research-article

Novel Information Measures for Fermatean Fuzzy Sets and Their Applications to Pattern Recognition and Medical Diagnosis

Authors:

Shahzaib Ashraf,

Muhammad Naeem,

M. K. Pandit Academic Editor:

Sheng DuAuthors Info & Claims

Computational Intelligence and Neuroscience, Volume 2023

https://doi.org/10.1155/2023/9273239

Published: 01 January 2023 Publication History

Abstract

Fermatean fuzzy sets (FFSs) have piqued the interest of researchers in a wide range of domains. The striking framework of the FFS is keen to provide the larger preference domain for the modeling of ambiguous information deploying the degrees of membership and nonmembership. Furthermore, FFSs prevail over the theories of intuitionistic fuzzy sets and Pythagorean fuzzy sets owing to their broader space, adjustable parameter, flexible structure, and influential design. The information measures, being a significant part of the literature, are crucial and beneficial tools that are widely applied in decision-making, data mining, medical diagnosis, and pattern recognition. This paper aims to expand the literature on FFSs by proposing many innovative Fermatean fuzzy sets-based information measures, namely, distance measure, similarity measure, entropy measure, and inclusion measure. We investigate the relationship between distance, similarity, entropy, and inclusion measures for FFSs. Another achievement of this research is to establish a systematic transformation of information measures (distance measure, similarity measure, entropy measure, and inclusion measure) for the FFSs. To accomplish this aim, new formulae for information measures of FFSs have been presented. To demonstrate the validity of the measures, we employ them in pattern recognition, building materials, and medical diagnosis. Additionally, a comparison between traditional and novel similarity measures is described in terms of counter-intuitive cases. The findings demonstrate that the innovative information measures do not include any absurd cases.

References

[1]

L. A. Zadeh, “Fuzzy sets,” Information and Control, vol. 8, no. 3, pp. 338–353, 1965.

[2]

S. Ashraf, T. Mahmood, S. Abdullah, and Q. Khan, “Different approaches to multi-criteria group decision making problems for picture fuzzy environment,” Bulletin of the Brazilian Mathematical Society, New Series, vol. 50, no. 2, pp. 373–397, 2019.

[3]

K. T. Atanassov, “Intuitionistic fuzzy sets,” in Intuitionistic Fuzzy Sets, pp. 1–137, Physica, Heidelberg, Germany, 1999.

[4]

R. R. Yager, “Pythagorean membership grades in multicriteria decision making,” IEEE Transactions on Fuzzy Systems, vol. 22, no. 4, pp. 958–965, 2014.

[5]

T. Senapati and R. R. Yager, “Fermatean fuzzy sets,” Journal of Ambient Intelligence and Humanized Computing, vol. 11, no. 2, pp. 663–674, 2020.

[6]

E. Szmidt and J. Kacprzyk, “Distances between intuitionistic fuzzy sets,” Fuzzy Sets and Systems, vol. 114, no. 3, pp. 505–518, 2000.

Digital Library

[7]

W. Wang and X. Xin, “Distance measure between intuitionistic fuzzy sets,” Pattern Recognition Letters, vol. 26, no. 13, pp. 2063–2069, 2005.

Digital Library

[8]

P. Grzegorzewski, “Distances between intuitionistic fuzzy sets and/or interval-valued fuzzy sets based on the Hausdorff metric,” Fuzzy Sets and Systems, vol. 148, no. 2, pp. 319–328, 2004.

Digital Library

[9]

T. Y. Chen, “A note on distances between intuitionistic fuzzy sets and/or interval-valued fuzzy sets based on the Hausdorff metric,” Fuzzy Sets and Systems, vol. 158, no. 22, pp. 2523–2525, 2007.

Digital Library

[10]

W. L. Hung and M. S. Yang, “Similarity measures of intuitionistic fuzzy sets based on Hausdorff distance,” Pattern Recognition Letters, vol. 25, no. 14, pp. 1603–1611, 2004.

Digital Library

[11]

D. Yong, S. Wenkang, D. Feng, and L. Qi, “A new similarity measure of generalized fuzzy numbers and its application to pattern recognition,” Pattern Recognition Letters, vol. 25, no. 8, pp. 875–883, 2004.

Digital Library

[12]

H. B. Mitchell, “On the Dengfeng–Chuntian similarity measure and its application to pattern recognition,” Pattern Recognition Letters, vol. 24, no. 16, pp. 3101–3104, 2003.

