A particularly useful assessment tool for evaluating uncertainty and dealing with fuzziness is the Fermatean fuzzy set (FFS), which expands the membership and non-membership degree requirements. Distance measurement has been extensively employed in several fields as an essential approach that may successfully disclose the differences between fuzzy sets. In this article, we discuss various novel distance measures in Fermatean hesitant fuzzy environments as research on distance measures for FFS is in its early stages. These new distance measures include weighted distance measures and ordered weighted distance measures. This justification serves as the foundation for the construction of the generalized Fermatean hesitation fuzzy hybrid weighted distance (DGFHFHWD) scale, as well as the discussion of its weight determination mechanism, associated attributes and special forms. Subsequently, we present a new decision-making approach based on DGFHFHWD and TOPSIS, where the weights are processed by exponential entropy and normal distribution weighting, for the multi-attribute decision-making (MADM) issue with unknown attribute weights. Finally, a numerical example of choosing a logistics transfer station and a comparative study with other approaches based on current operators and FFS distance measurements are used to demonstrate the viability and logic of the suggested method. The findings illustrate the ability of the suggested MADM technique to completely present the decision data, enhance the accuracy of decision outcomes and prevent information loss.
Citation: Chuan-Yang Ruan, Xiang-Jing Chen, Shi-Cheng Gong, Shahbaz Ali, Bander Almutairi. A decision-making framework based on the Fermatean hesitant fuzzy distance measure and TOPSIS[J]. AIMS Mathematics, 2024, 9(2): 2722-2755. doi: 10.3934/math.2024135
A particularly useful assessment tool for evaluating uncertainty and dealing with fuzziness is the Fermatean fuzzy set (FFS), which expands the membership and non-membership degree requirements. Distance measurement has been extensively employed in several fields as an essential approach that may successfully disclose the differences between fuzzy sets. In this article, we discuss various novel distance measures in Fermatean hesitant fuzzy environments as research on distance measures for FFS is in its early stages. These new distance measures include weighted distance measures and ordered weighted distance measures. This justification serves as the foundation for the construction of the generalized Fermatean hesitation fuzzy hybrid weighted distance (DGFHFHWD) scale, as well as the discussion of its weight determination mechanism, associated attributes and special forms. Subsequently, we present a new decision-making approach based on DGFHFHWD and TOPSIS, where the weights are processed by exponential entropy and normal distribution weighting, for the multi-attribute decision-making (MADM) issue with unknown attribute weights. Finally, a numerical example of choosing a logistics transfer station and a comparative study with other approaches based on current operators and FFS distance measurements are used to demonstrate the viability and logic of the suggested method. The findings illustrate the ability of the suggested MADM technique to completely present the decision data, enhance the accuracy of decision outcomes and prevent information loss.
| [1] |
Y. Seo, S. Kim, O. Kisi, V. P. Singh, Daily water level forecasting using wavelet decomposition and artificial intelligence techniques, J. Hydrol., 520 (2015), 224-243. https://doi.org/10.1016/j.jhydrol.2014.11.050 doi: 10.1016/j.jhydrol.2014.11.050
|
| [2] |
