Search Advanced

AIMS Mathematics

2020, Volume 5, Issue 2: 1050-1061. doi: 10.3934/math.2020073
Previous Article Next Article
Research article

A novel entropy measure of Pythagorean fuzzy soft sets

  • 1.
    Department of Mathematics, National Institute of Technology Calicut-673 601, India
  • 2.
    School of Mathematics, Thapar Institute of Engineering & Technology, Deemed University Patiala, Punjab, India
  • Received: 16 October 2019 Accepted: 19 December 2019 Published: 10 January 2020

  • MSC : 03E72, 62A86, 68T35, 90B50

  • Pythagorean fuzzy soft set (PFSS) is one of the useful extension of the Pythagorean fuzzy set (PFS) to deal with the vagueness and uncertainties in the data. The major advantages of PFSS over the other existing sets are to consider the parameterized tool of the family of PFS. Keeping this advantage, in this paper we define some new entropy measures for PFSS to compute the degree of fuzziness of the set. The axiomatic definition and their validity are stated. The larger the entropy, the lesser the vagueness and so, the decision making based on entropy is a useful one. Further, a decisionmaking algorithm is explored to solve the decision-making problem under the PFSS environment. A numerical example is given to validate the method and compare their performance with the existing intuitionistic fuzzy soft set entropy measures.

    Citation: T. M. Athira, Sunil Jacob John, Harish Garg. A novel entropy measure of Pythagorean fuzzy soft sets[J]. AIMS Mathematics, 2020, 5(2): 1050-1061. doi: 10.3934/math.2020073

    Related Papers:

  • Pythagorean fuzzy soft set (PFSS) is one of the useful extension of the Pythagorean fuzzy set (PFS) to deal with the vagueness and uncertainties in the data. The major advantages of PFSS over the other existing sets are to consider the parameterized tool of the family of PFS. Keeping this advantage, in this paper we define some new entropy measures for PFSS to compute the degree of fuzziness of the set. The axiomatic definition and their validity are stated. The larger the entropy, the lesser the vagueness and so, the decision making based on entropy is a useful one. Further, a decisionmaking algorithm is explored to solve the decision-making problem under the PFSS environment. A numerical example is given to validate the method and compare their performance with the existing intuitionistic fuzzy soft set entropy measures.


