A novel and extended view on some well‐known measures of intuitionistic fuzzy sets and  applications in medical diagnosis 

Document Type : Original Article

Authors

Department of Mathematics, Faculty of Science, University of Qom, Qom, IRAN

Abstract

Decision‐making in conditions of uncertainty, especially in the diagnosis of diseases, has always been  a challenging task in the field of research, which has been the focus of many researchers. Due to the  successful performance of intuitionistic fuzzy numbers in covering the uncertainty related to medical  problems, the main focus of this article is on this type of numbers. The theory of sizes as a  complementary and efficient tool in combination with disease diagnosis processes is a great help in  final decision‐making in order to speed up the treatment process. Although various measures have  been proposed for intuitionistic fuzzy numbers, however, by changing the attitudes, it is possible to  complete  the  measures  from  other  dimensions.  Choosing  a  suitable  size  can  cause  a  special  improvement in the final result or reduce the amount of calculations. Our main motivation for this  article is a new perspective on some of the prominent sizes and reducing the volume of their  operations. In this way, the rewriting and extension of some of the proposed measures are presented  based on a conceptual model. In some numerical examples from the literature of the research, a  comparative analysis is given for the new measures in comparison with other measures. In addition,  discussions on the effectiveness of the mentioned measurements are expressed using the findings  obtained from its application in the medical diagnosis problem.  

Keywords

Main Subjects

References

[1] Ali, J., Naeem, M. (2022) Distance and similarity measures for normal wiggly dual hesitant fuzzy sets and their application in medical diagnosis. Sci Rep 12, 13784. https://doi.org/10.1038/s41598-022-16078-6.

[2] Alias, S., Mohamad, D., Shuib, . A., MohdYusoff, N.S. ,AbdRhani, N. & FitriahMohamad, S. N. (2022) Medical Diagnosis via Distance-based Similarity Measure for Rough Neutrosophic Set. Neutrosophic Sets and Systems, 46, 142-150. Retrieved from http://fs.unm.edu/NSS2/index.php/111/article/view/1948.
 
[3] Atanassov, K.T. (1986) Intuitionistic fuzzy sets, Fuzzy Sets Syst. 20, 87–96.
 
[4] Avuçlu E. (2022) A novel method using Covid-19 dataset and machine learning algorithms for the most accurate diagnosis that can be obtained in medical diagnosis. Biomedical Signal Processing and Control, Volume 77.
 
[5] Balasubramaniam P., Ananthi V.P. (2014) Image fusion using intuitionistic fuzzy sets. Inf Fusion 20(1), 21–30.
 
[6] Barbara Pękala, Krzysztof Dyczkowski, Przemysław Grzegorzewski, Urszula Bentkowska (2021) Inclusion and similarity measures for interval-valued fuzzy sets based on aggregation and uncertainty assessment. Information Sciences, 547, 1182-1200.
 
[7] Broumi, S., Mamoni D., Abdellah B., Assia B. and Mohamed T. (2022) Medical Diagnosis Problems Based on Neutrosophic Sets and Their Hybrid Structures: A Survey. Neutrosophic Sets and Systems 49, 1. https://digitalrepository.unm.edu/nss_journal/vol49/iss1/1.
 
[8] Cheng C., Xiao F., Cao Z. (2019) A new distance for intuitionistic fuzzy sets based on similarity matrix. IEEE Access. 7, 70436-70446.
 
[9] Chen T.Y. (2007) A note on distances between intuitionistic fuzzy sets and/or interval-valued fuzzy sets based on the Hausdorff metric. Fuzzy Sets Syst 158, 2523–2525.
 
[10] De S.K., Biswas R., Roy A.R. (2001) An application of intuitionistic fuzzy sets in medical diagnosis. Fuzzy Sets Syst. 117, 209-213.
 
[11] Du W.S., Hu B.Q. (2015) Aggregation distance measure and its induced similarity measure between intuitionistic fuzzy sets. Pattern Recogn Lett. 60, 65-71.
 
[12] Ejegwa P. A., Modom E. S. (2015) Diagnosis of viral hepatitis using new distance measure of intuitionistic fuzzy sets. International Journal of Fuzzy Mathematical Archive, 8(1), 1–7.
 
[13] Grzegorzewski P. (2004) Distances between intuitionistic fuzzy sets and/or interval-valued fuzzy sets based on the Hausdorff metric.Fuzzy Sets Syst 148, 319–328.
 
[14] Habib, S., Ashraf, A., Arif Butt, M., & Ahmad, M. (2021) Medical diagnosis based on single-valued neutrosophic information. Neutrosophic Sets and Systems, 42, 302-323.
 
[15] Harish Garg, Dimple Rani (2022) Novel distance measures for intuitionistic fuzzy sets based on various triangle centers of isosceles triangular fuzzy numbers and their applications. Expert Systems with Applications, Volume 191.
 
[16] Hu J., Pan L., Yang Y., Chen H. (2019) A group medical diagnosis model based on intuitionistic fuzzy soft sets. Applied Soft Computing 77, 453-466.
 
[17] Hung W.L., Yang M.S. (2004) Similarity measures of intuitionistic fuzzy sets based on Hausdorff distance. Pattern Recognit Lett 25, 1603–1611.
 
