Abstract
In this paper, we build the divergence measure of intuitionistic fuzzy sets from the Archimedean t-conorm operators and give their properties. Next, we built the entropy and knowledge measures of intuitionistic fuzzy sets based on their divergence measures. In this paper, relationships between entropy and knowledge measures are also investigated, which gives us many interesting results. We then apply the proposed measures into building the multi-criteria decision-making model. Finally, a numerical example to illustrate the model is also given in this paper.
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References
Ansari MD, Mishra AR, Ansari FT (2018) New divergence and entropy measures for intuitionistic fuzzy sets on edge detection. Int J Fuzzy Syst 20(2):474–487
Atanassov K (1986) Intuitionistic fuzzy sets. Fuzzy Sets Syst 20:87–96
Atanassov K (1999) Intuitionistic fuzzy sets: theory and applications. Physica-Verlang, Wurzburg
Beliakov G, Bustince H, Goswami DP, Mukherjee UK, Pal NR (2011) On averaging operators for Atanassov’s intuitionistic fuzzy sets. Inf Sci 181(6):1116–1124
Chen SM (1995) Measures of similarity between vague sets. Fuzzy Sets Syst 74(2):217–223
Chen TY (2011) Bivariate models of optimism and pessimism in multi-criteria decision-making based on intuitionistic fuzzy sets. Inf Sci 181:2139–2165
Chen L, Peng J, Liu Z, Zhao R (2016) Pricing and effort decisions for a supply chain with uncertain information. Int J Prod Res 55(1):264–284
Chen L, Peng J, Zhang B, Rosyida I (2017) Diversified models for portfolio selection based on uncertain semivariance. Int J Syst Sci 48(3):637–648
Chu CH, Hung KC, Julian P (2014) A complete pattern recognition approach under Atanassov’s intuitionistic fuzzy sets. Knowl-Based Syst 66:36–45
Cuong BC (2014) Picture fuzzy sets. J Comput Sci Cybern 30(4):409–420
Farhadinia B (2013) A theoretical development on the entropy of interval-valued fuzzy sets based on the intuitionistic distance and its relationship with similarity measure. Knowl-Based Syst 39:79–84
Garg H, Kumar K (2018) 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(15):4959–4970
Gong Z, Zhang N, Chiclana F (2018) The optimization ordering model for intuitionistic fuzzy preference relations with utility functions. Knowl-Based Syst 162:174–184
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
Huang B, Li H, Feng G, Zhuang Y (2017) Inclusion measure-based multi-granulation intuitionistic fuzzy decision-theoretic rough sets and their application to ISSA. Knowl-Based Syst 138:220–231
Hung WL, Yang MS (2006) Fuzzy entropy on intuitionistic fuzzy sets. Int J Intell Syst 21(4):443–451
Joshi R, Kumar S (2018) A dissimilarity Jensen–Shannon divergence measure for intuitionistic fuzzy sets. Int J Intell Syst 33(11):2216–2235
Joshi R, Kumar S (2019) A dissimilarity measure based on Jensen Shannon divergence measure. Int J Gen Syst 48(3):280–301
Khatibi V, Montazer GA (2009) Intuitionistic fuzzy set vs. fuzzy set application in medical pattern recognition. Artif Intell Med 47(1):43–52
Le NT, Van Nguyen D, Ngoc CM, Nguyen TX (2018) New dissimilarity measures on picture fuzzy sets and applications. J Comput Sci Cybern 34(3):219–231
Li DF (2004) Some measures of dissimilarity in intuitionistic fuzzy structures. J Comput Syst Sci 68(1):115–122
Liang Z, Shi P (2003) Similarity measures on intuitionistic fuzzy sets. Pattern Recognit Lett 24(15):2687–2693
Liu P, Liu W (2018) Intuitionistic fuzzy interaction Maclaurin symmetric means and their application to multiple-attribute decision-making. Technol Econ Dev Econ 24(4):1533–1559
Liu B, Zhou Q, Ding RX, Ni W, Herrera F (2019a) Defective alternatives detection-based multi-attribute intuitionistic fuzzy large-scale decision making model. Knowl-Based Syst 186:1–14
Liu J, Zhou X, Huang B, Li H, Ju H (2019b) Combining similarity and divergence measures for intuitionistic fuzzy information clustering. J Intell Fuzzy Syst 36(4):3195–3209
Mishra AR, Kumari R, Sharma DK (2019) Intuitionistic fuzzy divergence measure-based multi-criteria decision-making method. Neural Comput Appl 31:2279–2294
Montes I, Pal NR, Janiš V, Montes S (2014) Divergence measures for intuitionistic fuzzy sets. IEEE Trans Fuzzy Syst 23(2):444–456
Montes I, Pal NR, Montes S (2018) Entropy measures for Atanassov intuitionistic fuzzy sets based on divergence. Soft Comput 22(15):5051–5071
Ngan RT, Ali M (2018) δ-equality of intuitionistic fuzzy sets: a new proximity measure and applications in medical diagnosis. Appl Intell 48(2):499–525
Nguyen HT, Walker CL, Walker EA (2018) A first course in fuzzy logic. CRC Press, Boca Raton
Otay İ, Oztaysi B, Onar SC, Kahraman C (2017) Multi-expert performance evaluation of healthcare institutions using an integrated intuitionistic fuzzy AHP&DEA methodology. Knowl-Based Syst 133:90–106
Rani P, Jain D, Hooda DS (2019) Extension of intuitionistic fuzzy TODIM technique for multi-criteria decision making method based on shapley weighted divergence measure. Granul Comput 4(3):407–420
