Search Advanced

AIMS Mathematics

2024, Volume 9, Issue 5: 12511-12528. doi: 10.3934/math.2024612
Previous Article Next Article
Research article

Interval-valued Pythagorean fuzzy entropy and its application to multi-criterion group decision-making

  • College of Mathematical Sciences, Bohai University, Jinzhou 121000, China
  • Received: 02 February 2024 Revised: 08 March 2024 Accepted: 20 March 2024 Published: 01 April 2024

  • MSC : 03E72, 03G25, 08A72

  • Entropy is an important tool of information measurement in the fuzzy set and its inference. The research on information measurement based on interval-valued Pythagorean fuzzy sets mostly involves the distance formula for interval-valued Pythagorean fuzzy numbers, but seldom involves the measurement of fuzziness. In view of this situation, we have aimed to propose new interval-valued Pythagorean fuzzy entropy and weighted exponential entropy schemes. Based on the interval-valued Pythagorean fuzzy weighted averaging operator, a strategy based on weighted exponential entropy is proposed to solve the multi-criteria group decision-making (MCGDM) problem in the interval-valued Pythagorean environment. Two examples illustrate that this paper provides a feasible new method to solve the MCGDM problem in an interval-valued Pythagorean fuzzy (IVPF) environment. Finally, by comparing with the existing methods, it is concluded that the entropy measure of IVPF schemes and the corresponding MCGDM method can select the optimal solution of the practical problem more precisely and accurately. Therefore, the comparative analysis shows that the proposed measurement method has the characteristics of flexibility and universality.

    Citation: Li Li, Mengjing Hao. Interval-valued Pythagorean fuzzy entropy and its application to multi-criterion group decision-making[J]. AIMS Mathematics, 2024, 9(5): 12511-12528. doi: 10.3934/math.2024612

    Related Papers:

  • Entropy is an important tool of information measurement in the fuzzy set and its inference. The research on information measurement based on interval-valued Pythagorean fuzzy sets mostly involves the distance formula for interval-valued Pythagorean fuzzy numbers, but seldom involves the measurement of fuzziness. In view of this situation, we have aimed to propose new interval-valued Pythagorean fuzzy entropy and weighted exponential entropy schemes. Based on the interval-valued Pythagorean fuzzy weighted averaging operator, a strategy based on weighted exponential entropy is proposed to solve the multi-criteria group decision-making (MCGDM) problem in the interval-valued Pythagorean environment. Two examples illustrate that this paper provides a feasible new method to solve the MCGDM problem in an interval-valued Pythagorean fuzzy (IVPF) environment. Finally, by comparing with the existing methods, it is concluded that the entropy measure of IVPF schemes and the corresponding MCGDM method can select the optimal solution of the practical problem more precisely and accurately. Therefore, the comparative analysis shows that the proposed measurement method has the characteristics of flexibility and universality.


