research-article

Pythagorean Fuzzy Information Measures and Their Applications

Authors:

Yong YangAuthors Info & Claims

International Journal of Intelligent Systems, Volume 32, Issue 10

Pages 991 - 1029

https://doi.org/10.1002/int.21880

Published: 03 August 2017 Publication History

Abstract

Pythagorean fuzzy set (PFS), originally proposed by Yager, is more capable than intuitionistic fuzzy set (IFS) to handle vagueness in the real world. The main purpose of this paper is to investigate the relationship between the distance measure, the similarity measure, the entropy, and the inclusion measure for PFSs. The primary goal of the study is to suggest the systematic transformation of information measures (distance measure, similarity measure, entropy, inclusion measure) for PFSs. For achieving this goal, some new formulae for information measures of PFSs are introduced. To show the efficiency of the proposed similarity measure, we apply it to pattern recognition, clustering analysis, and medical diagnosis. Some illustrative examples are given to support the findings and also demonstrate their practicality and effectiveness of similarity measure between PFSs.

References

[1]

Atanassov KT. Intuitionistic fuzzy sets. Fuzzy Sets Syst 1986;20:87–96.

[2]

Zadeh LA. Fuzzy sets. Inf Control 1965;8:338–356.

[3]

Xu ZS, Intuitionistic fuzzy aggregation operators. IEEE Trans Fuzzy Syst 2007;15:1179–1187.

Digital Library

[4]

Xu ZS, Xia MM. Induced generalized intuitionistic fuzzy operators. Knowl‐Based Syst 2011;24:197–209.

Digital Library

[5]

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

[6]

Xu ZS, Yager RR. Dynamic intuitionistic fuzzy multiple attribute decision making. Int J Approx Reason 2008;48:246–262.

Digital Library

[7]

Xu ZS. Choquet integrals of weighted intuitionistic fuzzy information. Inf Sci 2010;180:726–736.

Digital Library

[8]

Xu ZS. Approaches to multiple attribute group decision making based on intuitionistic fuzzy power aggregation operators. Knowl‐Based Syst 2011;24:749–760.

Digital Library

[9]

Xu ZS, Cai XQ. Recent advances in intuitionistic fuzzy information aggregation. Fuzzy Optim Decis Making 2010;9:359–381.

Digital Library

[10]

Zhao H, Xu ZS, Ni MF, Liu SS. Generalized aggregation operators for intuitionistic fuzzy sets. Int J Intell Syst 2010;25:1–30.

[11]

Yager RR. Pythagorean fuzzy subsets. In: Proc Joint IFSA World Congress and NAFIPS Annual Meeting, Edmonton, Canada; 2013. pp 57–61.

[12]

Yager RR, Abbasov AM. Pythagorean membership grades, complex numbers, and decision making. Int J Intell Syst 2014;28:436–452.

[13]

Hadi‐Vencheh A, Mirjaberi M. Fuzzy inferior ratio method for multiple attribute decision making problems. Inf Sci 2014;277:263–272.

[14]

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

Digital Library

[15]

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

[16]

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

Digital Library

[17]

Li Y, Olson DL, Qin Z. Similarity measures between intuitionistic fuzzy (vague) sets: a comparative analysis. Pattern Recognit Lett 2007;28:278–285.

Digital Library

[18]

Zadeh LA. The concept of a linguistic variable and its application to approximate reasoning I. Inf Sci 1975;8:199–249.

[19]

Zadeh LA. The concept of a linguistic variable and its application to approximate reasoning II. Inf Sci 1975;8:301–357.

[20]

Zadeh LA. The concept of a linguistic variable and its application to approximate reasoning III. Inf Sci 1975;9:43–80.

[21]

Peng XD, Yang Y, Song JP, Jiang Y. Pythagorean fuzzy soft set and its application. Comput Eng 2015;41:224–229.

[22]

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

[23]

Gou XJ, Xu ZS, Ren PJ. The properties of continuous Pythagorean fuzzy information. Int J Intell Syst 2016;31:401–424.