[18] Jafarian E., Rezvani M.A. (2013) A valuation-based method for ranking the intuitionistic fuzzy numbers. Journal of Intelligent Fuzzy System 24 (1), 133–144.
 
[19] Jiang Q., Jin X., Lee S.-J., and Yao S. (2019) A new similarity/distance measure between intuitionistic fuzzy sets based on the transformed isosceles triangles and its applications to pattern recognition. Expert System and Application 116, 439–453.
 
[20] Jiang Q., Lee S., Zeng X., Jin X., Hou J., Zhou W., and Yao S. (2022) A multi-focus image fusion scheme based on similarity measure of transformed isosceles triangles between intuitionistic fuzzy sets. IEEE Transaction Instrument and Meaurment., p. 14 pages. doi:10.1109/TIM.2022.3169571.
 
[21] Kononenko I. (2001) Machine learning for medical diagnosis: history, state of the art and perspective. Artificial Intelligence Medicin 23 (1), 89–109.
 
[22] Liang Z., Shi P. (2003) Similarity measures on intuitionistic fuzzy sets. Pattern Recognition Letters 24, 2687-2693.
 
[23] Luo M, Zhao R. (2018) A distance measure between intuitionistic fuzzy sets and its application in medical diagnosis. Artif Intell Med. 89, 34-39.
 
[24] Mahanta, J., Panda, S. (2021) A novel distance measure for intuitionistic fuzzy sets with diverse applications. Int. J. Intell. Syst. 36, 615–627.
 
[25] Meng D., Zhang X., Qin K. (2011) Soft rough fuzzy sets and soft fuzzy rough sets. Computational Mathematics and Application 62(12), 4635–4645.
 
[26] Mohiuddin Ahmed, A.N.M. Bazlur Rashid, EDSUCh: A robust ensemble data summarization method for effective medical diagnosis. Digital Communications and Networks, 2022.
 
[27] Mondal K., Pramanik S. (2015) Intuitionistic fuzzy similarity measure based on tangent function and its application to multi‐attribute decision making. Global J Adv Res. 2, 464-471.
 
[28] Ngan S.C. (2016) An activation detection-based similarity measure for intuitionistic fuzzy sets. Expert Syst Appl 60(1), 62–80.
 
[29] Own C.M. (2009) Switching between type‐2 fuzzy sets and intuitionistic fuzzy sets: an application in medical diagnosis. Appl Intell. 31, 283.
 
[30] Papakostas G.A. (2013) Distance and similarity measures between intuitionistic fuzzy sets: a comparative analysis from a pattern recognition point of view. Pattern Recognit Lett 34, 1609–1622.
 
[31] Ross Camidge D., Mandair D., Morgan R., Amini A., Rusthoven C.G. (2022) Quantifying The Medical Impact of A Missed Diagnosis of Non-Small Cell Lung Cancer on Chest Imaging. Clinical Lung Cancer 23(5), 377-385.
 
[32] Shakouri, B., Abbasi Shureshjani, R., Daneshian, B., and Hosseinzadeh Lotfi, F. (2020) A Parametric Method for Ranking Intuitionistic Fuzzy Numbers and Its Application to Solve Intuitionistic Fuzzy Network Data Envelopment Analysis Models. Complexity, 1-25. https://doi.org/10.1155/2020/6408613.
 
[33] Shen, F., Xu, J.P., Xu, Z.S. (2016) An outranking sorting method for multi-criteria group decision making using intuitionistic fuzzy sets, Information Science 334, 338–353.
 
[34] Szmidt E, Kacprzyk J. (2002) Using intuitionistic fuzzy sets in group decision making. Control Cybern 31:1055–1057.
 
[35] Szmidt E., Kacprzyk J. (2004) A similarity measure for intuitionistic fuzzy sets and its application in supporting medical diagnostic reasoning. In: ICAISC, pp 388–393.
 
[36] Szmidt E., Kacprzyk J. (2000) Distances between intuitionistic fuzzy sets. Fuzzy Sets Syst. 114, 505-518.
 
[37] Wang W., Xin X. (2005) Distance measure between intuitionistic fuzzy sets. Pattern Recognit Lett 26, 2063–2069.
 
[38] Wei C.P., Wang P., Zhang Y.Z. (2011) Entropy, similarity measure of interval‐valued intuitionistic fuzzy sets and their applications. Inf Sci. 181, 4273-4286.
 
[39] Xiao F. (2020) A distance measure for intuitionistic fuzzy sets and its application to pattern classification problems. IEEE Trans Syst Man Cybern: Syst. 1-13. http://dx.doi.org/10.1109/tsmc.2019.2958635.
 
[40] Zadeh, L.A. (1965) Fuzzy sets, Inf. Control. 8, 338–353.
 
[41] Zhang H., Yu L. (2013) New distance measures between intuitionistic fuzzy sets and interval-valued fuzzy sets. Inf Sci 245, 181–196.
 
[42] Zhang X., Zhou B., Li P. (2012) A general frame for intuitionistic fuzzy rough sets. Information Science 216, 34–49.
Fuzzy Systems and its Applications
Volume 6, Issue 1 - Serial Number 12
September 2023
Pages 223-244

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History

  • Receive Date: 01 October 2022
  • Revise Date: 06 February 2023
  • Accept Date: 28 June 2023

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