G. Wei, M. Lu, Pythagorean fuzzy power aggregation operators in multiple attribute decision making, Int. J. Intell. Syst., 33 (2018), 169-186. https://doi.org/10.1002/int.21946 doi: 10.1002/int.21946
|
| [3] |
O. Castillo, L. Amador-Angulo, J. R. Castro, M. Garcia-Valdez, A comparative study of type-1 fuzzy logic systems, interval type-2 fuzzy logic systems and generalized type-2 fuzzy logic systems in control problems, Inform. Sci., 354 (2016), 257-274. https://doi.org/10.1016/j.ins.2016.03.026 doi: 10.1016/j.ins.2016.03.026
|
| [4] |
G. Wei, Y. Wei, Similarity measures of Pythagorean fuzzy sets based on the cosine function and their applications, Int. J. Intell. Syst., 33 (2018), 634-652. https://doi.org/10.1002/int.21965 doi: 10.1002/int.21965
|
| [5] |
L. Sahoo, Some score functions on Fermatean fuzzy sets and its application to bride selection based on TOPSIS method, Int. J. Fuzzy Syst. Appl., 10 (2021), 18-29. https://doi.org/10.4018/IJFSA.2021070102 doi: 10.4018/IJFSA.2021070102
|
| [6] |
H. T. X. Chi, F. Y. Vincent, Ranking generalized fuzzy numbers based on centroid and rank index, Appl. Soft Comput., 68 (2018), 283-292. https://doi.org/10.1016/j.asoc.2018.03.050 doi: 10.1016/j.asoc.2018.03.050
|
| [7] |
M. S. Kuo, G. S. Liang, W. C. Huang, Extensions of the multicriteria analysis with pairwise comparison under a fuzzy environment, Int. J. Approx. Reason., 43 (2006), 268-285. https://doi.org/10.1016/j.ijar.2006.04.006 doi: 10.1016/j.ijar.2006.04.006
|
| [8] |
J. Pan, S. Rahman, Multiattribute utility analysis with imprecise information: An enhanced decision support technique for the evaluation of electric generation expansion strategies, Electr. Pow. Syst. Res., 46 (1998), 101-109. https://doi.org/10.1016/S0378-7796(98)00022-4 doi: 10.1016/S0378-7796(98)00022-4
|
| [9] |
S. Y. Chou, Y. H. Chang, C. Y. Shen, A fuzzy simple additive weighting system under group decision-making for facility location selection with objective/subjective attributes, Eur. J. Oper. Res., 189 (2008), 132-145. https://doi.org/10.1016/j.ejor.2007.05.006 doi: 10.1016/j.ejor.2007.05.006
|
| [10] | C. L. Hwang, K. Yoon, Methods for multiple attribute decision making, In: Multiple Attribute Decision Making, Berlin, Heidelberg: Springer, 1981, 58-191. https://doi.org/10.1007/978-3-642-48318-9_3 |
| [11] |
G. Nalcaci, A. Özmen, G. W. Weber, Long-term load forecasting: models based on MARS, ANN and LR methods, Cent. Eur. J. Oper. Res., 27 (2019), 1033-1049. https://doi.org/10.1007/s10100-018-0531-1 doi: 10.1007/s10100-018-0531-1
|
| [12] |
M. A. Ahmadi, M. Ebadi, A. Shokrollahi, S. M. J. Majidi, Evolving artificial neural network and imperialist competitive algorithm for prediction oil flow rate of the reservoir, Appl. Soft Comput., 13 (2013), 1085-1098. https://doi.org/10.1016/j.asoc.2012.10.009 doi: 10.1016/j.asoc.2012.10.009
|
| [13] |
A. F. Hayes, A. K. Montoya, A tutorial on testing, visualizing, and probing an interaction involving a multicategorical variable in linear regression analysis, Commun. Methods. Meas., 11 (2017), 1-30. https://doi.org/10.1080/19312458.2016.1271116 doi: 10.1080/19312458.2016.1271116
|
| [14] |
L. A. Zadeh, Fuzzy sets, Inf. Control, 8 (1965), 338-353. https://doi.org/10.1016/S0019-9958(65)90241-X doi: 10.1016/S0019-9958(65)90241-X
|
| [15] | K. T. Atanassov, Intuitionistic fuzzy sets, Fuzzy Sets Syst., 20 (1986), 87-96. https://dl.acm.org/doi/10.5555/1708507.1708520 |
| [16] |
Z. Xu, Intuitionistic fuzzy aggregation operator, IEEE T. Fuzzy Syst., 15 (2007), 1179-1187. https://doi.org/10.1109/TFUZZ.2006.890678 doi: 10.1109/TFUZZ.2006.890678
|
| [17] |
