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Vol 10, No 3:

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Trigonometric Divergence Measures of Intuitionistic Fuzzy Sets based on Jensen-Shannon Inequality for Solving Bacteria Detection and Decision-Making Problem
Abstract
In this present era, it is a big challenge to make a good decision in some circumstances with distinct attributes. Various authors have provided their individual decision-making methods about how to handle these circumstances and make the right decision. This study adopts to solve the multi-criteria decision-making problem and make an appropriate decision with the help of some different attributes. In this communication, we will develop two Jensen-Shannon trigonometric divergence measures for intuitionistic fuzzy sets on the conception of Jensen-Shannon inequality and axiomatically discuss the various properties. Both proposed measures are obtained by the setting of IFSs theory, and these are completely different innovative from the studies so far also different from each other. The present study is mainly furnished with the decision-making techniques included TOPSIS, MOORA, MADM and bacteria detection problem. Numerous authors have been provided their individual decision-making methods about how to handle these circumstances and make the right decision. Furthermore, with the help of a numerical example the developed divergence measures utilizing to solve the decision-making problem as well as bacteria detection problem for detect the correct bacteria based on the shape of unknown bacteria. In addition, the graphically representation of proposed and existing divergence measures by utilizing created techniques with their comparison. The representation of the proposed study will improve to solve the decision-making problems and provides the reliable decision.
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References
1. A. De Luca and S. Termini; A Definition of a Non-probabilistic Entropy in the Setting of Fuzzy Sets Theory. Information and Control, 20(4), 301–312 (1972).
2. A. Hari Ganesh and N. Jaimaruthi; Testing of Fuzzy Hypothesis Using Fuzzy Data under Fuzzy Environment Based On Left and Right Areas of Fuzzy Number. International Journal of Statistics and Reliability Engineering, 9(2), 262–281 (2022).
3. A.MariappanandM.Pachamuthu;AStatisticalHypothesisTestingofAnalysisofVarianceforTwoWay Classification in Fuzzy Environments. International Journal of Statistics and Reliability Engineering, 8(2), 222–231 (2020).
4. A. Ohlan; Intuitionistic Fuzzy Exponential Divergence: Application in Multi-Attribute Decision Making. Journal of Intelligent and Fuzzy Systems, 30(3), 1519–1530 (2016).
5. A. Rényi; On Measures of Entropy and Information. Fourth Berkeley Symposium on Mathematical Statistics and Probability, 1(c), 547–561 (1961).
6. A. Raj; M. Rahul; K. Singh and D. Motwani; Intuitionistic Fuzzy Divergence Measure-Based Electre Method for Performance of Cellular Mobile Telephone Service Providers. Neural Computing and Applications, 32(8), 3901–3921 (2020).
7. A. Rani; O. Sharma and P. Gupta; Logarithmic Information Measures for Fuzzy Soft Matrices. International Journal of Statistics and Reliability Engineering, 7(1), 131–139 (2020).
8. A.R. Mishra; Intuitionistic Fuzzy Information Measures with Application in Rating of Township Development. Iranian Journal of Fuzzy Systems, 13(3), 49–70 (2016).
9. A.R.Mishra;R.KumariandD.K.Sharma;IntuitionisticFuzzyDivergenceMeasure-BasedMulti-Criteria Decision-Making Method. Neural Computing and Applications, 31(7), 2279–2294 (2019).
10. A.R. Mishra; A.K. Garg; H. Purwar; P. Rana; H. Liao and A. Mardani; An Extended Intuitionistic Fuzzy Multi-Attributive Border Approximation Area Comparison Approach for Smartphone Selection using Discrimination Measures. Informatica (Netherlands), 32(1), 119–143 (2021).
11.A. Srivastava and S. Maheshwari; Decision Making in Medical Investigations using New Divergence Measures for Intuitionistic Fuzzy Sets. Iranian Journal of Fuzzy Systems, 13(1), 25–44 (2016).
