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Novel Intuitionistic Fuzzy Distance Based on Tendency and Its Application in Emergency Decision-Making

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Abstract

Intuitionistic fuzzy measures have been widely used in multi-attribute decision-making. However, in the complex decision-making process, only a few distance measures take individual tendencies into account. In this paper, we propose an intuitionistic fuzzy distance measure based on the tendency of decision makers, and give a novel emergency decision-making method using the distance. Firstly, according to the function transformation, we construct a novel distance measure that includes different tendency coefficients of intuitionistic indexes. These indexes are the membership, non-membership and hesitancy of the intuitionistic fuzzy set. Secondly, the proposed distance has been proved that it satisfies the axiomatic characteristics of distance measure. Then using a few examples to illustrate the novel distance in pattern recognition and fuzzy multi-attribute decision-making, while could adapt to decision-making problems more flexible by adjusting tendency coefficients of each intuitionistic index. Finally, applying the proposed distance measure to a real case of online public opinion in the proposed emergency decision-making in this paper, compared with other methods, our distance measure shows more reasonable, effective and superior results in the decision model.

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References

  1. Zadeh, L.A.: Fuzzy sets. Inf. Control 8(3), 338–353 (1965)

    Article  MATH  Google Scholar 

  2. Zadeh, L.A.: The concept of a linguistic variable and its application to approximate reasoning. Inf. Sci. 8(3), 199–249 (1974)

    MathSciNet  MATH  Google Scholar 

  3. Atanassov, K.T.: Intuitionistic fuzzy sets. Fuzzy Sets Syst. 20, 87–96 (1986)

    MATH  Google Scholar 

  4. Valderrama, J.F.B., Valderrama, D.J.L.B.: On lamda clustering method based on typicality degree and intuitionistic fuzzy sets. Expert Syst. Appl. 107, 196–221 (2018)

    Google Scholar 

  5. Gupta, P., Mehlawat, M.K., Grover, N., Pedrycz, W.: Multi-attribute group decision making based on extended TOPSIS method under interval-valued intuitionistic fuzzy environment. Appl. Soft Comput. 69, 554–567 (2018)

    Google Scholar 

  6. Wang, W.J., Zhan, J.M., Mi, J.S.: A three-way decision approach with probabilistic dominance relations under intuitionistic fuzzy information. Inf. Sci. 582, 114–145 (2022)

    MathSciNet  Google Scholar 

  7. Boran, F.E., Akay, D.: A biparametric similarity measure on intuitionistic fuzzy sets with applications to pattern recognition. Inf. Sci. 255, 45–57 (2014)

    MathSciNet  MATH  Google Scholar 

  8. Xiao, F.Y.: A distance measure for intuitionistic fuzzy sets and its application to pattern classification problems. IEEE Trans. Syst. 51(6), 3980–3992 (2019)

    Google Scholar 

  9. Xie, J.L., Wang, H.H., Garibaldi, J.M., Wu, D.R.: Network intrusion detection based on dynamic intuitionistic fuzzy sets. IEEE Trans. Fuzzy Syst. 4, 1–13 (2021)

    Google Scholar 

  10. Jin, F.F., Garg, H., Pei, L., et al.: Multiplicative consistency adjustment model and data envelopment analysis-driven decision-making process with probabilistic hesitant fuzzy preference relations. Int. J. Fuzzy Syst. 22(7), 2319–2332 (2020)

    Google Scholar 

  11. Jin, F.F., Liu, J., Zhou, L., et al.: Consensus-based linguistic distribution large-scale group decision making using statistical inference and regret theory. Group Decis. Negot. 30(4), 813–845 (2021)

    Google Scholar 

  12. Jin, F.F., Pei, L., Liu, J., et al.: Decision-making model with fuzzy preference relations based on consistency local adjustment strategy and DEA. Neural Comput. Appl. 32(15), 11607–11620 (2020)

    Google Scholar 

  13. Chen, S.M., Cheng, S.H., Chiou, C.H.: Fuzzy multiattribute group decision making based on intuitionistic fuzzy sets and evidential reasoning methodology. Inf. Fus. 27, 215–227 (2016)