    加载中


    [1] L. A. Zadeh, Fuzzy sets, Inform. Control, 8 (1965), 338–353.
    [2] K. T. Atanassov, Intuitionistic fuzzy sets, Fuzzy Sets Syst., 20 (1986), 87–96.
    [3] K. T. Atanassov, Intuitionistic Fuzzy Sets: Theory and Applications, Heidelberg: Physica-Verlag, 1999.
    [4] Z. S. Xu, Intuitionistic fuzzy aggregation operators, IEEE T. Fuzzy Syst., 15 (2007), 1179–1187. https://doi.org/10.1109/TFUZZ.2006.890678 doi: 10.1109/TFUZZ.2006.890678
    [5] Z. S. Xu, Intuitionistic Fuzzy Information Aggregation, Beijing: Science Press, 2008.
    [6] K. T. Atanassov, On Intuitionistic Fuzzy Sets Theory, Berlin: Springer, 2012.
    [7] Y. J. Lei, Intuitionistic Fuzzy Set Theory and Its Application, Beijing: Science Press, 2014.
    [8] X. N. Li, H. J. Yi, Intuitionistic fuzzy matroids, J. Intell. Fuzzy Syst., 33 (2017), 3653–3663.
    [9] E. B. Jamkhaneh, H. Garg, Some new operations over the generalized intuitionistic fuzzy sets and their application to decision-making process, Granul. Comput., 3 (2018), 111–122. https://doi.org/10.1007/s41066-017-0059-0 doi: 10.1007/s41066-017-0059-0
    [10] R. R. Yager, Pythagorean fuzzy subsets, In: IEEE Joint IFSA World Congress and NAFIPS Annual Meeting (IFSA/NAFIPS), 2013, 57–61. https://doi.org/10.1109/IFSA-NAFIPS.2013.6608375
    [11] R. R. Yager, Pythagorean membership grades in multicriteria decision making, IEEE T. Fuzzy Syst., 22 (2014), 958–965. https://doi.org/10.1109/TFUZZ.2013.2278989 doi: 10.1109/TFUZZ.2013.2278989
    [12] W. F. Liu, X. He, Pythagorean hesitant fuzzy set, in Chinese, Fuzzy Syst. Math., 30 (2016), 108–113.
    [13] X. D. Peng, Y. Yang, J. P. Song, Pythagorean fuzzy soft set and its application, Comput. Eng., 41 (2015), 225–229.
    [14] X. L. Zhang, Z. S. Xu, Extension of TOPSIS to multi-criteria decision making with Pythagorean fuzzy sets, Int. J. Intell. Syst., 29 (2014), 1061–1078. https://doi.org/10.1002/int.21676 doi: 10.1002/int.21676
    [15] X. He, Y. X. Du, W. F. Liu, Pythagorean fuzzy power average operators, in Chinese, Fuzzy Syst. Math., 30 (2016), 117–126.
    [16] X. L. Zhang, A novel approach based on similarity measure for Pythagorean fuzzy multiple criteria group decision, Int. J. Intell. Syst., 31 (2016), 593–611. https://doi.org/10.1002/int.21796 doi: 10.1002/int.21796
    [17] G. W. Wei, Pythagorean fuzzy interaction aggregation operators and their applications to multiple attribute decision making, J. Intell. Fuzzy Syst., 33 (2017), 2119–2132.
    [18] W. F. Liu, Y. X. Du, J. Chang, Pythagorean fuzzy interaction aggregation operators and applications in decision making, Control Decis., 32 (2017), 1034–1040.
    [19] G. W. Wei, M. Lu, Pythagorean fuzzy power aggregation operators in multiple attribute decision making, Int. J. Intell. Syst., 33 (2018), 169–186. https://doi.org/10.1002/int.21946 doi: 10.1002/int.21946
    [20] H. Ding, Y. L. Li, Multiple attribute group decision making method based on Pythagorean fuzzy power weighted average operator, Comput. Eng. Appl., 54 (2018), 1–6.
    [21] X. D. Peng, Y. Yang, Fundamental properties of interval-valued Pythagorean fuzzy aggregation operator, Int. J. Intell. Syst., 31 (2016), 444–487. https://doi.org/10.1002/int.21790 doi: 10.1002/int.21790
    [22] G. W. Wei, M. Lu, Pythagorean fuzzy maclaurin symmetric mean operators in multiple attribute decision making, Int. J. Intell. Syst., 33 (2016), 1043–1070. https://doi.org/10.1002/int.21911 doi: 10.1002/int.21911
    [23] Y. Q. Du, F. J. Hou, R. W. Zafar, Q. Yu, Y. Zhai, A novel method for multi-attribute decision making with interval-valued Pythagorean fuzzy linguistic information, Int. J. Intell. Syst., 32 (2017), 1085–1112. https://doi.org/10.1002/int.21881 doi: 10.1002/int.21881
