research-article

Pythagorean fuzzy linguistic Muirhead mean operators and their applications to multiattribute decision‐making

Authors:

Ya QinAuthors Info & Claims

International Journal of Intelligent Systems, Volume 35, Issue 2

Pages 300 - 332

https://doi.org/10.1002/int.22212

Published: 12 December 2019 Publication History

Abstract

Pythagorean fuzzy sets, as an extension of intuitionistic fuzzy sets to deal with uncertainty, have attracted much attention since their introduction, in both theory and application aspects. In this paper, we investigate multiple attribute decision‐making (MADM) problems with Pythagorean linguistic information based on some new aggregation operators. To begin with, we present some new Pythagorean fuzzy linguistic Muirhead mean (PFLMM) operators to deal with MADM problems with Pythagorean fuzzy linguistic information, including the PFLMM operator, the Pythagorean fuzzy linguistic‐weighted Muirhead mean operator, the Pythagorean fuzzy linguistic dual Muirhead mean operator and the Pythagorean fuzzy linguistic dual‐weighted Muirhead mean operator. The main advantages of these aggregation operators are that they can capture the interrelationships of multiple attributes among any number of attributes by a parameter vector P and make the information aggregation process more flexible by the parameter vector P. In addition, some of the properties of these new aggregation operators are proved and some special cases are discussed where the parameter vector takes some different values. Moreover, we present two new methods to solve MADM problems with Pythagorean fuzzy linguistic information. Finally, an illustrative example is provided to show the feasibility and validity of the new methods, to investigate the influences of parameter vector P on decision‐making results, and also to analyze the advantages of the proposed methods by comparing them with the other existing methods.

References

[1]

Atanassov K, Gargov G. Interval‐valued intuitionistic fuzzy sets. Fuzzy Set Syst. 1989;31:343‐349.

Digital Library

[2]

Yager RR. Pythagorean membership grades in multi‐criteria decision making. IEEE Trans Fuzzy Syst. 2014;22:958‐965.

[3]

Yager RR, Abbasov AM. Pythagorean membership grades, complex numbers, and decision making. Int J Intell Syst. 2013;28:436‐452.

[4]

Peng X, Yang Y. Fundamental properties of interval‐valued Pythagorean fuzzy aggregation operators. Int J Intell Syst. 2016;31:444‐487.

Digital Library

[5]

Peng X, Yuan H. Fundamental properties of Pythagorean fuzzy aggregation operators. Fund Inform. 2016;147(4):415‐446.

Digital Library

[6]

Peng X, Yang Y. Some results for Pythagorean fuzzy sets. Int J Intell Syst. 2015;30:1133‐1160.

Digital Library

[7]

Li D., Zeng W. Distance Measure of measure of Pythagorean fuzzy sets. Int J Intell Syst. 2018;32(2):348‐361.

[8]

Liu Y, Qin Y, Han Y. Multiple criteria decision making with probabilities in interval‐valued Pythagorean fuzzy setting. Int J Fuzzy Syst. 2018;20(2):558‐571.

[9]

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

Digital Library

[10]

Garg H. A novel correlation coefficients between Pythagorean fuzzy sets and its applications to decision‐making processes. Int J Intell Syst. 2016;31:1234‐1252.

Digital Library

[11]

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

Digital Library

[12]

Gou X, Xu Z, Ren P. The properties of continuous Pythagorean fuzzy information. Int J Intell Syst. 2016;31:401‐424.

Digital Library

[13]

Peng X, Dai J. 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. 2017;32:1187‐1214.

Digital Library

[14]

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

Digital Library

[15]

Ren P, Xu Z, Gou X. Pythagorean fuzzy TODIM approach to multi‐criteria decision making. Appl Soft Comput. 2016;42:246‐259.

Digital Library

[16]

Wang S, Liu J. Extension of the TODIM method to intuitionistic linguistic multiple attribute decision making. Symmetry. 2017;9:95.