    Google Scholar 

  14. Yao, O.Y., Witold, P.: A new model for intuitionistic fuzzy multi-attributes decision making. Eur. J. Oper. Res. 249(2), 677–682 (2016)

    MathSciNet  MATH  Google Scholar 

  15. Beliakov, G., Pagola, M., Wilkin, T.: Vector valued similarity measures for Atanassov’s intuitionistic fuzzy sets. Inf. Sci. 280, 352–367 (2014)

    MathSciNet  MATH  Google Scholar 

  16. Xu, D., Xu, Z.S., Liu, S.S., et al.: A spectral clustering algorithm based on intuitionistic fuzzy information. Knowl.-Based Syst. 53, 20–26 (2013)

  17. Kacprzyk, J.: Multistage Fuzzy Control: A Prescriptive Approach. Wiley, New York (1997)

    MATH  Google Scholar 

  18. Chen, S.M.: Measures of similarity between vague sets. Fuzzy Sets Syst. 74(2), 217–223 (1995)

    MathSciNet  MATH  Google Scholar 

  19. Hong, D.H., Kim, C.: A note on similarity measures between vague sets and between elements. Inf. Sci. 115(1–4), 83–96 (1999)

    MathSciNet  MATH  Google Scholar 

  20. Atanassov, K.: Intuitionistic Fuzzy Sets: Theory and Applications, Series in Fuzziness and Soft Computing, Physica-Verlag, Heidelberg (1999)

  21. Hung, W.L., Yang, M.S.: Similarity measures of intuitionistic fuzzy sets based on hausdorff distance. Pattern Recogn. Lett. 25(14), 1603–1611 (2004)

    Google Scholar 

  22. Grzegorzewski, P.: Distances between intuitionistic fuzzy sets and/or interval-valued fuzzy sets based on the hausdorff metric. Fuzzy Sets Syst. 148, 319–328 (2004)

    MathSciNet  MATH  Google Scholar 

  23. Wang, W.Q., Xin, X.L.: Distance measure between intuitionistic fuzzy sets. Pattern Recogn. Lett. 26(13), 2063–2069 (2005)

    Google Scholar 

  24. Hung, W.L., Yang, M.S.: On similarity measures between intuitionistic fuzzy sets. Int. J. Intell. Syst. 23(3), 364–383 (2008)

    MATH  Google Scholar 

  25. Wang, W.J.: New similarity measures on fuzzy sets and on elements. Fuzzy Sets Syst. 85(3), 305–309 (1997)

    MathSciNet  MATH  Google Scholar 

  26. Ngan, R.T., Cuong, B.C., Ali, M.: H-max distance measure of intuitionistic fuzzy sets in decision making. Appl. Soft Comput. 69, 393–425 (2018)

    Google Scholar 

  27. Li, D.F., Cheng, C.T.: New similarity measures of intuitionistic fuzzy sets and application to pattern recognitions. Pattern Recogn. Lett. 23(1–3), 221–225 (2002)

    MATH  Google Scholar 

  28. Mitchell, H.B.: On the Dengfeng-Chuntian similarity measure and its application to pattern recognition. Pattern Recogn. Lett. 24(16), 3101–3104 (2003)

    Google Scholar 

  29. Liang, Z.Z., Shi, P.F.: Similarity measures on intuitionistic fuzzy sets. Pattern Recogn. Lett. 24(15), 2687–2693 (2003)

    MATH  Google Scholar 

  30. Hung, W.L., Yang, M.S.: Similarity measures of intuitionistic fuzzy sets based on \({L_p}\) metric. Int. J. Approx. Reason. 46(1), 120–136 (2007)

  31. Szmidt, E., Kacprzyk, J.: Distances between intuitionistic fuzzy sets. Fuzzy Sets Syst. 114(3), 505–518 (2000)

    MathSciNet  MATH  Google Scholar 

  32. Yang, Y.J., Chiclana, F.: Consistency of 2D and 3D distances of intuitionistic fuzzy sets. Expert Syst. Appl. 39(10), 8665–8670 (2012)

    Google Scholar 

  33. Liu, H.W.: New similarity measures between intuitionistic fuzzy sets and between elements. Math. Comput. Model. 42(1–2), 61–70 (2005)