    加载中


    [1] L. A. Zadeh, Fuzzy sets, Information and Control, 8 (1965), 338-353. doi: 10.1016/S0019-9958(65)90241-X
    [2] K. T. Atanassov, Intuitionistic fuzzy sets, Fuzzy Set. Syst., 20 (1986), 87-96. doi: 10.1016/S0165-0114(86)80034-3
    [3] R. R. Yager, Pythagorean fuzzy subsets, Proceedings Joint IFSA World Congress and NAFIPS Annual Meeting, (2013), 57-61.
    [4] W. L. Hung, M. S. Yang, Similarity measures of intuitionistic fuzzy sets based on hausdorff distance, Pattern Recogn. Lett., 25 (2004), 1603-1611. doi: 10.1016/j.patrec.2004.06.006
    [5] H. Garg, K. Kumar, An advanced study on the similarity measures of intuitionistic fuzzy sets based on the set pair analysis theory and their application in decision making, Soft Comput., 22 (2018), 4959-4970. doi: 10.1007/s00500-018-3202-1
    [6] X. Peng, H. Garg, Multiparametric similarity measures on Pythagorean fuzzy sets with applications to pattern recognition, Appl. Intell., 49 (2019), 4058-4096. doi: 10.1007/s10489-019-01445-0
    [7] P. Burillo, H. Bustince, Entropy on intuitionistic fuzzy sets and on interval-valued fuzzy sets, Fuzzy Set. Syst., 78 (1996), 305-316. doi: 10.1016/0165-0114(96)84611-2
    [8] W. L. Hung, M. S. Yang, Fuzzy entropy on intuitionistic fuzzy sets, Int. J. Intell. Syst., 21 (2006), 443-451. doi: 10.1002/int.20131
    [9] I. K. Vlachos, G. D. Sergiadis, Intuitionistic fuzzy information - application to pattern recognition, Pattern Recogn. Lett., 28 (2007), 197-206. doi: 10.1016/j.patrec.2006.07.004
    [10] M. Zhang, W. Luo, X. Wang, Differential evolution with dynamic stochastic selection for constrained optimization, Inform. Sciences, 178 (2008), 3043-3074. doi: 10.1016/j.ins.2008.02.014
    [11] H. Garg, N. Agarwal, A. Tripathi, Generalized intuitionistic fuzzy entropy measure of order α and degree β and its applications to multi-criteria decision making problem, Int. J. Fuzzy Syst. Applications, 6 (2017), 86-107. doi: 10.4018/IJFSA.2017010105
    [12] H. Garg, Intuitionistic fuzzy hamacher aggregation operators with entropy weight and their applications to multi-criteria decision-making problems, Iran J. Sci. Technol. Trans. Electr. Eng., 43 (2019), 597-613. doi: 10.1007/s40998-018-0167-0
    [13] H. Garg, Generalized intuitionistic fuzzy entropy-based approach for solving multi-attribute decision-making problems with unknown attribute weights, Proceedings of the National Academy of Sciences, India Section A: Physical Sciences, 89 (2019), 129-139. doi: 10.1007/s40010-017-0395-0
    [14] G. Selvachandran, H. Garg, S. G. Quek, Vague entropy measure for complex vague soft sets, Entropy-Switz., 20 (2018), 403
    [15] X. Peng, G. Selvachandran, Pythagorean fuzzy set: state of the art and future directions, Artif. Intell. Rev., 52 (2019), 1873-1927. doi: 10.1007/s10462-017-9596-9
    [16] D. Molodtsov, Soft set theory - first results, Comput. Math. Appl., 27 (1999), 19-31.
    [17] M. Ali, F. Feng, X. Liu, On some new operations in soft set theory, Comput. Math. Appl., 57 (2009), 1547-1553. doi: 10.1016/j.camwa.2008.11.009
    [18] P. K. Maji, R. Biswas, Fuzzy soft, J. Fuzzy Math., 9 (2001), 589-602.
    [19] P. K. Maji, R. Biswas, A. Roy, Intuitionistic fuzzy soft sets, Journal of Fuzzy Mathematics, 9 (2001), 677-692.
    [20] F. Feng, C. Li, B. Davvaz, Soft sets combined with fuzzy sets and rough sets: a tentative approach, Soft Comput., 14 (2010), 899-911. doi: 10.1007/s00500-009-0465-6
    [21] M. Bora, T. J. Neog, D. K. Sut, Some new operations of intuitionistic fuzzy soft sets, IJSCE., 2 (2012), 2231-2307.
    [22] N. Cagman, I. Deli, Similarity measures of intuitionistic fuzzy soft sets and their decision making, doi: arXiv:1301.0456
    [23] P. Rajarajeswari, P. Dhanalakshmi, Similarity measures of intuitionistic fuzzy soft sets and its application in medical diagnosis, International Journal of Mathematical Archive, 5 (2014), 143-149.
