Intuitionistic fuzzy sets (IFSs) are widely applied to decision-support problems such as pattern recognition, multi-criteria decision-making, classification, and clustering analysis problems in an uncertain environment. Then, measures on IFS play an important role to determine either the relationship between objects or objects to standard ones. The main purpose of this paper is to investigate the distance measure of intuitionistic fuzzy sets (IFSs) based on the score function of intuitionistic fuzzy numbers and application in decision-support problems. The proposed measure has overcome some limitations of some existing measures. Next, the new measure is applied to solving pattern recognition, multi-criteria decision-making (MCDM) and classification problems. For the pattern recognition problem, a new index called degree of difference (DoD) is proposed. It is used to evaluate the measures when applied to the pattern recognition problem. The new index reflects confidence better than the degree of confidence (DoC) index when evaluating the application of measures to the pattern recognition problem. In this paper, numerical examples are given to analyze the effectiveness of the proposed measure.
AlcantudJ. C. R.KhamenehA. Z.KilicmanA. (2020). Aggregation of infinite chains of intuitionistic fuzzy sets and their application to choices with temporal intuitionistic fuzzy information. Information Sciences, 514, 106–117. https://doi.org/10.1016/j.ins.2019.12.008
2.
AlkanN.KahramanC. (2022). An intuitionistic fuzzy multi-distance based evaluation for aggregated dynamic decision analysis (IF-DEVADA): Its application to waste disposal location selection. Engineering Applications of Artificial Intelligence, 111, 104809. https://doi.org/10.1016/j.engappai.2022.104809
3.
ArifW.KhanW. A.KhanA.Viet LeH.Thi TranN.van PhamH. (2024). Multi-Criteria decision-making using connection number based TOPSIS method under tripolar fuzzy environment. IEEE Access, 12, 142127–142140. https://doi.org/10.1109/ACCESS.2024.3470336
4.
AshrafZ.KhanM. S.TiwariA.Danish LohaniQ. M. (2021). Difference sequence-based distance measure for intuitionistic fuzzy sets and its application in decision making process. Soft Computing, 25(14), 9139–9161. https://doi.org/10.1007/s00500-021-05875-2
ChengS. H. (2018). Autocratic multiattribute group decision making for hotel location selection based on interval-valued intuitionistic fuzzy sets. Information Sciences, 427, 77–87. https://doi.org/10.1016/j.ins.2017.10.018
7.
ChengC.XiaoF.CaoZ. (2019). A new distance for intuitionistic fuzzy sets based on similarity matrix. IEEE Access, 7, 70436–70446. https://doi.org/10.1109/ACCESS.2019.2919521
8.
DavoudabadiR.MousaviS. M.PatoghiA. (2023). A new fuzzy simulation approach for project evaluation based on concepts of risk, strategy, and group decision making with interval-valued intuitionistic fuzzy sets. Journal of Ambient Intelligence and Humanized Computing, 14(7), 8923–8941. https://doi.org/10.1007/s12652-022-04399-3
9.
EcerF. (2022). An extended MAIRCA method using intuitionistic fuzzy sets for coronavirus vaccine selection in the age of COVID-19. Neural Computing and Applications, 34(7), 5603–5623. https://doi.org/10.1007/s00521-021-06728-7
10.
EjegwaP. A.AgbetayoJ. M. (2023). Similarity-distance decision-making technique and its application via intuitionistic fuzzy pairs. Journal of Computational and Cognitive Engineering, 2(1), 68–74. https://doi.org/10.47852/bonviewJCCE512522514
11.
EjegwaP. A.OnyekeI. C. (2021). Intuitionistic fuzzy statistical correlation algorithm with applications to multi criteria-based decision-making processes. International Journal of Intelligent Systems, 36(3), 1386–1407. https://doi.org/10.1002/int.22347
12.
GargH.KumarK. (2020). A novel exponential distance and its based TOPSIS method for interval-valued intuitionistic fuzzy sets using connection number of SPA theory. Artificial Intelligence Review, 53(1), 595–624. https://doi.org/10.1007/s10462-018-9668-5
13.
