research-article

A Novel Method for Multiattribute Decision Making with Interval‐Valued Pythagorean Fuzzy Linguistic Information

Authors:

Yubing ZhaiAuthors Info & Claims

International Journal of Intelligent Systems, Volume 32, Issue 10

Pages 1085 - 1112

https://doi.org/10.1002/int.21881

Published: 03 August 2017 Publication History

Abstract

Pythagorean fuzzy set (PFS), proposed by Yager (2013), is a generalization of the notion of Atanassov's intuitionistic fuzzy set, which has received more and more attention. In this paper, first, we define the weighted Minkowski distance with interval‐valued PFSs. Second, inspired by the idea of the Pythagorean fuzzy linguistic variables, we define a new fuzzy variable called interval‐valued Pythagorean fuzzy linguistic variable set (IVPFLVS), and the operational laws, score function, accuracy function, comparison rules, and distance measures of the IVPFLVS are defined. Third, some aggregation operators are presented for aggregating the interval‐valued Pythagorean fuzzy linguistic information such as the interval‐valued Pythagorean fuzzy linguistic weighted averaging (IVPFLWA), interval‐valued Pythagorean fuzzy linguistic ordered weighted averaging (IVPFLOWA), interval‐valued Pythagorean fuzzy linguistic hybrid averaging, and generalized interval‐valued Pythagorean fuzzy linguistic ordered weighted average operators. Fourth, some desirable properties of the IVPFLWA and IVPFLOWA operators, such as monotonicity, commutativity, and idempotency, are discussed. Finally, based on the IVPFLWA or interval‐valued Pythagorean fuzzy linguistic geometric weighted operator, a practical example is provided to illustrate the application of the proposed approach and demonstrate its practicality and effectiveness.

References

References

[1]

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

[2]

Atanassov K, Gargov G. Interval valued intuitionistic fuzzy sets. Fuzzy Sets Syst 1989;31(3):343–349.

Digital Library

[3]

Guo S, Yin W, Guo S, Yin W. Multiple attribute decision making method based on 2‐type intuitionistic fuzzy Information. Fuzzy Syst Math 2013;27(3):128–133.

[4]

Liu PD. Some geometric aggregation operators based on interval intuitionistic uncertain linguistic variables and their application to group decision making. Appl Math Modell 2013;37:2430–2444.

[5]

Zhu B, Xu ZS, Xia MM. Dual hesitant fuzzy sets. J Appl Math 2012;11:2607–2645.

[6]

Liu XY, Ju YB Yang SH. Hesitant intuitionistic fuzzy linguistic aggregation operators and their applications to multiple attribute decision making. J Intell Fuzzy Syst 2014;27:1187–1201.

Digital Library

[7]

Xu ZS, Yager RR. Some geometric aggregation operators based on intuitionistic fuzzy sets. Int J Gen Syst 2006;35(4):417–433.

[8]

Xia M, Xu Z, Zhu B. Some issues on intuitionistic fuzzy aggregation operators based on Archimedean t‐conorm and t‐norm. Knowl‐Based Syst 2012;31(7):78–88.

Digital Library

[9]

Wan SP, Li DF. Fuzzy mathematical programming approach to heterogeneous multi‐attribute decision‐making with interval‐valued intuitionistic fuzzy truth degrees. Inf Sci 2015;325:484–503.

Digital Library

[10]

Hung WL, Yang MS. On similarity measures between intuitionistic fuzzy sets. Int J Intell Syst 2008;23(3):364–383.

Digital Library

[11]

Xu ZS, Da QL. An overview of operators for aggregating information. Int J Intell Syst 2003;18(9):953–969.

[12]

Xu ZS, Cai XQ. Nonlinear optimization models for multiple attribute group decision making with intuitionistic fuzzy information. Int J Intell Syst 2010, 25(6):489–513.

Digital Library

[13]

Ju YB, Liu XY, Yang SH. Interval‐valued dual hesitant fuzzy aggregation operators and their applications to multiple attribute decision making. J Intell Fuzzy Syst 2014;27(3):1203–1218.

Digital Library

[14]

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

Digital Library

[15]

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

Digital Library

[16]

Wei GW, Zhao XF, Lin R. Some induced aggregating operators with fuzzy number intuitionistic fuzzy information and their applications to group decision making. Int J Comput Intell Syst 2010;3(1):84–95.

[17]

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

[18]

Yager RR. Pythagorean membership grades in multicriteria decision making. IEEE Trans Fuzzy Syst 2014;22(4):958–965.

[19]

Yager RR, Abbasov AM. Pythagorean membership grades, complex numbers, and decision making. Int J Intell Syst 2013;28(5):436–452.

[20]

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

[21]

Zhang XL, Xu ZS. Extension of TOPSIS to multiple criteria decision making with Pythagorean fuzzy sets. Int J Intell Syst 2014;29(12):1061–1078.