    [24] H. Garg, R. Arora, Distance and similarity measures for dual hesistant fuzzy soft sets and their applications in multi criteria decision-making problem, Int. J. Uncertain. Quan., 7 (2017), 229-248. doi: 10.1615/Int.J.UncertaintyQuantification.2017019801
    [25] P. Muthukumar, G. S. S. Krishnan, A similarity measure of intuitionistic fuzzy soft sets and its application in medical diagnosis, Appl. Soft Comput., 41 (2016), 148-156. doi: 10.1016/j.asoc.2015.12.002
    [26] R. Arora, H. Garg, Robust aggregation operators for multi-criteria decision making with intuitionistic fuzzy soft set environment, Sci. Iran. E., 25 (2018), 931-942.
    [27] R. Arora, H. Garg, Prioritized averaging/geometric aggregation operators under the intuitionistic fuzzy soft set environment, Sci. Iran., 25 (2018), 466-482.
    [28] A. Khalid, M. Abbas, Distance measures and operations in intuitionistic and interval-valued intuitionistic fuzzy soft set theory, Int. J. Fuzzy Syst., 17 (2015), 490-497. doi: 10.1007/s40815-015-0048-x
    [29] N. Sarala, B. Suganya, An application of similarity measure of intuitionistic fuzzy soft set based on distance in medical diagnosis, Int. J. Sci. Res., 4 (2016), 2298-2303.
    [30] M. Agarwal, K. K. Biswas, M. Hanmandlu, Generalized intuitionistic fuzzy soft sets with applications in decision-making, Appl. Soft Comput., 13 (2013), 3552-3566. doi: 10.1016/j.asoc.2013.03.015
    [31] F. Feng, H. Fujita, M. I. Ali, Another view on generalized intuitionistic fuzzy soft sets and related multiattribute decision making methods, IEEE T. Fuzzy Syst., 27 (2019), 474-488. doi: 10.1109/TFUZZ.2018.2860967
    [32] H. Garg, R. Arora, Generalized and group-based generalized intuitionistic fuzzy soft sets with applications in decision-making, Appl. Intell., 48 (2018), 343-356. doi: 10.1007/s10489-017-0981-5
    [33] K. Hayat, M. I. Ali, J. C. R. Alcantud, Best concept selection in design process: An application of generalized intuitionistic fuzzy soft sets, J. Intell. Fuzzy Syst., 35 (2018), 5707-5720. doi: 10.3233/JIFS-172121
    [34] P. Majumdar, S. Samanta, Softness of a soft set: Soft set entropy, Ann. Fuzzy Math. Inform., 6 (2013), 59-68.
    [35] Y. Jiang, Y. Tang, H. Liu, Entropy on intuitionistic fuzzy soft sets and on interval-valued fuzzy soft sets, Inform. Sciences, 240 (2013), 95-114. doi: 10.1016/j.ins.2013.03.052
    [36] Z. Liu, K. Qin, Z. Pei, Similarity measure and entropy of fuzzy soft sets, The Scientific World J., 2014 (2014), 161607.
    [37] G. Selvachandran, P. Maji, R. Q. Faisal, Distance and distance induced intuitionistic entropy of generalized intuitionistic fuzzy soft sets, Appl. Intell., 47 (2017), 132-147. doi: 10.1007/s10489-016-0884-x
    [38] J. Zhan, J. C. R. Alcantud, A survey of parameter reduction of soft sets and corresponding algorithms, Artif. Intell. Rev., 52 (2019), 1839-1872 doi: 10.1007/s10462-017-9592-0
    [39] X. Peng, Y. Yang, J. Song, Pythagoren fuzzy soft set and its application, Comput. Eng., 41 (2015), 224-229.
    [40] T. M. Athira, S. J. John, H. Garg, Entropy and distance measures of pythagorean fuzzy soft sets and their applications, J. Intell. Fuzzy Syst., 37 (2019), 4071-4084. doi: 10.3233/JIFS-190217
    [41] X. D. Peng, H. Garg, Algorithms for interval-valued fuzzy soft sets in emergency decision making based on WDBA and CODAS with new information measure, Comput. Ind. Eng., 119 (2018), 439-452. doi: 10.1016/j.cie.2018.04.001
    [42] A. M. Khalil, S. G. Li, H. Garg, New operations on interval-valued picture fuzzy set, intervalvalued picture fuzzy soft set and their applications, IEEE Access, 7 (2019), 51236-51253. doi: 10.1109/ACCESS.2019.2910844
  • Reader Comments
  • © 2020 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(5286) PDF downloads(866) Cited by(46)

Preview PDF
Download XML
Export Citation
Article outline

Figures and Tables

Tables(1)

Other Articles By Authors

Related pages

Tools

/

DownLoad:  Full-Size Img  PowerPoint
Return
Return

Catalog