GhoushchiS. J.GhiaciA. M.BonabS. R.RanjbarzadehR. (2022). Barriers to circular economy implementation in designing of sustainable medical waste management systems using a new extended decision-making and FMEA models. Environmental Science and Pollution Research International, 29(53), 79735–79753. https://doi.org/10.1007/s11356-022-19018-z
14.
GohainB.ChutiaR.DuttaP. (2022). Distance measure on intuitionistic fuzzy sets and its application in decision-making, pattern recognition, and clustering problems. International Journal of Intelligent Systems, 37(3), 2458–2501. https://doi.org/10.1002/int.22780
15.
GohainB.DuttaP.GogoiS.ChutiaR. (2021). Construction and generation of distance and similarity measures for intuitionistic fuzzy sets and various applications. International Journal of Intelligent Systems, 36(12), 7805–7838. https://doi.org/10.1002/int.22608
16.
GrzegorzewskiP. (2004). Distances between intuitionistic fuzzy sets and/or interval-valued fuzzy sets based on the Hausdorff metric. Fuzzy Sets and Systems, 2, 319–328. https://doi.org/10.1016/j.fss.2003.08.005
17.
HaoZ.XuZ.ZhaoH.ZhangR. (2021). The context-based distance measure for intuitionistic fuzzy set with application in marine energy transportation route decision making. Applied Soft Computing, 101, 107044. https://doi.org/10.1016/j.asoc.2020.107044
18.
HatzimichailidisA. G.PapakostasG. A.KaburlasosV. G. (2012). A novel distance measure of intuitionistic fuzzy sets and its application to pattern recognition problems. International Journal of Intelligent Systems, 27(4), 396–409. https://doi.org/10.1002/int.21529
19.
HeX.LiY.QinK.MengD. (2020). Distance measures on intuitionistic fuzzy sets based on intuitionistic fuzzy dissimilarity functions. Soft Computing, 24(1), 523–541. https://doi.org/10.1007/s00500-019-03932-5
20.
JoshiR.KumarS.GuptaD.KaurH. (2018). A jensen-α-norm dissimilarity measure for intuitionistic fuzzy sets and its applications in multiple attribute decision making. International Journal of Fuzzy Systems, 20(4), 1188–1202. https://doi.org/10.1007/s40815-017-0389-8
21.
KhanW. A., et al. (2024). Some novel concepts of intuitionistic fuzzy directed graphs with application in selecting a suitable place for opening restaurant. Heliyon, 10(14), e33950. https://doi.org/10.1016/j.heliyon.2024.e33950
KozaeA. M.ShokryM.OmranM. (2020). Intuitionistic fuzzy set and its application in Corona COVID-19. Applied and Computational Mathematics, 9(5), 146–154. https://doi.org/10.11648/j.acm.20200905.11
24.
LanL. T. H.TuanT. M.NganT. T.GiangN. L.NgocV. T. N.Van HaiP. (2020). A new complex fuzzy inference system with fuzzy knowledge graph and extensions in decision making. IEEE Access, 8, 164899–164921. https://doi.org/10.1109/ACCESS.2020.3021097
25.
LiuQ. (2022). Evaluation and research on the logistics efficiency of agricultural products with intuitionistic fuzzy information. International Journal of Knowledge-Based and Intelligent Engineering Systems, 26(1), 47–52. https://doi.org/10.3233/KES-220006
26.
LiuY.JiangW. (2020). A new distance measure of interval-valued intuitionistic fuzzy sets and its application in decision making. Soft Computing, 24, 6987–7003. https://doi.org/10.1007/s00500-019-04332-5
27.
LiuJ.MaiJ.LiH.HuangB.LiuY. (2022). On three perspectives for deriving three-way decision with linguistic intuitionistic fuzzy information. Information Sciences, 588, 350–380. https://doi.org/10.1016/j.ins.2021.12.072
28.
LiuY.WeiG.LiuH.XuL. (2022). Group decision making for internet public opinion emergency based upon linguistic intuitionistic fuzzy information. International Journal of Machine Learning and Cybernetics, 13(3), 579–594. https://doi.org/10.1007/s13042-020-01262-9
29.