Digital Library

[22]

Peng XD, Yang Y. Some results for Pythagorean fuzzy sets. Int J Intell Syst 2015;30(11):1133–1160.

Digital Library

[23]

Gou X, Xu Z, Ren P. The properties of continuous Pythagorean fuzzy information. Int J Intell Syst 2016;31(5):401–424.

Digital Library

[24]

Peng XD, Yang Y. Fundamental properties of interval‐valued Pythagorean fuzzy aggregation operators. Int J Intell Syst 2015;31(5):444–487.

[25]

Liang W, Zhang XL, Liu MF. 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. https://doi.org/10.1155/2015/746572

[26]

Xu ZS and Xia MM. Distance and similarity measures for hesitant fuzzy sets. Inf Sci 2011;181(11):2128–2138.

Digital Library

[27]

Rodriguez R M, Martinez L, Herrera F. Hesitant fuzzy linguistic term sets for decision making. IEEE Trans Fuzzy Syst 2012;20(1):109–119.

[28]

Wei GW. Some generalized aggregating operators with linguistic information and their application to multiple attribute group decision making. Comput Ind Eng 2011;61(1):32–38.

Digital Library

[29]

RodríGuez RM, Martı Nez L, Herrera F. A group decision making model dealing with comparative linguistic expressions based on hesitant fuzzy linguistic term sets. Inf Sci 2013;241:28–42.

Digital Library

[30]

Xu ZS. A method for multiple attribute decision making with incomplete weight information in linguistic setting. Knowl‐Based Syst 2007;20(8):719–725.

Digital Library

[31]

Wang JQ, Li JJ. The multi‐criteria group decision making method based on multi‐granularity intuitionistic two semantics. Sci Tech Inf 2009;33(1):8–9.

[32]

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

[33]

Peng XD, Yang Y. Multiple attribute group decision making methods based on Pythagorean fuzzy linguistic set. Comput Eng Appl 2016; 52(23):50–55.

[34]

Herrera F, Herrera‐Viedma E. Linguistic decision analysis: steps for solving decision problems under linguistic information. Fuzzy Sets Syst 2000;115(1):67–82

Digital Library

[35]

Herrera F, Herrera‐Viedma E, Verdegay JL. A model of consensus in group decision making under linguistic assessments. Fuzzy Sets Syst 1996;79(1):73–87.

Digital Library

[36]

Liu PD, Wang YM. Multiple attribute group decision making methods based on intuitionistic linguistic power generalized aggregation operators. Appl Soft Comput 2015;29(5):2235–2246.

[37]

Xu ZS, Xia MM. Induced generalized intuitionistic fuzzy operators. Knowl‐Based Syst 2011;24(2):197–209.

Digital Library

[38]

Yager RR. Families of OWA operators. Fuzzy Sets Syst 1993;59(2):125–148.

Digital Library

[39]

Xu ZS, Da QL. The ordered weighted geometric averaging operators. Int J Intell Syst 2002; 17(7):709–716.

[40]

Ju YB, Yang SH. A new method for multiple attribute group decision‐making with intuitionistic trapezoid fuzzy linguistic information. Soft Comput 2015; 19(8):2211–2224.

Digital Library

[41]

Xu ZS. On consistency of the weighted geometric mean complex judgment matrix in AHP. Eur J Oper Res 2000;126(3):683–687.

Cited By

Rehman UMahmood T(2024)Prioritization of types of wireless sensor networks by applying decision-making technique based on bipolar complex fuzzy linguistic heronian mean operatorsJournal of Intelligent & Fuzzy Systems: Applications in Engineering and Technology10.3233/JIFS-23216746:1(967-990)Online publication date: 1-Jan-2024
https://dl.acm.org/doi/10.3233/JIFS-232167
Ali JAli JNaeem MMahmood W(2023)Generalized q-rung picture linguistic aggregation operators and their application in decision makingJournal of Intelligent & Fuzzy Systems: Applications in Engineering and Technology10.3233/JIFS-22229244:3(4419-4443)Online publication date: 1-Jan-2023
https://dl.acm.org/doi/10.3233/JIFS-222292
Işık GKaya İ(2022)A new integrated methodology for constructing linguistic pythagorean fuzzy statements for decision making problemsJournal of Intelligent & Fuzzy Systems: Applications in Engineering and Technology10.3233/JIFS-21338443:4(4883-4894)Online publication date: 1-Jan-2022
https://dl.acm.org/doi/10.3233/JIFS-213384
Show More Cited By

Recommendations

Multiattribute decision making based on interval-valued intuitionistic fuzzy values

In this paper, we present a new multiattribute decision making method based on the proposed interval-valued intuitionistic fuzzy weighted average operator and the proposed fuzzy ranking method for intuitionistic fuzzy values. First, we briefly review ...
Group decision making based on a novel aggregation operator under linguistic interval-valued Atanassov intuitionistic fuzzy information
Abstract
Efficient aggregation methods and order relationships are crucial in solving group decision making (GDM) problems with linguistic interval-valued Atanassov intuitionistic fuzzy information. Based on a novel score function, this paper first ...
Group decision making based on improved linguistic interval-valued Atanassov intuitionistic fuzzy weighted averaging aggregation operator of linguistic interval-valued Atanassov intuitionistic fuzzy numbers
Abstract
In this paper, we develop an improved linguistic interval-valued Atanassov intuitionistic fuzzy weighted averaging (ILIVAIFWA) aggregation operator (AO) of linguistic interval-valued Atanassov intuitionistic fuzzy numbers (LIVAIFNs). ...