H. Garg, A new generalized improved score function of interval-valued intuitionistic fuzzy sets and applications in expert systems, Appl. Soft Comput., 38 (2016), 988-999. https://doi.org/10.1016/j.asoc.2015.10.040 doi: 10.1016/j.asoc.2015.10.040
|
| [18] |
F. Feng, H. Fujita, M. I. Ali, R. R. Yager, X. Liu, Another view on generalized intuitionistic fuzzy soft sets and related multiattribute decision making methods, IEEE T. Fuzzy Syst., 27 (2019), 474-488. https://doi.org/10.1109/TFUZZ.2018.2860967 doi: 10.1109/TFUZZ.2018.2860967
|
| [19] |
R. R. Yager, A. M. Abbasov, Pythagorean membership grades, complex numbers, and decision making, Int. J. Intell. Syst., 28 (2013), 436-452. https://doi.org/10.1002/int.21584 doi: 10.1002/int.21584
|
| [20] |
Z. Li, G. Wei, M. Lu, Pythagorean fuzzy hamy mean operators in multiple attribute group decision making and their application to supplier selection, Symmetry, 10 (2018), 505. https://doi.org/10.3390/sym10100505 doi: 10.3390/sym10100505
|
| [21] |
K. Naeem, M. Riaz, X. Peng, D. Afzal, Pythagorean fuzzy soft MCGDM methods based on TOPSIS, VIKOR and aggregation operators, J. Intell. Fuzzy Syst., 37 (2019), 6937-6957. https://doi.org/10.3233/JIFS-190905 doi: 10.3233/JIFS-190905
|
| [22] |
M. Akram, M. Ramzan, M. Deveci, Linguistic Pythagorean fuzzy CRITIC-EDAS method for multiple-attribute group decision analysis, Eng. Appl. Artif. Intell., 119 (2023), 105777. https://doi.org/10.1016/j.engappai.2022.105777 doi: 10.1016/j.engappai.2022.105777
|
| [23] |
S. Singh, A. H. Ganie, On some correlation coefficients in Pythagorean fuzzy environment with applications, Int. J. Intell. Syst., 35 (2020), 682-717. https://doi.org/10.1002/int.22222 doi: 10.1002/int.22222
|
| [24] |
R. Verma, J. M. Merigó, On generalized similarity measures for Pythagorean fuzzy sets and their applications to multiple attribute decision‐making, Int. J. Intell. Syst., 34 (2019), 2556-2583. https://doi.org/10.1002/int.22160 doi: 10.1002/int.22160
|
| [25] |
T. Senapati, R. R. Yager, Fermatean fuzzy sets, J. Ambient Intell. Hum. Comput., 11 (2020), 663-674. https://doi.org/10.1007/s12652-019-01377-0 doi: 10.1007/s12652-019-01377-0
|
| [26] |
T. Senapati, R. R. Yager, Fermatean fuzzy weighted averaging/geometric operators and its application in multi-criteria decision-making methods, Eng. Appl. Artif. Intell., 85 (2019), 112-121. https://doi.org/10.1016/j.engappai.2019.05.012 doi: 10.1016/j.engappai.2019.05.012
|
| [27] |
Y. Pan, S. Z. Zeng, W. Chen, J. Gu, Service quality evaluation of crowdsourcing logistics platform based on Fermatean fuzzy TODIM and regret theory, Eng. Appl. Artif. Intell., 123 (2023), 106385. https://doi.org/10.1016/j.engappai.2023.106385 doi: 10.1016/j.engappai.2023.106385
|
| [28] |
A. H. Ganie, Multicriteria decision-making based on distance measures and knowledge measures of Fermatean fuzzy sets, Granul. Comput., 7 (2022), 979-998. https://doi.org/10.1007/s41066-021-00309-8 doi: 10.1007/s41066-021-00309-8
|
| [29] |
Z. Deng, J. Wang, New distance measure for Fermatean fuzzy sets and its application, Int. J. Intell. Syst., 37 (2022), 1903-1930. https://doi.org/10.1002/int.22760 doi: 10.1002/int.22760
|
| [30] |
C. Xu, J. Shen, Multi-criteria decision making and pattern recognition based on similarity measures for Fermatean fuzzy sets, J. Intell. Fuzzy Syst., 41 (2021), 5847-5863. https://doi.org/10.3233/JIFS-201557 doi: 10.3233/JIFS-201557
|
| [31] |
L. Sahoo, A new score function based Fermatean fuzzy transportation problem, Results Control Optim., 4 (2022), 100040. https://doi.org/10.1016/j.rico.2021.100040 doi: 10.1016/j.rico.2021.100040
|
| [32] |