    MathSciNet  MATH  Google Scholar 

  34. Szmidt, E., Kacprzyk, J.: A similarity Measure for Intuitionistic Fuzzy Sets and Its Application in Supporting Medical Diagnostic Reasoning, Lect. Notes Artif. Intell., Berlin, vol. 3070, pp. 388–393 (2004)

  35. Ye, J.: Cosine similarity measures for intuitionistic fuzzy sets and their applications. Math. Comput. Model. 53(1–2), 91–97 (2011)

    MathSciNet  MATH  Google Scholar 

  36. Chen, S.M., Chang, C.H.: A novel similarity measure between Atanassov’s intuitionistic fuzzy sets based on transformation techniques with applications to pattern recognition. Inf. Sci. 291, 96–114 (2015)

    Article  Google Scholar 

  37. Chen, S.M., Cheng, S.H., Lan, T.C.: A novel similarity measure between intuitionistic fuzzy sets based on the centroid points of transformed fuzzy numbers with applications to pattern recognition. Inf. Sci. 343, 15–40 (2016)

    MathSciNet  MATH  Google Scholar 

  38. Jiang, Q., Jin, X., Lee, S.J., Yao, S.W.: A new similarity/distance measure between intuitionistic fuzzy sets based on the transformed isosceles triangles and its applications to pattern recognition. Expert Syst. Appl. 116, 439–453 (2019)

    Google Scholar 

  39. Garg, H., Rani, D.: Novel distance measures for intuitionistic fuzzy sets based on various triangle centers of isosceles triangular fuzzy numbers and their applications. Expert Syst. Appl. 191, 116–228 (2022)

    Google Scholar 

  40. Vlachos, I.K., Sergiadis, G.D.: Intuitionistic fuzzy information? Applications to pattern recognition. Pattern Recogn. Lett. 28(2), 197–206 (2007)

    Google Scholar 

  41. Garg, H., Kumar, K.: 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 (2018)

    MATH  Google Scholar 

  42. Hwang, C.M., Yang, M.S., Hung, W.L.: New similarity measures of intuitionistic fuzzy sets based on the Jaccard index with its application to clustering. Int. J. Intell. Syst. 33(8), 1672–1688 (2018)

    Google Scholar 

  43. Agell, N., Ganzewinkel, C.J.V., Sánchez, M., Roselló, L., et al.: A consensus model for Delphi processes with linguistic terms and its application to chronic pain in neonates definition. Appl. Soft Comput. 35, 942–948 (2015)

    Google Scholar 

  44. Yue, N., Xie, J.L., Chen, S.L.: Some new basic operations of probabilistic linguistic term sets and their application in multi-criteria decision making. Soft. Comput. 24(16), 1–18 (2020)

    MATH  Google Scholar 

  45. Iancu, I.: Intuitionistic fuzzy similarity measures based on frank t-norms family. Pattern Recogn. Lett. 42, 128–136 (2014)

    Google Scholar 

  46. Zhang, H.M., Yu, L.Y.: New distance measures between intuitionistic fuzzy sets and interval-valued fuzzy sets. Inf. Sci. 245, 181–196 (2013)

    MathSciNet  MATH  Google Scholar 

  47. Zhang, C.Y., Fu, H.Y.: Similarity measures on three kinds of fuzzy sets. Pattern Recogn. Lett. 27(12), 1307–1317 (2006)

    Google Scholar 

  48. Fan, Z.F., Tian, Y.Y., Lang, L., et al.: Research on the evaluation and decision of emergency plan of network public opinion emergencies under uncertain environment. Math. Pract. Theory 49(8), 9–17 (2019). (In Chinese)

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Funding

This work was supported in part by the National Natural Science Foundation of China (Nos.12271211, 12071179), the National Natural Science Foundation of Fujian Province (Nos. 2021J01861), the Project of Education Department of Fujian Province (No. JT180263), the Youth Innovation Fund of Xiamen City (3502Z20206020), the Open Fund of Digital Fujian Big Data Modeling and Intelligent Computing Institute, Pre-Research Fund of Jimei University.

