New similarity measure and distance measure for Pythagorean fuzzy set

Atanassov K (1986) Intuitionistic fuzzy sets. Fuzzy Sets Syst 20:87–96 Yager RR (2014) Pythagorean membership grades in multicriteria decision making. IEEE Trans Fuzzy Syst 22:958–965 Zhang XL, Xu ZS (2014) Extension of TOPSIS to multiple criteria decision making with Pythagorean fuzzy sets. Int J Intell Syst 29:1061–1078 Peng XD, Yang Y (2015) Some results for Pythagorean fuzzy sets. Int J Intell Syst 30:1133–1160 Peng XD, Yang Y (2016) Fundamental properties of interval-valued Pythagorean fuzzy aggregation operators. Int J Intell Syst 31:444–487 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 31:921–943 Liu ZM, Liu PD, Liu WL, Pang JY (2017) Pythagorean uncertain linguistic partitioned bonferroni mean operators and their application in multi-attribute decision making. J Intell Fuzzy Syst 32:2779–2790 Liang DC, Xu ZS (2017) The new extension of TOPSIS method for multiple criteria decision making with hesitant Pythagorean fuzzy sets. Appl Soft Comput 60:167–179 Peng XD, Yuan H (2016) Fundamental properties of Pythagorean fuzzy aggregation operators. Fund Inf 147:415–446 Garg H (2017) Confidence levels based Pythagorean fuzzy aggregation operators and its application to decision-making process. Comput Math Org Ther 23:546–571 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 Ma ZM, Xu ZS (2016) Symmetric pythagorean fuzzy weighted geometric/averaging operators and their application in multicriteria decision-making problems. Int J Intell Syst 31:1198–1219 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 Wei G, Lu M (2018) Pythagorean fuzzy maclaurin symmetric mean operators in multiple attribute decision making. Int J Intell Syst 33:1043–1070 Khan MSA, Abdullah S, Ali A, Amin F (2018) Pythagorean fuzzy prioritized aggregation operators and their application to multi-attribute group decision making. Granul Comput. https://doi.org/10.1007/s41066-018-0093-6 Gao H, Lu M, Wei G, Wei Y (2018) Some novel Pythagorean fuzzy interaction aggregation operators in multiple attribute decision making. Fund Inf 159:385–428 Liu Y, Qin Y, Han Y (2018) Multiple criteria decision making with probabilities in interval-valued pythagorean fuzzy setting. Int J Fuzzy Syst 20:558–571 Zeng S (2017) Pythagorean fuzzy multiattribute group decision making with probabilistic information and OWA approach. Int J Intell Syst 32:1136–1150 Yang Y, Chen ZS, Chen YH, Chin KS (2018) Interval-valued Pythagorean Fuzzy frank power aggregation operators based on an isomorphic frank dual triple. Int J Comput Intell Syst 11:1091–1110 Qin J (2018) Generalized Pythagorean fuzzy maclaurin symmetric means and its application to multiple attribute SIR group decision model. Int J Fuzzy Syst 20:943–957 Yang Y, Li YL, Ding H, Qian GS, Lyu HX (2018) The pythagorean fuzzy Frank aggregation operators based on isomorphism Frank t-norm and s-norm and their application. Control Decis 33:1471–1480 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 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 Liang DC, Xu ZS, Liu D, Wu Y (2018) Method for three-way decisions using ideal TOPSIS solutions at Pythagorean fuzzy information. Inf Sci 435:282–295 Xue W, Xu ZS, Zhang X, Tian X (2018) Pythagorean fuzzy LINMAP method based on the entropy theory for railway project investment decision making. Int J Intell Syst 33:93–125 Chen TY (2018) Remoteness index-based Pythagorean fuzzy VIKOR methods with a generalized distance measure for multiple criteria decision analysis. Inf Fusion 41:129–150 Chen TY (2018) An effective correlation-based compromise approach for multiple criteria decision analysis with Pythagorean fuzzy information. J Intell Fuzzy Syst 35:3529–3541 Peng X, Selvachandran G (2018) Pythagorean fuzzy set: state of the art and future directions. Artif Intell Rev. https://doi.org/10.1007/s10462-017-9596-9 Chen TY (2018) A novel VIKOR method with an application to multiple criteria decision analysis for hospital-based post-acute care within a highly complex uncertain environment. Neural Comput Appl. https://doi.org/10.1007/s00521-017-3326-8 Ren PJ, Xu ZS, Gou XJ (2016) Pythagorean fuzzy TODIM approach to multi-criteria decision making. Appl Soft Comput 42:246259 Chen TY (2018) An outranking approach using a risk attitudinal assignment model involving Pythagorean fuzzy information and its application to financial decision making. Appl Soft Comput 71:460–487 Wei G, Wei Y (2018) Similarity measures of Pythagorean fuzzy sets based on the cosine function and their applications. Int J Intell Syst 33:634–652 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 Peng X, Yuan H, Yang Y (2017) Pythagorean fuzzy information measures and their