LiuZ.XiaoF. (2020). An intuitionistic linguistic MCDM model based on probabilistic exceedance method and evidence theory.Applied Intelligence, 50(6), 1979–1995. https://doi.org/10.1007/s10489-020-01638-y
30.
LongC. K.Van HaiP.TuanT. M.Hong LanL. T.NganT. T.ChuanP. M.SonL. H. (2023). A novel Q-learning-based FKG-Pairs approach for extreme cases in decision making. Engineering Applications of Artificial Intelligence, 120. https://doi.org/10.1016/j.engappai.2023.105920
31.
LuoM.ZhaoR. (2018). A distance measure between intuitionistic fuzzy sets and its application in medical diagnosis. Artificial Intelligence in Medicine, 89, 34–39. https://doi.org/10.1016/j.artmed.2018.05.002
32.
MahantaJ.PandaS. (2021). A novel distance measure for intuitionistic fuzzy sets with diverse applications. International Journal of Intelligent Systems, 36(2), 615–627. https://doi.org/10.1002/int.22312
33.
MalikM.GuptaS. K. (2022). An application of fully intuitionistic fuzzy multi-objective linear fractional programming problem in E-education system. International Journal of Fuzzy Systems, 24(8), 3544–3563. https://doi.org/10.1007/s40815-022-01348-2
34.
NganR. T.CuongB. C.AliM. (2018). H-max distance measure of intuitionistic fuzzy sets in decision making. Applied Soft Computing, 69, 393–425. https://doi.org/10.1016/j.asoc.2018.04.036
35.
Nguyen VuS. L.NguyenT. D.PhamV. H. (2024). A Robust Component-Based Template Matching Approach Using Document Layout Graph for Extracting Information. Advances and Trends in Artificial Intelligence. Theory and Applications. IEA/AIE 2024. Lecture Notes in Computer Science, vol 14748, Singapore, Springer.
36.
OhlanA. (2022). Novel entropy and distance measures for interval-valued intuitionistic fuzzy sets with application in multi-criteria group decision-making. International Journal of General Systems, 51(4), 413–440. https://doi.org/10.1080/03081079.2022.2036138
37.
ParkashO.KumarR. (2017). Modified fuzzy divergence measure and its applications to medical diagnosis and MCDM. Risk and Decision Analysis, 6(3), 231–237. https://doi.org/10.3233/RDA-170126
38.
PatelA.JanaS.MahantaJ. (2023). Intuitionistic fuzzy EM-SWARA-TOPSIS approach based on new distance measure to assess the medical waste treatment techniques. Applied Soft Computing, 144, 110521. https://doi.org/10.1016/j.asoc.2023.110521
39.
PatelA.KumarN.MahantaJ. (2023). A 3d distance measure for intuitionistic fuzzy sets and its application in pattern recognition and decision-making problems. New Mathematics and Natural Computation, 19(02), 447–472. https://doi.org/10.1142/S1793005723500163
40.
PerçinS. (2022). Circular supplier selection using interval-valued intuitionistic fuzzy sets. Environment. Development and Sustainability, 24(4), 5551–5581. https://doi.org/10.1007/s10668-021-01671-y
41.
PhamH. V.DuongP. V.TranD. T.LeeJ. H. (2023). A novel approach of voterank-based knowledge graph for improvement of multi-attributes influence nodes on social networks. Journal of Artificial Intelligence and Soft Computing, 13(3), 165–180. https://doi.org/10.2478/jaiscr-2023-0013
42.
PhamH. V.HoangT. L.HungN. Q., et al. (2023). Proposed intelligent decision support system using hedge algebra integrated with picture fuzzy relations for improvement of decision-making in medical diagnoses. International Journal of Fuzzy Systems, 25, 3260–3270. https://doi.org/10.1007/s40815-023-01548-4
43.
PhamH. V.MooreP. (2024). Applied hedge algebra approach with multilingual large language models to extract hidden rules in datasets for improvement of generative AI applications. Information, 15, 381. https://doi.org/10.3390/info15070381
44.
PhamV. H.NguyenQ. H.TruongV. P.TranL. P. T. (2022). The proposed context matching algorithm and its application for user preferences of tourism in COVID-19 pandemic. In International Conference on innovative computing and communications, lecture notes in networks and systems (vol. 471, pp. 285–293). Singapore: Springer. https://doi.org/10.1007/978-981-19-2535-1_22
45.
