New similarity and distance measures of Pythagorean fuzzy sets and its application to selection of advertising platforms

Zadeh L.A. , Fuzzy sets, Information and Control 8 (1965), 338–353.

Atanassov K.T. , Intuitionistic fuzzy sets, Fuzzy Sets and Systems 20 (1986), 87–96.

Chen S.M. , Lee L.W. , Liu H.C. and Yang S.W. , Multiattribute decision making based on interval-valued intuitionistic fuzzy values, Expert Systems with Applications 39 (2012), 10343–10351.

Chen S.M. , Yang M.W. , Yang S.W. , Sheu T.W. and Liau C.J. , Multicriteria fuzzy decision making based on interval-valued intuitionistic fuzzy sets, Expert Systems with Applications 39 (2012), 12085–12091.

Chen T.Y. , Experimental analysis of multi-attribute decision-making based on Atanassov intuitionistic fuzzy sets: a discussion of anchor dependency and accuracy functions, International Journal of Systems Science 43 (2012), 1077–1103.

Lu J.P. and Wei C. , TODIM method for performance appraisal on social-integration-based rural reconstruction with interval-valued intuitionistic fuzzy, Journal of Intelligent & Fuzzy Systems 37 (2019), 1731–1740.

Wu L.P. , Gao H. and Wei C. , VIKOR method for financing risk assessment of rural tourism projects under interval-valued intuitionistic fuzzy environment, Journal of Intelligent & Fuzzy Systems 37 (2019), 2001–2008.

Wu L.P. , Wei G.W. , Wu J. and Wei C. , Some Interval-Valued Intuitionistic Fuzzy Dombi Heronian Mean Operators and their Application for Evaluating the Ecological Value of Forest Ecological Tourism Demonstration Areas, International Journal of Environmental Research and Public Health 17 (2020), 829.

Yager R.R. , Pythagorean fuzzy subsets, in: 2013 joint IFSA world congress and NAFIPS annual meeting (IFSA/NAFIPS), IEEE, 2013, pp. 57–61.

Yager R.R. , Pythagorean membership grades in multicriteria decision making, IEEE Transactions on Fuzzy Systems 22 (2013), 958–965.

Zhang X.L. and Xu Z.S. , Extension of TOPSIS to Multiple Criteria Decision Making with Pythagorean Fuzzy Sets, International Journal of Intelligent Systems 29 (2014), 1061–1078.

Peng X.D. and Yang Y. , Some Results for Pythagorean Fuzzy Sets, International Journal of Intelligent Systems 30 (2015), 1133–1160.

Liang D.C. , Zhang Y.R.J. , Xu Z.S. and Darko A.P. , Pythagorean fuzzy Bonferroni mean aggregation operator and its accelerative calculating algorithm with the multithreading, International Journal of Intelligent Systems 33 (2018), 615–633.

Liang D.C. , Xu Z.S. and Darko A.P. , Projection Model for Fusing the Information of Pythagorean Fuzzy Multicriteria Group Decision Making Based on Geometric Bonferroni Mean, International Journal of Intelligent Systems 32 (2017), 966–987.

Wei G.W. and Lu M. , Pythagorean Fuzzy Maclaurin Symmetric Mean Operators in Multiple Attribute Decision Making, International Journal of Intelligent Systems 33 (2018), 1043–1070.

Wei G.W. and Lu M. , Pythagorean fuzzy power aggregation operators in multiple attribute decision making, International Journal of Intelligent Systems 33 (2018), 169–186.

Gou X.J. , Xu Z.S. and Ren P.J. , The Properties of Continuous Pythagorean Fuzzy, International Journal of Intelligent Systems 31 (2016), 401–424.

Ren P.J. , Xu Z.S. and Gou X.J. , Pythagorean fuzzy TODIM approach to multi-criteria decision making, Applied Soft Computing 42 (2016), 246–259.

Zeb A. , Khan M.S.A. and Ibrar M. , Approaches to multi-attribute decision making with risk preference under extended Pythagorean fuzzy environment, Journal of Intelligent & Fuzzy Systems 36 (2019), 325–335.

Li Z.X. , Wei G.W. and Lu M. , Pythagorean Fuzzy Hamy Mean Operators in Multiple Attribute Group Decision Making and Their Application to Supplier Selection, Symmetry-Basel 10 (2018), 505.