applications. Int J Intell Syst 32:991–1029 Xu ZS, Yager RR (2006) Some geometric aggregation operators based on intuitionistic fuzzy sets. Int J Gen Syst 35:417–433 Li Y, Olson DL, Qin Z (2007) Similarity measures between intuitionistic fuzzy (vague) sets: a comparative analysis. Pattern Recognit Lett 28:278–285 Chen SM (1997) Similarity measures between vague sets and between elements. IEEE Trans Syst Man Cyber 27:153–158 Chen SM, Chang CH (2015) A novel similarity measure between Atanssov’s intuitionistic fuzzy sets based on transformation techniques with applications to pattern recognition. Inf Sci 291:96–114 Hung WL, Yang MS (2004) Similarity measures of intuitionistic fuzzy sets based on Hausdorff distance. Pattern Recognit Lett 25:1603–1611 Hong DH, Kim C (1999) A note on similarity measures between vague sets and between elements. Inf Sci 115:83–96 Li DF, Cheng CT (2002) New similarity measures of intuitionistic fuzzy sets and application to pattern recognitions. Pattern Recognit Lett 23:221–225 Li F, Xu ZY (2001) Measures of similarity between vague sets. J Softw 12:922–927 Liang ZZ, Shi PF (2003) Similarity measures on intuitionistic fuzzy sets. Pattern Recognit Lett 24:2687–2693 Mitchell HB (2003) On the Dengfeng–Chuntian similarity measure and its application to pattern recognition. Pattern Recognit Lett 24:3101–3104 Ye J (2011) Cosine similarity measures for intuitionistic fuzzy sets and their applications. Math Comput Model 53:91–97 Boran FE, Akay D (2014) A biparametric similarity measure on intuitionistic fuzzy sets with applications to pattern recognition. Inf Sci 255:45–57 Huang HH, Liang Y (2018) Hybrid L1/2+2 method for gene selection in the Cox proportional hazards model. Comput Meth Prog Biol 164:65–73 Shen KW, Wang JQ (2018) Z-VIKOR method based on a new weighted comprehensive distance measure of Z-number and its application. IEEE Trans Fuzzy Syst. https://doi.org/10.1109/TFUZZ.2018.2816581 Peng HG, Wang JQ (2018) A Multicriteria Group Decision-Making Method Based on the Normal Cloud Model With Zadeh’s Z-numbers. IEEE Trans Fuzzy Syst. https://doi.org/10.1109/TFUZZ.2018.2816909 Liao HC, Xu ZS, Herrera-Viedma E, Herrera F (2018) Hesitant fuzzy linguistic term set and its application in decision making: a state-of-the-art survey. Int J Fuzzy Syst. https://doi.org/10.1007/s40815-017-0432-9 Alcantud JCR, Torra V (2018) Decomposition theorems and extension principles for hesitant fuzzy sets. Inf Fusion 41:48–56 Alcantud JCR, Mathew TJ (2017) Separable fuzzy soft sets and decision making with positive and negative attributes. Appl Soft Comput 59:586–595 Garg H (2018) Generalised Pythagorean fuzzy geometric interactive aggregation operators using Einstein operations and their application to decision making. J Exp Theor Artif Intell. https://doi.org/10.1080/0952813X.2018.1467497 Garg H (2018) New exponential operational laws and their aggregation operators for interval-valued Pythagorean fuzzy multicriteria decision-making. Int J Intell Syst 33(3):653–683 Garg H (2018) Some methods for strategic decision-making problems with immediate probabilities in Pythagorean fuzzy environment. Int J Intell Syst 33(4):687–712 Garg H (2018) Linguistic Pythagorean fuzzy sets and its applications in multiattribute decision-making process. Int J Intell Syst 33(6):1234–1263 Garg H (2018) Hesitant Pythagorean fuzzy sets and their aggregation operators in multiple-attribute decision-making. Int J Uncertain Quant 8:267–289 Nie RX, Tian ZP, Wang JQ, Hu JH (2018) Pythagorean fuzzy multiple criteria decision analysis based on Shapley fuzzy measures and partitioned normalized weighted Bonferroni mean operator. Int J Intell Syst. https://doi.org/10.1002/int.22051 Zhou H, Wang J, Zhang H (2017) Stochastic Multi-criteria decision-making approach based on SMAA-ELECTRE with extended grey numbers. Int Trans Oper Res. https://doi.org/10.1111/itor.12380 Tian ZP, Wang JQ, Zhang HY, Wang TL (2018) Signed distance-based consensus in multi-criteria group decision-making with multi-granular hesitant unbalanced linguistic information. Comput Ind Eng 124:125–138 Peng XD, Dai JG (2018) A bibliometric analysis of neutrosophic set: two decades review from 1998–2017. Artif Intell Rev. https://doi.org/10.1007/s10462-018-9652-0 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 32:955–968 Peng XD, Dai JG, Garg H (2018) Exponential operation and aggregation operator for q-rung orthopair fuzzy set and their decision-making method with a new score function. Int J Intell Syst. https://doi.org/10.1002/int.22028 Zhan J, Alcantud JCR (2018) A novel type of soft rough covering and its application to multicriteria group decision making. Artif Intell Rev. https://doi.org/10.1007/s10462-018-9617-3