L. Zhou, S. Wan, J. Dong, A Fermatean fuzzy ELECTRE method for multi-criteria group decision-making, Informatica, 33 (2022), 181-224. https://doi.org/10.15388/21-INFOR463 doi: 10.15388/21-INFOR463
|
| [33] |
V. Torra, Hesitant fuzzy sets, Int. J. Intell. Syst., 25 (2010), 529-539. https://doi.org/10.1002/int.20418 doi: 10.1002/int.20418
|
| [34] |
J. Peng, J. Wang, X. Wu, Novel multi-criteria decision-making approaches based on hesitant fuzzy sets and prospect theory, Int. J. Inf. Tech. Decis., 15 (2016), 621-643. https://doi.org/10.1142/S0219622016500152 doi: 10.1142/S0219622016500152
|
| [35] |
J. Peng, J. Wang, X. Wu, H. Zhang, X. Chen, The fuzzy cross-entropy for intuitionistic hesitant fuzzy sets and their application in multi-criteria decision-making, Int. J. Syst. Sci., 46 (2015), 2335-2350. https://doi.org/10.1080/00207721.2014.993744 doi: 10.1080/00207721.2014.993744
|
| [36] |
B. Farhadinia, Information measures for hesitant fuzzy sets and interval-valued hesitant fuzzy sets, Inform. Sci., 240 (2013), 129-144. https://doi.org/10.1016/j.ins.2013.03.034 doi: 10.1016/j.ins.2013.03.034
|
| [37] |
M. Khan, S. Abdullah, A. Ali, F. Amin, F. Hussain, Pythagorean hesitant fuzzy Choquet integral aggregation operators and their application to multi-attribute decision-making, Soft Comput., 23 (2019), 251-267. https://doi.org/10.1007/s00500-018-3592-0 doi: 10.1007/s00500-018-3592-0
|
| [38] |
A. Hussain, M. I. Ali, T. Mahmood, Hesitant q-rung orthopair fuzzy aggregation operators with their applications in multi-criteria decision making, Iran. J. Fuzzy Syst., 17 (2020), 117-134. https://doi.org/10.22111/IJFS.2020.5353 doi: 10.22111/IJFS.2020.5353
|
| [39] |
H. M. A. Farid, M. Riaz, B. Almohsin, D. Marinkovic, Optimizing filtration technology for contamination control in gas processing plants using hesitant q-rung orthopair fuzzy information aggregation, Soft Comput., 2023. https://doi.org/10.1007/s00500-023-08588-w doi: 10.1007/s00500-023-08588-w
|
| [40] |
A. R. Mishra, S. M. Chen, P. Rani, Multiattribute decision making based on Fermatean hesitant fuzzy sets and modified VIKOR method, Inform. Sci., 607 (2022), 1532-1549. https://doi.org/10.1016/j.ins.2022.06.037 doi: 10.1016/j.ins.2022.06.037
|
| [41] |
M. Kirişci, Fermatean Hesitant Fuzzy Sets for Multiple Criteria Decision-Making with Applications, Fuzzy Inform. Eng., 15 (2023), 100-127. https://doi.org/10.26599/fie.2023.9270011 doi: 10.26599/fie.2023.9270011
|
| [42] |
A. Khan, M. Aslam, Q. Iqbal, Cyclone disaster assessment based on Fermatean hesitant fuzzy information and extended TOPSIS method, J. Intell. Fuzzy Syst., 44 (2023), 10633-10660. https://doi.org/10.3233/JIFS-222144 doi: 10.3233/JIFS-222144
|
| [43] |
H. Lai, H. Liao, Y. Long, E. K. Zavadskas, A Hesitant Fermatean Fuzzy CoCoSo Method for Group Decision-Making and an Application to Blockchain Platform Evaluation, Int. J. Fuzzy Syst., 24 (2022), 2643-2661. https://doi.org/10.1007/s40815-022-01319-7 doi: 10.1007/s40815-022-01319-7
|
| [44] |
Y. Wang, X. Ma, H. Qin, H. Sun, W. Wei, Hesitant Fermatean fuzzy Bonferroni mean operators for multi-attribute decision-making, Complex Intell. Syst., 2023. https://doi.org/10.1007/s40747-023-01203-3 doi: 10.1007/s40747-023-01203-3
|
| [45] |
C. Y. Ruan, X. J. Chen, L. N. Han, Fermatean Hesitant Fuzzy Prioritized Heronian Mean Operator and Its Application in Multi-Attribute Decision Making, Comput. Mater. Con., 75 (2023), 3204-3222. https://doi.org/10.32604/cmc.2023.035480 doi: 10.32604/cmc.2023.035480
|
| [46] |
L. Sha, Y. Shao, Fermatean Hesitant Fuzzy Choquet Integral Aggregation Operators, IEEE Access, 11 (2023), 38548-38562. https://doi.org/10.1109/ACCESS.2023.3267512 doi: 10.1109/ACCESS.2023.3267512
|
| [47] |