Digital Library

[24]

Zhang XL. 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

[25]

Peng XD, 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

[26]

Reformat MZ, Yager RR. Suggesting recommendations using Pythagorean fuzzy sets illustrated using Netflix movie data. In: Information Processing and Management of Uncertainty in Knowledge‐Based Systems, Montpellier, France; 2014. pp 546–556.

[27]

Peng XD, Yuan HY. Fundamental properties of Pythagorean fuzzy aggregation operators. Fund Inform 2016;147:415–446.

Digital Library

[28]

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

[29]

Ren PJ, Xu ZS, Gou XJ. Pythagorean fuzzy TODIM approach to multi‐criteria decision making. Appl Soft Comput 2016;42:246–259.

Digital Library

[30]

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

Digital Library

[31]

Boran FE, Akay D. A biparametric similarity measure on intuitionistic fuzzy sets with applications to pattern recognition. Inf Sci 2014;255:45–57.

Digital Library

[32]

Chen SM. Similarity measures between vague sets and between elements. IEEE Trans Syst Man Cyber 1997;27:153–158.

Digital Library

[33]

Chen SM, Chang CH. A novel similarity measure between Atanssov's intuitionistic fuzzy sets based on transformation techniques with applications to pattern recognition. Inf Sci 2015;291:96–114.

Digital Library

[34]

De SK, Biswas R, Roy AR. An application of intuitionistic fuzzy sets in medical diagnosis. Fuzzy Sets Syst 2001;117:209–213.

[35]

Deng GN, Jiang YL, Fu JC. Monotonic similarity measures between intuitionistic fuzzy sets and their relationship with entropy and inclusion measure. Inf Sci 2015;316:348–369.

Digital Library

[36]

Du WS, Hu BQ. Aggregation distance measure and its induced similarity measure between intuitionistic fuzzy sets. Pattern Recognit Lett 2015;60:65–71.

[37]

Guo KH, Song Q. On the entropy for Atanassov's intuitionistic fuzzy sets: An interpretation from the perspective of amount of knowledge. Appl Soft Comput 2014;24:328–340.

Digital Library

[38]

Hung KC, Wang PK. An integrated intuitionistic fuzzy similarity measures for medical problems. Int J Comput Intell Syst 2014;7:327–343.

[39]

Hung WL, Yang MS. Similarity measures of intuitionistic fuzzy sets based on Hausdorff distance. Pattern Recognit Lett 2004;25:1603–1611.

Digital Library

[40]

Hwang CM, Yang MS, Hung WL, Lee MG. A similarity measure of intuitionistic fuzzy sets based on the Sugeno integral with its application to pattern recognition. Inf Sci 2012;189:93–109.

Digital Library

[41]

Hong DH, Kim C. A note on similarity measures between vague sets and between elements. Inf Sci 1999;115:83–96.

[42]

Li DF, Cheng CT. New similarity measures of intuitionistic fuzzy sets and application to pattern recognitions. Pattern Recognit Lett 2002;23:221–225.

Digital Library

[43]

Li F, Xu ZY. Measures of similarity between vague sets. J Softw 2001;12:922–927.

[44]

Li JQ, Deng GN, Li HX, Zeng WY. The relationship between similarity measure and entropy of intuitionistic fuzzy sets. Inf Sci 2012;188:314–321.

Digital Library

[45]

Liang X, Wei CP, Xia MM. New entropy, similarity measure of intuitionistic fuzzy sets and their applications in group decision making. Int J Comput Intell Syst 2013;6:987–1001.

[46]

Liang ZZ, Shi PF. Similarity measures on intuitionistic fuzzy sets. Pattern Recognit Lett 2003;24:2687–2693.

Digital Library

[47]

Mitchell HB. On the Dengfeng–Chuntian similarity measure and its application to pattern recognition. Pattern Recognit Lett 2003;24:3101–3104.

Digital Library

[48]

Own CM. Switching between type‐2 fuzzy sets and intuitionistic fuzzy sets: a application in medical diagnosis. Appl Intell 2009;31:283–291.