12. C.E. Shannon; A Mathematical Theory of Communication. Bell System Technical Journal, 27(4), 623–656 (1948).
13. E.B. Jamkhaneh and H. Garg; Some New Operations over the Generalized Intuitionistic Fuzzy Sets and Their Application to Decision-Making Process. Granular Computing, 3(2), 111–122 (2018).
14.F. Li; Z.H. Lu and L.J. Cai; The Entropy of Vague Sets Based on Fuzzy Sets. Journal of Hauzhong University Sci. Tech., 31(1), 24–25 (2003).
15. G. Beliakov; M. Pagola and T. Wilkin; Vector Valued Similarity Measures for Atanassov’s Intuitionistic Fuzzy Sets. Information Sciences, 280, 352–367 (2014).
16. H. Garg and D. Rani; Novel Exponential Divergence Measure of Complex Intuitionistic Fuzzy Sets with an Application to Decision-Making Process. Scientia Iranica, 28(4), 2439 – 2456 (2021).
17. I. Montes; N.R. Pal; V. Janis and S. Montes; Divergence Measures for Intuitionistic Fuzzy Sets. IEEE Transactions on Fuzzy Systems, 23(2), 444–456 (2015).
18. I.K. Vlachos and G.D. Sergiadis; Intuitionistic Fuzzy Information - Applications to Pattern Recognition. Pattern Recognition Letters, 28(2), 197–206 (2007).
19. J. Fan and W. Xie; Distance Measure and Induced Fuzzy Entropy. Fuzzy Sets and Systems, 104(2), 305– 314 (1999).
20. J. Lin; Divergence Measures Based on the Shannon Entropy. IEEE Transactions on Information Theory, 37(1), 145–151 (1991).
21.J. Mao; D. Yao and C. Wang; A Novel Cross-Entropy and Entropy Measures of IFSs and Their Applications. Knowledge-Based Systems, 48, 37–45 (2013).
22. J. Ye; Two Effective Measures of Intuitionistic Fuzzy Entropy. Computing (Vienna/New York), 87(1–2), 55–62 (2010).
23. K. Hung; Applications of Medical Information : Using an Enhanced Likelihood Measured Approach Based on Intuitionistic Fuzzy Sets. IIE Transactions on Healthcare Systems Engineering, 8300(2), 224–231 (2012).
24. K.T. Atanassov; Intuitionistic Fuzzy Sets. Fuzzy Sets and Systems, 20(1), 87–96 (1986).
25.K.T. Atanassov; New Operations Defined over the intuitionistic Fuzzy Sets. Fuzzy Sets and Systems, 61(2), 137–142 (1994).
26. L.A. Zadeh; Fuzzy Sets. Information and Control, 8, 338–353 (1965).
27.M.D. Ansari; A.R. Mishra and F.T. Ansari; New Divergence and Entropy Measures for Intuitionistic Fuzzy Sets on Edge Detection. International Journal of Fuzzy Systems, 20(2), 474–487 (2018).
28. M. Luo and R. Zhao; A Distance Measure between Intuitionistic Fuzzy Sets and Its Application in Medical Diagnosis. Artificial Intelligence in Medicine, 89, 34–39 (2018).
29.M. Xia and Z. Xu; Entropy/Cross Entropy-Based Group Decision Making under Intuitionistic Fuzzy Environment. Information Fusion, 13(1), 31–47 (2012).
30.N.R. Pal and S.K. Pal; Object-background Segmentation using New Definitions of Entropy. IEE Proceedings E: Computers and Digital Techniques, 136(4), 284–295 (1989).
31. N.R. Pal and D. Bhandari; Some New Information Measures for Fuzzy Sets. Information Sciences, 67(1), 209–228 (1993).
32.O. Sharma; P. Gupta and A. Sheoran; Dimensionality Reduction using Fuzzy Soft Set Theory. International Journal of Statistics and Reliability Engineering, 4(2), 154–158 (2017).
33. P. Arora and V.P. Tomar; Novel Generalized Divergence Measure on Intuitionistic Fuzzy Sets and Its Application. Advances in Fuzzy Systems, 2021, p. 5544993 (2021).