[17]

Wan S‐P, Jin Z, Dong J‐Y. Pythagorean fuzzy mathematical programming method for multi‐attribute group decision making with Pythagorean fuzzy truth degrees. Knowl Inform Syst. 2018;55(2):437‐466.

Digital Library

[18]

Zhang X. Multicriteria Pythagorean fuzzy decision analysis: a hierarchical QUALIFLEX approach with the closeness index‐based ranking methods. Inform Sci. 2016;330:104‐124.

Digital Library

[19]

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

Digital Library

[20]

Du Y, Hou F, Zafar W, Yu Q, Zhai Y. A novel method for multiattribute decision making with interval‐valued Pythagorean fuzzy linguistic information. Int J Intell Syst. 2017;32(10):1085‐1112.

Digital Library

[21]

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

Digital Library

[22]

Garg H. Confidence levels based Pythagorean fuzzy aggregation operators and its application to decision‐making process. Comput Math Organ Theory. 2017;23(4):546‐571.

Digital Library

[23]

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

Digital Library

[24]

Liang W, Zhang X, Liu M. The maximizing deviation method based on interval‐valued Pythagorean fuzzy weighted aggregating operator for multiple criteria group decision analysis. Discr Dyn Nat Soc. 2015;2015:1‐15.

[25]

Liu C, Tang G, Liu P. An approach to multicriteria group decision‐making with unknown weight information based on Pythagorean fuzzy uncertain linguistic aggregation operators. Math Probl Eng. 2017;2017:1‐18.

[26]

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

Digital Library

[27]

Rahman K, Abdullah S, Ahmed R, Ullah M. Pythagorean fuzzy Einstein weighted geometric aggregation operator and their application to multiple attribute group decision making. J Intell Fuzzy Syst. 2017;33:635‐647.

Digital Library

[28]

Wei G, Lu M. Pythagorean fuzzy Maclaurin symmetric mean operators in multiple attribute decision making. Int J Intell Syst. 2018;33(5):1043‐1070.

Digital Library

[29]

Zeng S, Chen J, Li X. A hybrid method for Pythagorean fuzzy multiple‐criteria decision making. Int J Inf Tech Decis Mak. 2015;14:403‐422.

[30]

Herrera F, Martłnez L. An approach for combining linguistic and numerical information based on 2‐tuple fuzzy representation model in decision making. Int J Uncertain Fuzz Knowl‐Based Syst. 2000;8(5):539‐562.

Digital Library

[31]

Herrera F, Martłnez L. A 2‐tuple fuzzy linguistic representation model for computing with words. IEEE Trans Fuzzy Syst. 2000;8(6):746‐752.

Digital Library

[32]

Merig JM, Casanovas M. Decision making with distance measures and linguistic aggregation operators. Int J Fuzzy Syst. 2010;12:190‐198.

[33]

Merig JM, Casanovas M, Martłnez L. Linguistic aggregation operators for linguistic decision making based on the Dempster‐Shafer theory of evidence. Int J Uncertain Fuzziness Knowl‐Based Syst. 2010;18:287‐304.

[34]

Xu Z. Uncertain linguistic aggregation operators based approach to multiple attribute group decision making under uncertain linguistic environment. Inform Sci. 2004;168:171‐184.

Digital Library

[35]

Wang JQ, Li JJ. The multi‐criteria group decision making method based on multi‐granularity intuitionistic two semantics. Sci Technol Inf. 2009;33:8‐9.

[36]

Zhang H. Linguistic intuitionistic fuzzy sets and application in MAGDM. J Appl Math. 2014;2014:1‐11.

[37]

Chen Z, Liu P, Pei Z. An approach to multiple attribute group decision making based on linguistic intuitionistic fuzzy numbers. Int J Comput Int Syst. 2015;8:747‐760.

[38]

Ju YB, Liu XY, Ju DW. Some new intuitionistic linguistic aggregation operators based on Maclaurin symmetric mean and their applications to multiple attribute group decision making. Soft Comput. 2016;20:4521‐4548.