Rao C, Lin H, Liu M (2020) Design of comprehensive evaluation index system for P2P credit risk of “three rural” borrowers. Soft Comput 24:11493–11509
Rao C, Liu M, Goh M, Wen J (2020) 2-stage modified random forest model for credit risk assessment of P2P network lending to “Three Rurals” borrowers. Appl Soft Comput 95:1–12
Shi LL, Ye J (2013) Study on fault diagnosis of turbine using an improved cosine similarity measure for vague sets. J Appl Sci 13(10):1781–1786
Smarandache F (1999) A unifying field in logics, neutrosophy: neutrosophic probability, set and logic. American Research Press, Rehoboth
Song Y, Fu Q, Wang YF, Wang X (2019) Divergence-based cross entropy and uncertainty measures of Atanassov’s intuitionistic fuzzy sets with their application in decision making. Appl Soft Comput 84:1–15
Szmidt E, Kacprzyk J (2001) Entropy for intuitionistic fuzzy sets. Fuzzy Sets Syst 118(3):467–477
Thao NX (2020a) Similarity measures of picture fuzzy sets based on entropy and their application in MCDM. Pattern Anal Appl 23(3):1203–1213
Thao NX (2020b) A new correlation coefficient of the Pythagorean fuzzy sets and its applications. Soft Comput 24:9467–9478
Thao NX (2021) MOORA models based on new score function of interval-valued intuitionistic sets and apply to select materials for mushroom cultivation. Neural Comput Appl. https://doi.org/10.1007/s00521-020-05648-2
Thao NX, Đinh NV (2015) Rough picture fuzzy set and picture fuzzy topologies. J Comput Sci Cybern 31(3):245–254
Thao NX, Duong TTT (2019) Selecting target market by similar measures in interval intuitionistic fuzzy set. Technol Econ Dev Econ 25(5):934–950
Thao NX, Smarandache F (2019) A new fuzzy entropy on pythagorean fuzzy sets. J Intell Fuzzy Syst 37(1):1065–1074
Thao NX, Smarandache F, Dinh NV (2017) Support-neutrosophic set: a new concept in soft computing. Neutrosophic Sets Syst 16:93–98
Thao NX, Cuong BC, Ali M, Lan LH (2018) Fuzzy equivalence on standard and rough neutrosophic sets and applications to clustering analysis. In: Information systems design and intelligent applications, pp 834–842
Thao NX, Ali M, Smarandache F (2019a) An intuitionistic fuzzy clustering algorithm based on a new correlation coefficient with application in medical diagnosis. J Intell Fuzzy Syst 36(1):189–198
Thao NX, Ali M, Nhung LT, Gianey HK, Smarandache F (2019b) A new multi-criteria decision making algorithm for medical diagnosis and classification problems using divergence measure of picture fuzzy sets. J Intell Fuzzy Syst 37(6):7785–7796
Verma R, Sharma BD (2013) Exponential entropy on intuitionistic fuzzy set. Kybernetika 49(1):114–127
Vlachos IK, Sergiadis GD (2007) Intuitionistic fuzzy information–applications to pattern recognition. Pattern Recognit Lett 28(2):197–206
Wang W, Xin X (2005) Distance measure between intuitionistic fuzzy sets. Pattern Recognit Lett 26(13):2063–2069
Wei CP, Gao ZH, Guo TT (2012) An intuitionistic fuzzy entropy measure based on the trigonometric function. Control Decis 27:571–574
Xia M, Xu Z, Zhu B (2012) Some issues on intuitionistic fuzzy aggregation operators based on Archimedean t-conorm and t-norm. Knowl-Based Syst 31:78–88
Xiao Q, Chen L, Xie M, Wang C (2020) Optimal contract design in sustainable supply chain: Interactive impacts of fairness concern and overconfidence. J Oper Res Soc. https://doi.org/10.1080/01605682.2020.1727784
Xuan Thao N (2018) A new correlation coefficient of the intuitionistic fuzzy sets and its application. J Intell Fuzzy Syst 35(2):1959–1968
Xuan Thao N, Van Dinh N (2015) Support-intuitionistic fuzzy set: a new concept for soft computing. Int J Intell Syst Appl 7(4):11–16
Ye J (2010) Two effective measures of intuitionistic fuzzy entropy. Computing 87(1–2):55–62
Ye J (2011) Cosine similarity measures for intuitionistic fuzzy sets and their applications. Math Comput Model 53:91–97
Ye J (2016) Similarity measures of intuitionistic fuzzy sets based on cosine function for the decision making of mechanical design schemes. J Intell Fuzzy Syst 30(1):151–158
Zadeh L (1965) Fuzzy sets. Inf Control 8:338–353
Zeng WY, Li HX (2006) Relationship between similarity measure and entropy of interval valued fuzzy sets. Fuzzy Sets Syst 157:1477–1484
Zhang QS, Jiang SY (2008) A note on information entropy measures for vague sets and its applications. Inf Sci 178(21):4184–4191
Zhu YJ, Li DF (2016) A new definition and formula of entropy for intuitionistic fuzzy sets. J Intell Fuzzy Syst 30(6):3057–3066
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NXT reads the documentation and builds the measures, builds the model and applies.
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Thao, N.X. Some new entropies and divergence measures of intuitionistic fuzzy sets based on Archimedean t-conorm and application in supplier selection. Soft Comput 25, 5791–5805 (2021). https://doi.org/10.1007/s00500-021-05575-x
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DOI: https://doi.org/10.1007/s00500-021-05575-x