Tang X.Y. , Wei G.W. and Gao H. , Pythagorean fuzzy Muirhead mean operators in multiple attribute decision making for evaluating of emerging technology commercialization, Economic Research-Ekonomska Istrazivanja 32 (2019), 1667–1696.

Tang X.Y. , Wei G.W. and Gao H. , Models for multiple attribute decision making with interval-valued pythagorean fuzzy muirhead mean operators and their application to green suppliers selection, Informatica 30 (2019), 153–186.

Wei G.W. , Wang J. , Lu M. , Wu J. and Wei C. , Similarity Measures of Spherical Fuzzy Sets Based on Cosine Function and Their Applications, IEEE Access 7 (2019), 159069–159080.

Wei G.W. , The generalized dice similarity measures for multiple attribute decision making with hesitant fuzzy linguistic, Economic Research-Ekonomska Istrazivanja 32 (2019), 1498–1520.

Peng X.D. , New similarity measure and distance measure for Pythagorean fuzzy set, Complex & Intelligent Systems 5 (2019), 101–111.

Peng X.D. and Dai J.G. , Research on the assessment of classroom teaching quality with q-rung orthopair fuzzy information based on multiparametric similarity measure and combinative distance-based assessment, International Journal of Intelligent Systems (2019) https://doi.org/10.1002/int.22109.

Ye J. , Cosine similarity measures for intuitionistic fuzzy sets and their applications, Mathematical and computer modelling 53 (2011), 91–97.

Shi L.L. and Ye I. , Similarity Measure for Vague Sets, Journal of Applied Sciences 13 (2013), 1781–1786.

Ye J. , Similarity measures of intuitionistic fuzzy sets based on cosine function for the decision making of mechanical design schemes, Journal of Intelligent & Fuzzy Systems 30 (2016), 151–158.

Wei G. and Yu W. , Similarity measures of Pythagorean fuzzy sets based on the cosine function and their applications, International Journal of Intelligent Systems 33 (2018), 634–652.

Zhang Q. , Hu J. , Feng J. , Liu A. and Li Y. , New Similarity Measures of Pythagorean Fuzzy Sets and Their Applications, IEEE Access 7 (2019), 138192–138202.

Hussian Z. and Yang M.S. , Distance and similarity measures of Pythagorean fuzzy sets based on the Hausdorff metric with application to fuzzy TOPSIS, International Journal of Intelligent Systems 34 (2019), 2633–2654.

Li Z.X. and Lu M. , Some novel similarity and distance and measures of Pythagorean fuzzy sets and their applications, Journal of Intelligent & Fuzzy Systems 37 (2019), 1781–1799.

Zhang X. and Xu Z. , Extension of TOPSIS to multiple criteria decision making with Pythagorean fuzzy sets, International Journal of Intelligent Systems 29 (2014), 1061–1078.

Ren P. , Xu Z. and Gou X. , Pythagorean fuzzy TODIM approach to multi-criteria decision making, Applied Soft Computing 42 (2016), 246–259.

Chen T.-Y. , Remoteness index-based Pythagorean fuzzy VIKOR methods with a generalized distance measure for multiple criteria decision analysis, Information Fusion 41 (2018), 129–150.

Yager R.R. and Abbasov A.M. , Pythagorean membership grades, complex numbers, and decision making, International Journal of Intelligent Systems 28 (2013), 436–452.

Li D. and Zeng W. , Distance measure of Pythagorean fuzzy sets, International Journal of Intelligent Systems 33 (2018), 348–361.

Zeng W. , Li D. and Yin Q. , Distance and similarity measures of Pythagorean fuzzy sets and their applications to multiple criteria group decision making, International Journal of Intelligent Systems 33 (2018), 2236–2254.

Chen T.-Y. , Novel generalized distance measure of Pythagorean fuzzy sets and a compromise approach for multiple criteria decision analysis under uncertainty, IEEE Access 7 (2019), 58168–58185.

Chen T.-Y. , Multiple Criteria Group Decision Making Using a Parametric Linear Programming Technique for Multidimensional Analysis of Preference Under Uncertainty of Pythagorean Fuzziness, IEEE Access 7 (2019), 174108–174128.

Yager R. and Xu Z. , Intuitionistic and interval-valued intuitionistic fuzzy preference relations and their measures of similarity for the evaluation of agreement within a group, Fuzzy Optimization and Decision Making 8 (2009), 123–139.

Zhang X. , A novel approach based on similarity measure for Pythagorean fuzzy multiple criteria group decision making, International Journal of Intelligent Systems 31 (2016), 593–611.