A. R. Mishra, P. Liu, P. Rani, COPRAS method based on interval-valued hesitant Fermatean fuzzy sets and its application in selecting desalination technology, Appl. Soft Comput., 119 (2022), 108570. https://doi.org/10.1016/j.asoc.2022.108570 doi: 10.1016/j.asoc.2022.108570
|
| [48] |
I. Demir, Novel correlation coefficients for interval-valued Fermatean hesitant fuzzy sets with pattern recognition application, Turkish J. Math., 47 (2023), 213-233. https://doi.org/10.55730/1300-0098.3355 doi: 10.55730/1300-0098.3355
|
| [49] |
W. Zeng, H. Cui, Y. Liu, Q. Yin, Z. Xu, Novel distance measure between intuitionistic fuzzy sets and its application in pattern recognition, Iran. J. Fuzzy Syst., 19 (2022), 127-137. https://doi.org/10.22111/IJFS.2022.6947 doi: 10.22111/IJFS.2022.6947
|
| [50] |
Y. Washizawa, S. Hotta, Mahalanobis distance on extended Grassmann manifolds for variational pattern analysis, IEEE T. Neur. Net. Learn. Syst., 25 (2014), 1980-1990. https://doi.org/10.1109/TNNLS.2014.2301178 doi: 10.1109/TNNLS.2014.2301178
|
| [51] |
H. Kamacı, F. Marinkovic, S. Petchimuthu, M. Riaz, S. Ashraf, Novel distance-measures-based extended TOPSIS method under linguistic linear Diophantine fuzzy information, Symmetry, 14 (2022), 2140. https://doi.org/10.3390/sym14102140 doi: 10.3390/sym14102140
|
| [52] |
D. Liu, Y. Liu, L. Wang, Distance measure for Fermatean fuzzy linguistic term sets based on linguistic scale function: An illustration of the TODIM and TOPSIS methods, Int. J. Intell. Syst., 34 (2019), 2807-2834. https://doi.org/10.1002/int.22162 doi: 10.1002/int.22162
|
| [53] |
S. Yang, Y. Pan, S. Zeng, Decision making framework based Fermatean fuzzy integrated weighted distance and TOPSIS for green low-carbon port evaluation, Eng. Appl. Artif. Intell., 114 (2022), 105048. https://doi.org/10.1016/j.engappai.2022.105048 doi: 10.1016/j.engappai.2022.105048
|
| [54] |
M. Kirişci, New cosine similarity and distance measures for Fermatean fuzzy sets and TOPSIS approach, Knowl. Inf. Syst., 65 (2023), 855-868. https://doi.org/10.1007/s10115-022-01776-4 doi: 10.1007/s10115-022-01776-4
|
| [55] |
A. H. Ganie, Multicriteria decision-making based on distance measures and knowledge measures of Fermatean fuzzy sets, Granul. Comput., 7 (2022), 979-998. https://doi.org/10.1007/s41066-021-00309-8 doi: 10.1007/s41066-021-00309-8
|
| [56] |
Z. Deng, J. Wang, New distance measure for Fermatean fuzzy sets and its application, Int. J. Intell. Syst., 37 (2022), 1903-1930. https://doi.org/10.1002/int.22760 doi: 10.1002/int.22760
|
| [57] |
S. Zeng, J. Gu, X. Peng, Low‑carbon cities comprehensive evaluation method based on Fermatean fuzzy hybrid distance measure and TOPSIS, Artif. Intell. Rev., 56 (2023), 8591-8607. https://doi.org/10.1007/s10462-022-10387-y doi: 10.1007/s10462-022-10387-y
|
| [58] |
Z. Xu, J. Chen, Ordered weighted distance measure, J. Syst. Sci. Syst. Eng., 17 (2008), 432-445. https://doi.org/10.1007/s11518-008-5084-8 doi: 10.1007/s11518-008-5084-8
|
| [59] |
L. Zhou, J. Wu, H. Chen, Linguistic continuous ordered weighted distance measure and its application to multiple attributes group decision making, Appl. Soft Comput., 25 (2014), 266-276. https://doi.org/10.1016/j.asoc.2014.09.027 doi: 10.1016/j.asoc.2014.09.027
|
| [60] |
S. Zeng, J. M. Merigo, D. Palacios-Marques, H. Jin, F. Gu, Intuitionistic fuzzy induced ordered weighted averaging distance operator and its application to decision making, J. Intell. Fuzzy Syst., 32 (2017), 11-22. https://doi.org/10.3233/JIFS-141219 doi: 10.3233/JIFS-141219
|
| [61] |
Y. Qin, Y. Liu, Z. Hong, Multicriteria decision making method based on generalized Pythagorean fuzzy ordered weighted distance measures, J. Intell. Fuzzy Syst., 33 (2017), 3665-3675. https://doi.org/10.3233/JIFS-17506 doi: 10.3233/JIFS-17506