Digital Library

[13]

Z. Liang and P. Shi, “Similarity measures on intuitionistic fuzzy sets,” Pattern Recognition Letters, vol. 24, no. 15, pp. 2687–2693, 2003.

Digital Library

[14]

Z. Xu, “Some similarity measures of intuitionistic fuzzy sets and their applications to multiple attribute decision making,” Fuzzy Optimization and Decision Making, vol. 6, no. 2, pp. 109–121, 2007.

Digital Library

[15]

Z. S. Xu and J. Chen, “An overview of distance and similarity measures of intuitionistic fuzzy sets,” International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, vol. 16, no. 04, pp. 529–555, 2008.

[16]

Z. Xu and R. R. Yager, “Intuitionistic and interval-valued intutionistic fuzzy preference relations and their measures of similarity for the evaluation of agreement within a group,” Fuzzy Optimization and Decision Making, vol. 8, no. 2, pp. 123–139, 2009.

Digital Library

[17]

W. Y. Zeng and P. Guo, “Normalized distance, similarity measure, inclusion measure and entropy of interval-valued fuzzy sets and their relationship,” Information Sciences, vol. 178, no. 5, pp. 1334–1342, 2008.

Digital Library

[18]

C. P. Wei, P. Wang, and Y. Z. Zhang, “Entropy, similarity measure of interval-valued intuitionistic fuzzy sets and their applications,” Information Sciences, vol. 181, no. 19, pp. 4273–4286, 2011.

Digital Library

[19]

L. Dengfeng and C. Chuntian, “New similarity measures of intuitionistic fuzzy sets and application to pattern recognitions,” Pattern Recognition Letters, vol. 23, no. 1-3, pp. 221–225, 2002.

Digital Library

[20]

S. Ashraf, S. Abdullah, T. Mahmood, F. Ghani, and T. Mahmood, “Spherical fuzzy sets and their applications in multi-attribute decision making problems,” Journal of Intelligent and Fuzzy Systems, vol. 36, no. 3, pp. 2829–2844, 2019.

Digital Library

[21]

S. Ashraf and S. Abdullah, “Emergency decision support modeling for COVID-19 based on spherical fuzzy information,” International Journal of Intelligent Systems, vol. 35, no. 11, pp. 1601–1645, 2020.

Digital Library

[22]

X. T. Nguyen, V. D. Nguyen, V. H. Nguyen, and H. Garg, “Exponential similarity measures for Pythagorean fuzzy sets and their applications to pattern recognition and decision-making process,” Complex & Intelligent Systems, vol. 5, no. 2, pp. 217–228, 2019.

[23]

X. Zhang, “A novel approach based on similarity measure for Pythagorean fuzzy multiple criteria group decision making,” International Journal of Intelligent Systems, vol. 31, no. 6, pp. 593–611, 2016.

Digital Library

[24]

Z. Zhang, J. Yang, Y. Ye, Y. Hu, and Q. Zhang, “A type of score function on intuitionistic fuzzy sets with double parameters and its application to pattern recognition and medical diagnosis,” Procedia Engineering, vol. 29, pp. 4336–4342, 2012.

[25]

P. A. Ejegwa, “Personnel Appointments: a Pythagorean fuzzy sets approach using similarity measure,” Journal of Information and Computational Science, vol. 14, no. 2, pp. 94–102, 2019.

[26]

P. A. Ejegwa, “Distance and similarity measures for Pythagorean fuzzy sets,” Granular Computing, vol. 5, no. 2, pp. 225–238, 2020.

[27]

J. Ye, “Cosine similarity measures for intuitionistic fuzzy sets and their applications,” Mathematical and Computer Modelling, vol. 53, no. 1-2, pp. 91–97, 2011.

Digital Library

[28]

J. Ye, “Interval-valued intuitionistic fuzzy cosine similarity measures for multiple attribute decision-making,” International Journal of General Systems, vol. 42, no. 8, pp. 883–891, 2013.

[29]

D. Liu, X. Chen, and D. Peng, “Cosine similarity measure between hybrid intuitionistic fuzzy sets and its application in medical diagnosis,” Computational and Mathematical Methods in Medicine, 2018.

