A novel parametric intuitionistic fuzzy entropy measure with applications to image edge detection

Authors

  • Vaishali Manish Joshi
    Symbiosis Institute of Technology, Symbiosis International (Deemed University), Pune 412115, India;
    Dr. Vishwanath Karad MIT World Peace University, Pune 411038, India
  • Javid Gani Dar
    Department of Applied Sciences, Symbiosis Institute of Technology, Symbiosis International (Deemed University), Pune 412115, India

Keywords:

Edge detection, Image processing, Rényi entropy, Intuitionistic fuzzy sets, Generalized fuzzy entropy

Abstract

In digital image processing, edge detection is a fundamental operation used to identify intensity discontinuities in an image. In this paper, we propose a novel one-parameter generalization of an entropy measure for intuitionistic fuzzy sets (IFSs). IFSs provide additional flexibility by incorporating membership, non-membership, and hesitation information. A proof of validity is given for the proposed measure, together with numerical and graphical demonstrations. The entropy measure is applied to generate an edge map in which pixels exhibiting higher uncertainty are marked as image edges. Experimental results for standard benchmark images and real photographic images demonstrate superior edge localization and improved quantitative performance compared with existing fuzzy-entropy-based techniques.

Dimensions

[1] E. Szmidt & J. Kacprzyk, ``Entropy for intuitionistic fuzzy sets'', Fuzzy Sets and Systems 118 (2001) 467. https://doi.org/10.1016/S0165-0114(98)00402-3.

[2] M. Ansari, A. Mishra & F. Ansari, ``New divergence and entropy measure for intuitionistic fuzzy sets on edge detection'', International Journal of Fuzzy Systems 20 (2018) 474. https://doi.org/10.1007/s40815-017-0348-4.

[3] J. M. S. Prewitt, Object enhancement and extraction, in Picture Processing and Psychopictorics, B. S. Lipkin & A. Rosenfeld (Eds.), Academic Press, New York, NY, USA, 1970, pp. 75--149. https://books.google.com.ng/bookshl=en&lr=&id=vpw_pC9JBAC&oi=fnd&pg=PA75&dq=%E2%80%9CObject+enhancement+and+extraction%E2%80%9D&ots=sBIaZmoyL9&sig=87drWS9o2qyy1PYbSQHNbx_ZFUQ&redir_esc=y#v=onepage&q=%E2%80%9CObject%20enhancement%20and%20extraction%E2%80%9D&f=false

[4] J. Canny, ``A computational approach to edge detection'', IEEE Transactions on Pattern Analysis and Machine Intelligence 8 (1986) 679. https://doi.org/10.1109/TPAMI.1986.4767851.

[5] C. E. Shannon, ``A mathematical theory of communication'', Bell System Technical Journal 27 (1948) 379. https://doi.org/10.1002/j.1538-7305.1948.tb01338.x.

[6] A. R'enyi, ``On measures of entropy and information'', Proceedings of the Fourth Berkeley Symposium on Mathematical Statistics and Probability, Berkeley, CA, USA, 1961, pp. 547--561. Available online: https://projecteuclid.org/euclid.bsmsp/1200512181.

[7] J. Havrda & F. Charv'at, ``Quantification method of classification processes: concept of structural $a$-entropy'', Kybernetika 3 (1967) 30. Available online: https://www.kybernetika.cz/content/1967/1/30/paper.pdf.

[8] A. M. Mathai & H. J. Haubold, ``Pathway model, superstatistics, Tsallis statistics and a generalized measure of entropy'', Physica A: Statistical Mechanics and its Applications 375 (2007) 110. https://doi.org/10.1016/j.physa.2006.09.002.

[9] M. Mittal, A. Verma, I. Kaur, B. Kaur, M. Sharma, L. M. Goyal, S. Roy & T.-H. Kim, ``An efficient edge detection approach to provide better edge connectivity for image analysis'', IEEE Access 7 (2019) 33240. https://doi.org/10.1109/ACCESS.2019.2902579.

[10] J. N. Kapur, Measures of Fuzzy Information, Mathematical Sciences Trust Society, New Delhi, India, 1997.

[11] D. Bhandari & N. R. Pal, ``Some new information measures for fuzzy sets'', Information Sciences 67 (1993) 209. https://doi.org/10.1016/0020-0255(93)90073-U.

[12] L. A. Zadeh, ``Fuzzy sets'', Information and Control 8 (1965) 338. https://doi.org/10.1016/S0019-9958(65)90241-X.

[13] A. De Luca & S. Termini, ``A definition of a nonprobabilistic entropy in the setting of fuzzy sets theory'', Information and Control 20 (1972) 301. https://doi.org/10.1016/S0019-9958(72)90199-4.