Dice L.R. , Measures of the amount of ecologic association between species, Ecology 26 (1945), 297–302.

Peng X. and Yang Y. , Some results for Pythagorean fuzzy sets, International Journal of Intelligent Systems 30 (2015), 1133–1160.

Takahashi W. , Nonlinear functional analysis, Fixed Point Theory and its Applications, (2000).

Hardy G.H. , Littlewood J.E. , Pólya G. , Littlewood D. and Pólya G. , Inequalities, Cambridge University Press, 1952.

Yager R.R. and Filev D.P. , Essentials of fuzzymodeling and control, New York, 388 (1994).

Hadi-Vencheh A. and Mirjaberi M. , Fuzzy inferior ratio method for multiple attribute decision making problems, Information Sciences 277 (2014), 263–272.

Amaldoss W. and He C. , Product variety, informative advertising, and price competition, Journal of Marketing Research 47 (2010), 146–156.

Zavadskas E.K. , Antucheviciene J. , Saparauskas J. and Turskis Z. , MCDM methods WASPAS and MULTIMOORA: Verification of robustness of methods when assessing alternative solutions, Economic Computation and Economic Cybernetics Studies and Research 47 (2013), 5–20.

Stanujkic D. , Karabasevic D. , Zavadskas E.K. , Smarandache F. and Brauers W.K.M. , A Bipolar Fuzzy Extension of the MULTIMOORA Method, Informatica 30 (2019), 135–152.

Garg H. and Rani D. , Complex Interval-valued Intuitionistic Fuzzy Sets and their Aggregation Operators, Fundamenta Informaticae 164 (2019), 61–101.

Wei G.W. , He Y. , Lei F. , Wu J. and Wei C. , MABAC method for multiple attribute group decision making with probabilistic uncertain linguistic, Information Journal of Intelligent & Fuzzy Systems 39 (2020), 3315–3327.

Wei G.W. , He Y. , Lei F. , Wu J. , Wei C. and Guo Y.F. , Green supplier selection with an uncertain probabilistic linguistic MABAC method, Journal of Intelligent & Fuzzy Systems 39 (2020), 3125–3136.

Wei G.W. , Lu J.P. , Wei C. and Wu J. , Probabilistic linguistic GRA method for multiple attribute group decision making, Journal of Intelligent & Fuzzy Systems 38 (2020), 4721–4732.

Wei G.W. , Wang J. , Lu J.P. , Wu J. , Wei C. , Alsaadi F.E. and Hayat T. , VIKOR method for multiple criteria group decision making under 2-tuple linguistic neutrosophic environment, Economic Research-Ekonomska Istrazivanja 33 (2020), 3185–3208.

Jahan A. and Zavadskas E.K. , ELECTRE-IDAT for design decision-making problems with interval data and target-based criteria, Soft Computing 23 (2019), 129–143.

Zavadskas E.K. , Antucheviciene J. and Chatterjee P. , Multiple-Criteria Decision-Making (MCDM) Techniques for Business Processes Information Management, Information 10 (2019).

Lei F. , Lu J.P. , Wei G.W. , Wu J. , Wei C. and Guo Y.F. , GRA method for waste incineration plants location problem with probabilistic linguistic multiple attribute group decision making, Journal of Intelligent & Fuzzy Systems 39 (2020), 2909–2920.

Lei F. , Wei G. , Wu J. , Wei C. and Guo Y. , QUALIFLEX method for MAGDM with probabilistic uncertain linguistic information and its application to green supplier selection, Journal of Intelligent & Fuzzy Systems 39 (2020), 6819–6831.

Wang P. , Wang J. , Wei G. , Wu J. , Wei C. and Wei Y. , CODAS Method for Multiple Attribute Group Decision Making Under 2-Tuple Linguistic Neutrosophic Environment, Informatica 31 (2020), 161–184.

Gao H. , Ran L.G. , Wei G.W. , Wei C. and Wu J. , VIKOR method for MAGDM based on q-rung interval-valued orthopair fuzzy information and its application to supplier selection of medical consumption products, International Journal of Environmental Research and Public Health 17 (2020), 525.

Wei G.W. and Gao H. , Pythagorean 2-tuple linguistic power aggregation operators in multiple attribute decision making,ž, ivanja 31 (2020), 904–933.

Yu G.F. , Li D.F. and Fei W. , A novel method for heterogeneous multi-attribute group decision making with preference deviation, Computers & Industrial Engineering 124 (2018), 58–64.