[30]

G. Wei and Y. Wei, “Similarity measures of Pythagorean fuzzy sets based on the cosine function and their applications,” International Journal of Intelligent Systems, vol. 33, no. 3, pp. 634–652, 2018.

Digital Library

[31]

X. Peng, “New similarity measure and distance measure for Pythagorean fuzzy set,” Complex and Intelligent Systems, vol. 5, no. 2, pp. 101–111, 2019.

[32]

X. Peng, H. Yuan, and Y. Yang, “Pythagorean fuzzy information measures and their applications,” International Journal of Intelligent Systems, vol. 32, no. 10, pp. 991–1029, 2017.

Digital Library

[33]

V. Torra and Y. Narukawa, “On hesitant fuzzy sets and decision,” in Proceedings of the 2009 IEEE International Conference on Fuzzy Systems, pp. 1378–1382, IEEE, Jeju Island, Korea, August 2009.

[34]

R. R. Yager and N. Alajlan, “Approximate reasoning with generalized orthopair fuzzy sets,” Information Fusion, vol. 38, pp. 65–73, 2017.

Digital Library

[35]

F. Xiao and W. Ding, “Divergence measure of Pythagorean fuzzy sets and its application in medical diagnosis,” Applied Soft Computing, vol. 79, pp. 254–267, 2019.

Digital Library

[36]

Q. Zhou, H. Mo, and Y. Deng, “A new divergence measure of pythagorean fuzzy sets based on belief function and its application in medical diagnosis,” Mathematics, vol. 8, no. 1, p. 142, 2020.

[37]

Z. Deng and J. Wang, “New distance measure for Fermatean fuzzy sets and its application,” International Journal of Intelligent Systems, vol. 37, no. 3, pp. 1903–1930, 2021.

Digital Library

[38]

Y. Li, D. L. Olson, and Z. Qin, “Similarity measures between intuitionistic fuzzy (vague) sets: a comparative analysis,” Pattern Recognition Letters, vol. 28, no. 2, pp. 278–285, 2007.

Digital Library

[39]

X. Peng and L. Liu, “Information measures for q-rung orthopair fuzzy sets,” International Journal of Intelligent Systems, vol. 34, no. 8, pp. 1795–1834, 2019.

Digital Library

[40]

S. M. Chen, “Similarity measures between vague sets and between elements,” IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics), vol. 27, no. 1, pp. 153–158, 1997.

Digital Library

[41]

S. M. Chen and C. H. Chang, “A novel similarity measure between Atanassov’s intuitionistic fuzzy sets based on transformation techniques with applications to pattern recognition,” Information Sciences, vol. 291, pp. 96–114, 2015.

Digital Library

[42]

D. H. Hong and C. Kim, “A note on similarity measures between vague sets and between elements,” Information Sciences, vol. 115, no. 1-4, pp. 83–96, 1999.

[43]

F. Li and Z. Xu, “Measures of similarity between vague sets,” Journal of Software, vol. 12, no. 6, pp. 922–927, 2001.

[44]

X. Zhang, “A novel approach based on similarity measure for Pythagorean fuzzy multiple criteria group decision making,” International Journal of Intelligent Systems, vol. 31, no. 6, pp. 593–611, 2016.

Digital Library

[45]

F. E. Boran and D. Akay, “A biparametric similarity measure on intuitionistic fuzzy sets with applications to pattern recognition,” Information Sciences, vol. 255, pp. 45–57, 2014.

Digital Library

[46]

E. Szmidt and J. Kacprzyk, “A similarity measure for intuitionistic fuzzy sets and its application in supporting medical diagnostic reasoning,” in International Conference on Artificial Intelligence and Soft Computing, pp. 388–393, Springer, Berlin, Heidelberg, 2004.

[47]

E. Szmidt and J. Kacprzyk, “Intuitionistic fuzzy sets in intelligent data analysis for medical diagnosis,” in International Conference on Computational Science, pp. 263–271, Springer, Berlin, Heidelberg, 2001.

[48]

C. M. Own, “Switching between type-2 fuzzy sets and intuitionistic fuzzy sets: an application in medical diagnosis,” Applied Intelligence, vol. 31, no. 3, pp. 283–291, 2009.

Digital Library

[49]

S. K. De, R. Biswas, and A. R. Roy, “An application of intuitionistic fuzzy sets in medical diagnosis,” Fuzzy Sets and Systems, vol. 117, no. 2, pp. 209–213, 2001.