Digital Library

[49]

Papakostas GA, Hatzimichailidis AG, Kaburlasos VG. Distance and similarity measures between intuitionistic fuzzy sets: a comparative analysis from a pattern recognition point of view. Pattern Recognit Lett 2014;34:1609–1622.

[50]

Peng XD, Yang Y, Zhu YL. Similarity measure and its application based on multi‐parametric intuitionistic fuzzy sets. Comput Eng Appl 2015;51:122–125.

[51]

Szmidt E, Kacprzyk J. Entropy for intuitionistic fuzzy sets. Fuzzy Sets Syst 2001;118:467–477.

Digital Library

[52]

Szmidt E, Kacprzyk J. A similarity measure for intuitionistic fuzzy sets and its application in supporting medical diagnostic reasoning. In: International Conference Artificial Intelligence and Soft Computing, Zakopane, Poland; 2004. pp. 388–393.

[53]

Szmidt E, Kacprzyk J. Intuitionistic fuzzy sets in intelligent data analysis for medical diagnosis. In: International Conference Computational Science, San Francisco, CA; 2001. pp. 263–271.

[54]

Vlachos IK, Sergiadis GD. Intuitionistic fuzzy information–applications to pattern recognition. Pattern Recognit Lett 2007;28:197–206.

Digital Library

[55]

Wei CP, Wang P, Zhang YZ. Entropy, similarity measure of interval‐valued intuitionistic fuzzy sets and their applications. Inf Sci 2011;181:4273–4286.

Digital Library

[56]

Xia MM, Xu ZS. Entropy/cross entropy‐based group decision making under intuitionistic fuzzy environment. Inf Fusion 2012;13:31–47.

Digital Library

[57]

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

Digital Library

[58]

Ye J. Cosine similarity measures for intuitionistic fuzzy sets and their applications. Math Comput Model 2011;53:91–97.

Digital Library

[59]

Xu ZS, Chen J, Wu JJ. Clustering algorithm for intuitionistic fuzzy sets. Inf Sci 2008;178:3775–3790.

Digital Library

[60]

Zhang HM, Xu ZS, Chen Q. On clustering approach to intuitionistic fuzzy sets. Control Decis 2007;22:882–888.

[61]

Molodtsov D. Soft set theory—first results. Comput Math Appl 1999;37:19–31.

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Published In

cover image International Journal of Intelligent Systems

International Journal of Intelligent Systems Volume 32, Issue 10

October 2017

124 pages

ISSN:0884-8173

DOI:10.1002/int.2017.32.issue-10

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© 2017 Wiley Periodicals, Inc.

Publisher

John Wiley and Sons Ltd.

United Kingdom

Publication History

Published: 03 August 2017

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https://dl.acm.org/doi/10.1016/j.eswa.2024.124135
Jin FZheng XLiu JZhou LChen H(2024)Group consensus reaching process based on information measures with probabilistic linguistic preference relationsExpert Systems with Applications: An International Journal10.1016/j.eswa.2024.123573249:PAOnline publication date: 1-Sep-2024
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Meng ZLin RWu B(2024)Multi-criteria group decision making based on graph neural networks in Pythagorean fuzzy environmentExpert Systems with Applications: An International Journal10.1016/j.eswa.2023.122803242:COnline publication date: 16-May-2024
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Sun GWang M(2024)Pythagorean fuzzy information processing based on centroid distance measure and its applicationsExpert Systems with Applications: An International Journal10.1016/j.eswa.2023.121295236:COnline publication date: 1-Feb-2024
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Mao KWang YYe JZhou WLin YFang B(2024)Belief structure-based Pythagorean fuzzy entropy and its application in multi-source information fusionApplied Soft Computing10.1016/j.asoc.2023.110860148:COnline publication date: 27-Feb-2024
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Garg HÜnver MAydoğan BOlgun M(2023)An extended TOPSIS and entropy measure based on Sugeno integral in Pythagorean fuzzy set settingJournal of Intelligent & Fuzzy Systems: Applications in Engineering and Technology10.3233/JIFS-23145445:2(2537-2549)Online publication date: 1-Jan-2023
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