. J Southeast Univ 20(4):482–485
Xu ZS, Xia MM (2011) Distance and similarity measures for hesitant fuzzy sets. Inf Sci 181(11):2128–2138
Xu ZS, Yager RR (2006) Some geometric aggregation operators based on intuitionistic fuzzy sets. Int J Gen Syst 35(4):417–433
Xu ZS, Yager RR (2011) Intuitionistic fuzzy Bonferroni means. IEEE Trans Syst Man Cybernet B 41(2):568–578
Xu ZS, Chen J, Wu J (2008) Clustering algorithm for intuitionistic fuzzy sets. Inf Sci 178:3775–3790
Xue YX, You JX, Lai X, Liu H (2016) An interval-valued intuitionistic fuzzy mabac approach for material selection with incomplete weight information. Appl Soft Comput 38:703–713
Yager RR (2013) Pythagorean fuzzy subsets. In: Proceedings of the Joint IFSA World Congress and NAFIPS Annual Meeting, pp 57–61
Yager RR (2014) Pythagorean membership grades in multicriteria decision making. IEEE Trans Fuzzy Syst 22(4):958–965
Yager RR, Abbasov AM (2013) Pythagorean membership grades, complex numbers, and decision making. Int J Intell Syst 28(5):436–452
Yang Y, Ding H, Chen ZS, Li YL (2016) A note on extension of topsis to multiple criteria decision making with pythagorean fuzzy sets. Int J Intell Syst 31(1):68–72
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(1):47–61
Zavadskas EK, Kaklauskas A, Sarka V (1994) The new method of multicriteria complex proportional assessment of projects. Technol Econ Dev Eco 1:131–139
Zeng SZ (2017) Pythagorean fuzzy multiattribute group decision making with probabilistic information and owa approach. Int J Intell Syst 33(11):1136–1150
Zeng SZ, Chen J, Li X (2016) A hybrid method for pythagorean fuzzy multiple-criteria decision making. Int J Inf Technol Decis 15(2):403–422
Zhang C, Li D (2016) Pythagorean fuzzy rough sets and its applications in multi-attribute decision making. J Chin Compu Syst 37(7):1531–1535
Zhang C, Li D, Ren R (2016) Pythagorean fuzzy multigranulation rough set over two universes and its applications in merger and acquisition. Int J Intell Syst 31(9):921–943
Zhang RT, Wang J, Zhu X, Xia M, Yu M (2017) Some generalized pythagorean fuzzy bonferroni mean aggregation operators with their application to multi-attribute group decision making. Complexity https://doi.org/10.1155/2017/5286135
Zhang XL (2016a) Multicriteria pythagorean fuzzy decision analysis: a hierarchical qualiflex approach with the closeness index-based ranking methods. Inf Sci 330:104–124
Zhang XL (2016b) A novel approach based on similarity measure for pythagorean fuzzy multiple criteria group decision making. Int J Intell Syst 31(6):593–611
Zhang XL (2017) Pythagorean fuzzy clustering analysis: A hierarchical clustering algorithm with the ratio index-based ranking methods. Int J Intell Syst. https://doi.org/10.1002/int.21915