SongY.WangX.QuanW.HuangW. (2019). A new approach to construct similarity measure for intuitionistic fuzzy sets. Soft Computing, 23(6), 1985–1998. https://doi.org/10.1007/s00500-017-2912-0
ThaoN. X. (2021a). MOORA Models based on new score function of interval-valued intuitionistic sets and apply to select materials for mushroom cultivation. Neural Computing and Applications, 33, 10975–10985. https://doi.org/10.1007/s00521-020-05648-2
48.
ThaoN. X. (2021b). Some new entropies and divergence measures of intuitionistic fuzzy sets based on Archimedean t-conorm and application in supplier selection. Soft Computing, 25(7), 5791–5805. https://doi.org/10.1007/s00500-021-05575-x
49.
ThaoN. X.AliM.NhungL. T.GianeyH. K.SmarandacheF. (2019). A new multi-criteria decision-making algorithm for medical diagnosis and classification problems using divergence measure of picture fuzzy sets. Journal of Intelligent & Fuzzy Systems, 37(6), 7785–7796. https://doi.org/10.3233/JIFS-182697
50.
ThaoN. X.DuongT. T. T. (2019). Selecting target market by similar measures in interval intuitionistic fuzzy set. Technological and Economic Development of Economy, 25(5), 934–950. https://doi.org/10.3846/tede.2019.10290
51.
TranD. Q.NguyenX. T.NguyenD. D.NguyenQ. T. (2022). A novel entropy of intuitionistic fuzzy sets based on similarity and its application in finance. Journal of Intelligent & Fuzzy Systems, 43(4), 3899–3909. https://doi.org/10.3233/JIFS-211563
52.
Van PhamH., et al. (2023). Proposed distance and entropy measures of picture fuzzy sets in decision support systems. Journal of Intelligent & Fuzzy Systems, 44(4), 6775–67916. https://doi.org/10.3233/JIFS-221556
53.
Van PhamH.KhoaN. D.BuiT. T. H.GiangN. T. H.MooreP. (2022). Applied picture fuzzy sets for group decision-support in the evaluation of pedagogic systems. International journal of mathematical. Engineering and Management Sciences, 7(2), 243–257. https://doi.org/10.33889/IJMEMS.2022.7.2.016
54.
Van PhamH.TuanN. T.TuanL. M.MooreP. (2024). IDGCN: A proposed knowledge graph embedding with graph convolution network for context-aware recommendation systems. Journal of Organizational Computing and Electronic Commerce, 35(2), 136–156. https://doi.org/10.1080/10919392.2024.2435111
55.
WangF.WanS. (2021). A comprehensive group decision-making method with interval-valued intuitionistic fuzzy preference relations. Soft Computing, 25(1), 343–362. https://doi.org/10.1007/s00500-020-05145-7
56.
WangZ.XiaoF.DingW. (2020). Interval-valued intuitionistic fuzzy jenson-shannon divergence and its application in multi-attribute decision making. Applied Intelligence, 52(14), 16168–16184. https://doi.org/10.1007/s10489-022-03347-0
XiaoF. (2019). A distance measure for intuitionistic fuzzy sets and its application to pattern classification problems. IEEE transactions on systems. Man, and Cybernetics: Systems, 51(6), 3980–3992. https://doi.org/10.1109/TSMC.2019.2958635
59.
XieD.XiaoF.PedryczW. (2022). Information quality for intuitionistic fuzzy values with its application in decision making. Engineering Applications of Artificial Intelligence, 109, 104568. https://doi.org/10.1016/j.engappai.2021.104568
60.
Xuan ThaoN. (2018). A new correlation coefficient of the intuitionistic fuzzy sets and its application. Journal of Intelligent Fuzzy Systems, 35(2), 1959–1968. https://doi.org/10.3233/JIFS-171589
61.
YangY.ChiclanaF. (2012). Consistency of 2D and 3D distances of intuitionistic fuzzy sets. Expert Systems with Applications, 39(10), 8665–8670. https://doi.org/10.1016/j.eswa.2012.01.199