Digital Library

[50]

I. K. Vlachos and G. D. Sergiadis, “Intuitionistic fuzzy information–applications to pattern recognition,” Pattern Recognition Letters, vol. 28, no. 2, pp. 197–206, 2007.

Digital Library

Cited By

Fan JLei TWu M(2024)MEREC-MABAC method based on cumulative prospect theory for picture fuzzy setsExpert Systems with Applications: An International Journal10.1016/j.eswa.2024.124749255:PCOnline publication date: 1-Dec-2024
https://dl.acm.org/doi/10.1016/j.eswa.2024.124749
AlShaqsi JWang WDrogham OAlkhawaldeh R(2024)Quantitative and qualitative similarity measure for data clustering analysisCluster Computing10.1007/s10586-024-04664-427:10(14977-15002)Online publication date: 1-Dec-2024
https://dl.acm.org/doi/10.1007/s10586-024-04664-4
Kirişci M(2023)Data analysis for panoramic X-ray selectionEngineering Applications of Artificial Intelligence10.1016/j.engappai.2023.106824126:PAOnline publication date: 1-Nov-2023
https://dl.acm.org/doi/10.1016/j.engappai.2023.106824

Recommendations

Fermatean fuzzy similarity measures based on Tanimoto and Sørensen coefficients with applications to pattern classification, medical diagnosis and clustering analysis
Abstract
Fermatean fuzzy sets (FFSs) have emerged as a powerful tool for handling uncertain information and have been successfully applied in various domains. However, the existing similarity measures for FFSs often face challenges in accurately capturing ...
Highlights
- Sixteen new similarity measures for FFSs are proposed based on Tanimoto and Sørensen coefficients.
- The desirable properties of the proposed similarity measures are analyzed.
- The behavior of the proposed similarity measures are ...
A novel similarity/dissimilarity measure for intuitionistic fuzzy sets and its application in pattern recognition

Among the most interesting measures in intuitionistic fuzzy sets (IFSs) theory, the similarity measure is an essential tool to compare and determine degree of similarity between IFSs. Although there exist many similarity measures for IFSs, most of them ...
A novel similarity measure between Atanassov's intuitionistic fuzzy sets based on transformation techniques with applications to pattern recognition

In this paper, we propose a new similarity measure between Atanassov's intuitionistic fuzzy sets (AIFSs) based on transformation techniques and apply the proposed similarity measure between AIFSs to deal with pattern recognition problems. First, we ...

Comments

Please enable JavaScript to view thecomments powered by Disqus.

Information & Contributors

Information

Published In

cover image Computational Intelligence and Neuroscience

Computational Intelligence and Neuroscience Volume 2023, Issue

2023

2916 pages

ISSN:1687-5265

EISSN:1687-5273

Issue’s Table of Contents

Copyright © 2023 Shahzaib Ashraf et al.

This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Publisher

Hindawi Limited

London, United Kingdom

Publication History

Published: 01 January 2023

Qualifiers

Research-article

Contributors

Other Metrics

View Article Metrics

Bibliometrics & Citations

Bibliometrics

Article Metrics

3
Total Citations
View Citations
0
Total Downloads

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

Reflects downloads up to 27 Nov 2024

Other Metrics

View Author Metrics

Citations

Cited By

Fan JLei TWu M(2024)MEREC-MABAC method based on cumulative prospect theory for picture fuzzy setsExpert Systems with Applications: An International Journal10.1016/j.eswa.2024.124749255:PCOnline publication date: 1-Dec-2024
https://dl.acm.org/doi/10.1016/j.eswa.2024.124749
AlShaqsi JWang WDrogham OAlkhawaldeh R(2024)Quantitative and qualitative similarity measure for data clustering analysisCluster Computing10.1007/s10586-024-04664-427:10(14977-15002)Online publication date: 1-Dec-2024
https://dl.acm.org/doi/10.1007/s10586-024-04664-4
Kirişci M(2023)Data analysis for panoramic X-ray selectionEngineering Applications of Artificial Intelligence10.1016/j.engappai.2023.106824126:PAOnline publication date: 1-Nov-2023
https://dl.acm.org/doi/10.1016/j.engappai.2023.106824

View Options

View options

Login options

Check if you have access through your login credentials or your institution to get full access on this article.

Full Access

Get this Publication

Media

Figures

Other

Tables

View Issue’s Table of Contents