34.P. Rani and D. Jain; Intuitionistic Fuzzy PROMETHEE Technique for Multi-Criteria Decision Making Problems Based on Entropy Measure. Communications in Computer and Information Science, 721, 290– 301 (2017).
35. P. Rani; D. Jain and D.S. Hooda; Extension of Intuitionistic Fuzzy TODIM Technique for Multi-Criteria Decision Making Method Based on Shapley Weighted Divergence Measure. Granular Computing, 4(3), 407–420 (2019).
36. Q.S. Zhang and S.Y. Jiang; A Note on Information Entropy Measures for Vague Sets and Its Applications. Information Sciences, 178(21), 4184–4191 (2008).
37.R. Boora and V. Tomar; Two Trigonometric Intuitionistic Fuzzy Similarity Measures. International Journal of Decision Support System Technology, 14(1), 1–23 (2022).
38. R. Kaushik; R.K. Bajaj and T. Kumar; On Intuitionistic Fuzzy Divergence Measure with Application to Edge Detection. Procedia Computer Science, 70, 2–8 (2015).
39. R. Verma and B.D. Sharma; On Generalized Intuitionistic Fuzzy Divergence (Relative Information) and Their Properties. Journal of Uncertain Systems, 6(4), 308–320 (2012).
40. R. Verma and B.D. Sharma; A New Measure of Inaccuracy with Its Application to Multi-Criteria Decision Making under Intuitionistic Fuzzy Environment. Journal of Intelligent & Fuzzy Systems, 27, 1811–1824 (2014).
41.R. Verma and S. Maheshwari; A New Measure of Divergence with Its Application to Multi-Criteria Decision Making under Fuzzy Environment. Neural Computing and Applications, 28(8), 2335–2350 (2017).
42.S. Gahlot and R.N. Saraswat; A New Tool for Detection of Bacteria and Pattern Recognition by Intuitionistic Fuzzy Measure. Journal of Xi’an University of Architecture & Technology, 11(12), 1416– 1423 (2019).
43. S. Kullback and R.A. Leibler; On Information and Sufficient. The Annals of Mathematical Statistics, 22, 79–86 (1951).
44. S. Maheshwari and A. Srivastava; Application of Intuitionistic Fuzzy Cross Entropy Measure in Decision Making for Medical Diagnosis. International Journal of Mathematical and Computational Sciences, 9(4), 254–258 (2015).
45.S. Montes; I. Couso; P. Gil and C. Bertoluzza Divergence Measure between Fuzzy Sets. International Journal of Approximate Reasoning, 30(3), 91–105 (2005). 46.V. Khatibi and G.A. Montazer; Intuitionistic Fuzzy Set vs. Fuzzy Set Application in Medical Pattern Recognition. Artificial Intelligence in Medicine, 47(1), 43–52 (2009).
47. V.P. Tomar and A. Ohlan; New Parametric Generalized Exponential Fuzzy Divergence Measure. Journal of Uncertainty Analysis and Applications, 2(1), 1–14 (2014).
48. W. Brauers and E.K. Zavadskas; The MOORA Method and Its Application to Privatization in a Transition Economy. Control and Cybernetics, 35(2), 445–469 (2016).
49.W.L. Hung and M.S. Yang; On the J-Divergence of Intuitionistic Fuzzy Sets with Its Application to Pattern Recognition. Information Sciences, 178(6), 1641–1650 (2008).
50. X.G. Shang and W.S. Jiang; A Note on Fuzzy Information Measures. Pattern Recognition Letters, 18(5), 425–432 (1997).
51.Z. Xu and R.R. Yager; Some Geometric Aggregation Operators based on Intuitionistic Fuzzy Sets. International Journal of General Systems, 35(4), 37–41 (2006).
52.Z. Xu and H. Hu; Projection Models for Intuitionistic Fuzzy Multiple Attribute Decision Making. International Journal of Information Technology & Decision Making, 9(2), 267–280 (2010).

ISSN(P) 2350-0174

ISSN(O) 2456-2378

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