|
| [62] |
Z. Xu, M. Xia, Distance and similarity measures for hesitant fuzzy sets, Inform. Sci., 181 (2011), 2128-2138. https://doi.org/10.1016/j.ins.2011.01.028 doi: 10.1016/j.ins.2011.01.028
|
| [63] |
H. Liu, J. You, X. You, Evaluating the risk of healthcare failure modes using interval 2-tuple hybrid weighted distance measure, Comput. Ind. Eng., 78 (2014), 249-258. https://doi.org/10.1016/j.cie.2014.07.018 doi: 10.1016/j.cie.2014.07.018
|
| [64] |
S. Zeng, J. Chen, X. Li, A hybrid method for Pythagorean fuzzy multiple-criteria decision making, Int. J. Inf. Tech. Decis., 15 (2016), 403-422. https://doi.org/10.1142/S0219622016500012 doi: 10.1142/S0219622016500012
|
| [65] |
Q. Ding, Y. Wang, M. Goh, TODIM dynamic emergency decision-making method based on hybrid weighted distance under probabilistic hesitant fuzzy information, Int. J. Fuzzy Syst., 23 (2021), 474-491. https://doi.org/10.1007/s40815-020-00978-8 doi: 10.1007/s40815-020-00978-8
|
| [66] |
S. Zeng, J. Gu, X. Peng, Low-carbon cities comprehensive evaluation method based on Fermatean fuzzy hybrid distance measure and TOPSIS, Artif. Intell. Rev., 56 (2023), 8591-8607. https://doi.org/10.1007/s10462-022-10387-y doi: 10.1007/s10462-022-10387-y
|
| [67] |
Z. Xu, An overview of methods for determining OWA weights, Int. J. Intell. Syst., 20 (2005), 843-865. https://doi.org/10.1002/int.20097 doi: 10.1002/int.20097
|
| [68] |
X. Gou, Z. Xu, H. Liao, Hesitant fuzzy linguistic entropy and cross-entropy measures and alternative queuing method for multiple criteria decision making, Inform. Sci., 388 (2017), 225-246. https://doi.org/10.1016/j.ins.2017.01.033 doi: 10.1016/j.ins.2017.01.033
|
| [69] |
J. Rezaei, T. Nispeling, J. Sarkis, L. Tavasszy, A supplier selection life cycle approach integrating traditional and environmental criteria using the best worst method, J. Clean. Prod., 135 (2016), 577-588. https://doi.org/10.1016/j.jclepro.2016.06.125 doi: 10.1016/j.jclepro.2016.06.125
|
| [70] |
K. Krishnamoorthy, M. Lee, Improved tests for the equality of normal coefficients of variation, Comput. Stat., 29 (2014), 215-232. https://doi.org/10.1007/s00180-013-0445-2 doi: 10.1007/s00180-013-0445-2
|
| [71] |
S. Zeng, Y. Hu, C. Llopis-Albert, Stakeholder-inclusive multi-criteria development of smart cities, J. Bus. Res., 154 (2023), 113281. https://doi.org/10.1016/j.jbusres.2022.08.045 doi: 10.1016/j.jbusres.2022.08.045
|
| [72] |
B. Sennaroglu, G. V. Celebi, A military airport location selection by AHP integrated PROMETHEE and VIKOR methods, Transport. Res. D-Tr. E., 59 (2018), 160-173. https://doi.org/10.1016/j.trd.2017.12.022 doi: 10.1016/j.trd.2017.12.022
|
| [73] |
M. S. A. Khan, F. Anjum, I. Ullah, T. Senapati, S. Moslem, Priority Degrees and Distance Measures of Complex Hesitant Fuzzy Sets With Application to Multi-Criteria Decision Making, IEEE Access, 11 (2023), 13647-13666. https://doi.org/10.1109/ACCESS.2022.3232371 doi: 10.1109/ACCESS.2022.3232371
|
| [74] |
X. Sha, C. Yin, Z. Xu, Weighted hesitant fuzzy Lance distance measure of dimension reduction based on exponential entropy and its application, Control. Decis., 35 (2020), 728-734. https://doi.org/10.13195/j.kzyjc.2018.0910 doi: 10.13195/j.kzyjc.2018.0910
|
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Chuan-Yang Ruan, Xiang-Jing Chen, Shi-Cheng Gong, Shahbaz Ali, Bander Almutairi. A decision-making framework based on the Fermatean hesitant fuzzy distance measure and TOPSIS[J]. AIMS Mathematics, 2024, 9(2): 2722-2755. doi: 10.3934/math.2024135
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