    [24] A. Zadeh, Fuzzy sets and systems, In: Proceedings of the Symposium on Systems Theory. New York Polytechnic Institute of Brooklyn, 1965, 29–37.
    [25] Q. S. Zhang, S. Y. Jiang, B. G. Jia, S. H. Luo, Some information measures for interval-valued intuitionistic fuzzy sets, Int. J. Inform. Sci., 180 (2010), 5130–5145. https://doi.org/10.1016/j.ins.2010.08.038 doi: 10.1016/j.ins.2010.08.038
    [26] Q. Q. Sun, X. N. Li, Information measures of interval valued Pythagorean fuzzy sets and their applications, in Chinese, J. Shandong Uni. (Natural Science), 54 (2019), 43–53.
    [27] X. D. Peng, H. Y. Yuan, Y. Yang, Pythagorean fuzzy information measures and their applications, Int. J. Intell. Syst., 32 (2017), 991–1029. https://doi.org/10.1002/int.21880 doi: 10.1002/int.21880
    [28] Y. Xu, A two-stage multi-criteria decision-making method with interval-valued q-Rung Orthopair fuzzy technology for selecting bike-sharing recycling supplier, Eng. Appl. Artific. Intell., 119 (2023), 105827. https://doi.org/10.1016/j.engappai.2023.105827 doi: 10.1016/j.engappai.2023.105827
    [29] A. R. Mishra, P. Rani, A. F. Alrasheedi, R. Dwivedi, Evaluating the blockchain-based healthcare supply chain using interval-valued Pythagorean fuzzy entropy-based decision support system, Eng. Appl. Artific. Intell., 126 (2023), 107112. https://doi.org/10.1016/j.engappai.2023.107112 doi: 10.1016/j.engappai.2023.107112
    [30] Y. Bengio, A. Courville, P. Vincent, Representation learning: a review and new perspectives, IEEE T. Pattern Anal. Mach. Intell., 35 (2013), 1798–1828. https://doi.org/10.1109/TPAMI.2013.50 doi: 10.1109/TPAMI.2013.50
    [31] H. Garg, A novel accuracy function under interval-valued Pythagorean fuzzy environment for solving multi-criteria decision making problem, Int. J. Intell. Syst., 31 (2016), 529–540.
    [32] N. R. Pal, S. K. Pal, Entropy, a new definition and its applications, IEEE T. Syst. Man Cybernet, 21 (1991), 1260–1270. https://doi.org/10.1109/21.120079 doi: 10.1109/21.120079
    [33] Z. Wang, K. W. Li, W. Wang, An approach to multiattribute decision making with interval-valued intuitionistic fuzzy assessments and incomplete weights, Inform. Sci., 179 (2016), 3026–3040. https://doi.org/10.1016/j.ins.2009.05.001 doi: 10.1016/j.ins.2009.05.001
    [34] J. Ye, Fuzzy cross entropy of interval-valued intuitionistic fuzzy sets and its optimal decision-making method based on the weights of alternatives, Expert Syst. Appl., 38 (2011), 6179–6183. https://doi.org/10.1016/j.eswa.2010.11.052 doi: 10.1016/j.eswa.2010.11.052
    [35] M. Dugenci, A new distance measure for interval valued intuitionistic fuzzy sets and its application to group decision making problems with incomplete weights information, Appl. Soft Comput., 41 (2016), 120–134. https://doi.org/10.1016/j.asoc.2015.12.026 doi: 10.1016/j.asoc.2015.12.026
    [36] J. H. Park, Y. Park, Y. Kwun, X. Tan, Extension of the TOPSIS method for decision making problems under interval-valued intuitionistic fuzzy environment, Appl. Math. Model., 35 (2011), 2544–2556. https://doi.org/10.1016/j.apm.2010.11.025 doi: 10.1016/j.apm.2010.11.025
  • Reader Comments
  • © 2024 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
通讯作者: 陈斌, bchen63@163.com
  • 1. 

    沈阳化工大学材料科学与工程学院 沈阳 110142

  1. 本站搜索
  2. 百度学术搜索
  3. 万方数据库搜索
  4. CNKI搜索
AIMS Mathematics
1.8 3.4

Metrics

Article views(241) PDF downloads(28) Cited by(0)

Preview PDF
Download XML
Export Citation
Article outline

Figures and Tables

Tables(12)

Other Articles By Authors

Related pages

Tools

/

DownLoad:  Full-Size Img  PowerPoint
Return
Return

Catalog