[14] K. T. Atanassov, ``Intuitionistic fuzzy sets'', Fuzzy Sets and Systems 20 (1986) 87. https://doi.org/10.1016/S0165-0114(86)80034-3.

[15] K. T. Atanassov, ``Review and new results on intuitionistic fuzzy sets'', International Journal of Bioautomation 20 (2016) S7. https://www.biomed.bas.bg/bioautomation/2016/vol_20.s1/files/20.s1_03.pdf

[16] P. Burillo & H. Bustince, ``Entropy on intuitionistic fuzzy sets and on interval-valued fuzzy sets'', Fuzzy Sets and Systems 78 (1996) 305. https://doi.org/10.1016/0165-0114(96)84611-2.

[17] I. K. Vlachos & G. D. Sergiadis, ``Intuitionistic fuzzy information: applications to pattern recognition'', Pattern Recognition Letters 28 (2007) 197. https://doi.org/10.1016/j.patrec.2006.07.004.

[18] W.-L. Hung & M.-S. Yang, ``Fuzzy entropy on intuitionistic fuzzy sets'', International Journal of Intelligent Systems 21 (2006) 443. https://doi.org/10.1002/int.20131.

[19] V. Arya & S. Kumar, ``A novel VIKOR--TODIM approach based on Havrda--Charv'at--Tsallis entropy of intuitionistic fuzzy sets to evaluate management information system'', Fuzzy Information and Engineering 11 (2019) 357. https://doi.org/10.1080/16168658.2020.1840317.

[20] F. Li, Z. Lu & L. Cai, ``The entropy of vague sets based on fuzzy sets'', Journal of Huazhong University of Science and Technology 31 (2003) 24.

[21] I. Sobel & G. Feldman, ``A 3 $times$ 3 isotropic gradient operator for image processing'', Stanford Artificial Intelligence Project, Stanford, CA, USA, 1968.

[22] D. Marr & E. Hildreth, ``Theory of edge detection'', Proceedings of the Royal Society of London B: Biological Sciences 207 (1980) 187. https://doi.org/10.1098/rspb.1980.0020.

[23] Q. Zhang & S. Jiang, ``A note on information entropy measures for vague sets and its applications'', Information Sciences 178 (2008) 4184. https://doi.org/10.1016/j.ins.2008.07.003.

[24] K. Pandey, A. Mishra, P. Rani, J. Ali & R. Chakrabortty, ``Selecting features by utilizing intuitionistic fuzzy entropy method'', Decision Making: Applications in Management and Engineering 6 (2023) 111. https://doi.org/10.31181/dmame07012023p.

[25] M. Versaci & F. C. Morabito, ``Image edge detection: a new approach based on fuzzy entropy and fuzzy divergence'', International Journal of Fuzzy Systems 23 (2021) 918. https://doi.org/10.1007/s40815-020-01030-5.

[26] R. P. K. Reddy & C. Nagaraju, ``Improved Canny edge detection technique using S-membership function'', International Journal of Engineering and Advanced Technology 8 (2019) 43. https://doi.org/10.35940/IJEAT.E7419.088619.

[27] J. Ye, ``Two effective measures of intuitionistic fuzzy entropy'', Computing 87 (2010) 55. https://doi.org/10.1007/s00607-009-0075-2.

[28] C. Wei, Z. Gao & T. Guo, ``An intuitionistic fuzzy entropy measure based on trigonometric function'', Control and Decision 27 (2012) 571. https://www.semanticscholar.org/paper/An-intuitionistic-fuzzy-entropy-measure-based-on-Guo/d0f3a45015874871719fee9de8a1cc8d914ba0bf.

[29] T. Chaira & A. K. Ray, ``A new measure using intuitionistic fuzzy set theory and its application to edge detection'', Applied Soft Computing 8 (2008) 919. https://doi.org/10.1016/j.asoc.2007.07.004.

fig 1

Published

2026-07-22

How to Cite

A novel parametric intuitionistic fuzzy entropy measure with applications to image edge detection. (2026). Journal of the Nigerian Society of Physical Sciences, 8(3), 3359. https://doi.org/10.46481/jnsps.2026.3359

Issue

Volume 8, Issue 3, August 2026

Section

Mathematics & Statistics
Copyright & Licensing

Copyright (c) 2026 Vaishali Manish Joshi, Javid Gani Dar (Author)

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

How to Cite

A novel parametric intuitionistic fuzzy entropy measure with applications to image edge detection. (2026). Journal of the Nigerian Society of Physical Sciences, 8(3), 3359. https://doi.org/10.46481/jnsps.2026.3359

Similar Articles

11-20 of 108

You may also start an advanced similarity search for this article.