Comments

Please enable JavaScript to view thecomments powered by Disqus.

Information & Contributors

Information

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

Issue’s Table of Contents

© 2017 Wiley Periodicals, Inc.

Publisher

John Wiley and Sons Ltd.

United Kingdom

Publication History

Published: 03 August 2017

Qualifiers

Research-article

Contributors

Other Metrics

View Article Metrics

Bibliometrics & Citations

Bibliometrics

Article Metrics

18
Total Citations
View Citations
0
Total Downloads

Downloads (Last 12 months)0
Downloads (Last 6 weeks)0

Reflects downloads up to 27 Feb 2025

Other Metrics

View Author Metrics

Citations

Cited By

Rehman UMahmood T(2024)Prioritization of types of wireless sensor networks by applying decision-making technique based on bipolar complex fuzzy linguistic heronian mean operatorsJournal of Intelligent & Fuzzy Systems: Applications in Engineering and Technology10.3233/JIFS-23216746:1(967-990)Online publication date: 1-Jan-2024
https://dl.acm.org/doi/10.3233/JIFS-232167
Ali JAli JNaeem MMahmood W(2023)Generalized q-rung picture linguistic aggregation operators and their application in decision makingJournal of Intelligent & Fuzzy Systems: Applications in Engineering and Technology10.3233/JIFS-22229244:3(4419-4443)Online publication date: 1-Jan-2023
https://dl.acm.org/doi/10.3233/JIFS-222292
Işık GKaya İ(2022)A new integrated methodology for constructing linguistic pythagorean fuzzy statements for decision making problemsJournal of Intelligent & Fuzzy Systems: Applications in Engineering and Technology10.3233/JIFS-21338443:4(4883-4894)Online publication date: 1-Jan-2022
https://dl.acm.org/doi/10.3233/JIFS-213384
Ejegwa PFeng YTang SAgbetayo JDai X(2022)New Pythagorean fuzzy-based distance operators and their applications in pattern classification and disease diagnostic analysisNeural Computing and Applications10.1007/s00521-022-07679-335:14(10083-10095)Online publication date: 24-Aug-2022
https://dl.acm.org/doi/10.1007/s00521-022-07679-3
Arora HNaithani A(2022)Performance of exponential similarity measures in supply of commodities in containment zones during COVID‐19 pandemic under Pythagorean fuzzy setsInternational Journal of Intelligent Systems10.1002/int.2306437:12(11815-11829)Online publication date: 29-Dec-2022
https://dl.acm.org/doi/10.1002/int.23064
Lv WZeng SZhou JLi TKoe A(2022)Interval‐valued Pythagorean fuzzy linguistic KPCA model based on TOPSIS and its application for emergency group decision makingInternational Journal of Intelligent Systems10.1002/int.2284937:9(6415-6437)Online publication date: 30-Jul-2022
https://dl.acm.org/doi/10.1002/int.22849
Xian SWan WYang Z(2020)Interval‐valued Pythagorean fuzzy linguistic TODIM based on PCA and its application for emergency decisionInternational Journal of Intelligent Systems10.1002/int.2228435:12(2049-2086)Online publication date: 20-Oct-2020
https://dl.acm.org/doi/10.1002/int.22284
Liu YLiu JQin Y(2019)Pythagorean fuzzy linguistic Muirhead mean operators and their applications to multiattribute decision‐makingInternational Journal of Intelligent Systems10.1002/int.2221235:2(300-332)Online publication date: 12-Dec-2019
https://dl.acm.org/doi/10.1002/int.22212
Wang LLi N(2019)Pythagorean fuzzy interaction power Bonferroni mean aggregation operators in multiple attribute decision makingInternational Journal of Intelligent Systems10.1002/int.2220435:1(150-183)Online publication date: 20-Nov-2019
https://dl.acm.org/doi/10.1002/int.22204
Jana CMuhiuddin GPal M(2019)Some Dombi aggregation of Q‐rung orthopair fuzzy numbers in multiple‐attribute decision makingInternational Journal of Intelligent Systems10.1002/int.2219134:12(3220-3240)Online publication date: 18-Oct-2019
https://dl.acm.org/doi/10.1002/int.22191
Show More Cited By

View Options

View options

Figures

Tables

Media

View Issue’s Table of Contents