Digital Library

[39]

Liu P. Some geometric aggregation operators based on interval intuitionistic uncertain linguistic variables and their application to group decision making. Appl Math Model. 2013;37(4):2430‐2444.

[40]

Liu P, Jin F. Methods for aggregating intuitionistic uncertain linguistic variables and their application to group decision making. Inform Sci. 2012;205:58‐71.

Digital Library

[41]

Liu P, Rong L, Chu Y, Li Y. Intuitionistic linguistic weighted Bonferroni mean operator and its application to multiple attribute decision making. Sci World J. 2014;2014:545049.

[42]

Liu P, Wang P. Some improved linguistic intuitionistic fuzzy aggregation operators and their applications to multiple‐attribute decision making. Int J Inf Tech Decis Mak. 2017;16:817‐850.

[43]

Zhang HY, Peng HG, Wang J, Wang JQ. An extended outranking approach for multi‐criteria decision‐making problems with linguistic intuitionistic fuzzy numbers. Appl Soft Comput. 2017;59:462‐474.

Digital Library

[44]

Peng X, Yang Y. Multiple attribute group decision making methods based on Pythagorean fuzzy linguistic set. Comput Eng Appl. 2016;52:50‐54.

[45]

Liu P, Li D. Some Muirhead mean operators for intuitionistic fuzzy numbers and their applications to group decision making. PLOS One. 2017;12:e0168767.

[46]

Beg I, Rashid T. An Intuitionistic 2‐tuple linguistic information model and aggregation operators. Int J Intell Syst. 2016;31:569‐592.

Digital Library

[47]

Qin J, Liu X. 2‐tuple linguistic Muirhead mean operators for multiple attribute group decision making and its application to supplier selection. Kybernetes. 2016;45:2‐29.

[48]

Liu PD, Yu XC. 2‐Dimension uncertain linguistic power generalized weighted aggregation operator and its application in multiple attribute group decision making. Knowl‐Based Syst. 2014;57:69‐80.

Digital Library

[49]

Muirhead RF. Some methods applicable to identities and inequalities of symmetric algebraic functions of n letters. Proc Edinburgh Math Soc. 1902;21(3):44‐162.

[50]

Qin J, Liu X. An approach to intuitionistic fuzzy multiple attribute decision making based on Maclaurin symmetric mean operators. J Intell Fuzzy Syst. 2014;27:2177‐2190.

Cited By

Liu QChen X(2024)Evaluating ergonomic requirements of graphical user interfaceApplied Soft Computing10.1016/j.asoc.2024.112465167:PCOnline publication date: 1-Dec-2024
https://dl.acm.org/doi/10.1016/j.asoc.2024.112465
Qi XAli ZMahmood TLiu P(2023)An approach for combining MULTIMOORA method and Muirhead mean operators based on the complex Pythagorean fuzzy uncertain linguistic representation modelApplied Intelligence10.1007/s10489-022-04408-053:14(17561-17592)Online publication date: 7-Jan-2023
https://dl.acm.org/doi/10.1007/s10489-022-04408-0

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Information & Contributors

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Published In

cover image International Journal of Intelligent Systems

International Journal of Intelligent Systems Volume 35, Issue 2

February 2020

118 pages

ISSN:0884-8173

DOI:10.1002/int.v35.2

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© 2019 Wiley Periodicals, Inc.

Publisher

John Wiley and Sons Ltd.

United Kingdom

Publication History

Published: 12 December 2019

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Cited By

Liu QChen X(2024)Evaluating ergonomic requirements of graphical user interfaceApplied Soft Computing10.1016/j.asoc.2024.112465167:PCOnline publication date: 1-Dec-2024
https://dl.acm.org/doi/10.1016/j.asoc.2024.112465
Qi XAli ZMahmood TLiu P(2023)An approach for combining MULTIMOORA method and Muirhead mean operators based on the complex Pythagorean fuzzy uncertain linguistic representation modelApplied Intelligence10.1007/s10489-022-04408-053:14(17561-17592)Online publication date: 7-Jan-2023
https://dl.acm.org/doi/10.1007/s10489-022-04408-0

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