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Authors and Affiliations

  1. School of Science, Jimei University, Xiamen, 361021, Fujian, China

    Jialiang Xie, Xueqing Xu & Feng Li

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  1. Jialiang Xie
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  2. Xueqing Xu
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  3. Feng Li
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Contributions

JX gave the overall framework of the paper and introduction, and XX completed the experiment and the first draft, FL prooved the theorem and revised the paper.

Corresponding author

Correspondence to Feng Li.

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All authors declare that they have no conflict of interest.

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This article does not contain any studies with human participants or animals performed by any of the authors.

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Informed consent was obtained from all individual participants included in the study.

Appendix

Appendix

Example 2

(This data is adapted from [13, 24, 26, 27, 33, 37]). Three known patterns \({A_1}\), \({A_2}\), \({A_3}\) in terms of IFSs are shown as follows:

$${{A_1} = \{< {x}_1 ,1.0,0.0> ,< {x}_2 ,0.8,0.0> , < {x}_3 ,0.7,0.1 > \} } {{A_2} = \{< {x}_1 ,0.8,0.1> ,< {x}_2 ,1.0,0.0> , < {x}_3 ,0.9,0.0 > \} } {{A_3} = \{< {x}_1 ,0.6,0.2> ,< {x}_2 ,0.8,0.0> , < {x}_3 ,1.0,0.0 > \} }$$

then the target of this issue is to classify the pattern B in one of the classes \(A_1, A_2\), and \(A_3\) using distance measures, where

$${{B} = \{< {x}_1 ,0.5,0.3> ,< {x}_2 ,0.6,0.2> , < {x}_3 ,0.8,0.1 > \} }$$

The classification results for different distance measures are shown in Table 8. It can be observed that the pattern B is classified as \({A_3}\) by the proposed distance measure \({d_{mn}}\). Furthermore, most of distance measures, such as \({d_c}\), \({d_{HK}}\), \({d_{LC}}\), etc, classify B as \(A_3\), except for \({{d_{H}}}\) that classifies B as \({{A_1}}\). There still exists some distance measures such as \({d_{VS}}\), which fail to classify B due to “the antilogarithm of natural log is zero”. This result shows that the proposed distance measure has stronger recognition ability in pattern recognition compared with other distance measures.

Table 8 Comparison results for distance measures in Example 2
Full size table

Example 3

(The data is from [45]) Three patterns \({A_1}\),\({A_2}\),\({A_3}\) in terms of IFSs in the universe \({X = \{ {x}_1 ,{x}_2 ,{x}_3 ,{x}_4 ,{x}_5 ,{x}_6 \} }\) are shown as follows:

$${{A_1} = \{< {x}_1 ,0.94,0.0> ,< {x}_2 ,0.88,0.0> , < {x}_3 ,0.82,0.0 >,} {< {x}_4 ,0.78,0.02> ,< {x}_5 ,0.75,0.05> , < {x}_6 ,0.72,0.08 > \} } {{A_2} = \{< {x}_1 ,0.86,0.07> ,< {x}_2 ,0.92,0.04> , < {x}_3 ,0.98,0.01 >, } {< {x}_4 ,0.98,0.0> ,< {x}_5 ,0.95,0.0> , < {x}_6 ,0.92,0.0 > \} } {{A_3} = \{< {x}_1 ,0.66,0.14> ,< {x}_2 ,0.72,0.08> , < {x}_3 ,0.78,0.02 > , } {< {x}_4 ,0.84,0.0> ,< {x}_5 ,0.9,0.0> , < {x}_6 ,0.96,0.0 >\} }$$

The pattern B needs to be classified into one of \({A_1}\),\({A_2}\),\({A_2}\) using the distance measures, where

$${B = \{< {x}_1 ,0.53,0.27> ,< {x}_2 ,0.56,0.24> , < {x}_3 ,0.59,0.21 > , } {< {x}_4 ,0.64,0.18> ,< {x}_5 ,0.7,0.15> , < {x}_6 ,0.76,0.12 >\}}$$

The classification results for different distance measures are shown in Table 9.

Table 9 Comparison results for distance measures in Example 3
Full size table

It can be observed that sample B is classified to the pattern \({A_3}\) by the proposed distance measure \({d_{mn}}\). Most measures can classify the sample B as the pattern \({A_3}\), except for \({d_{VS}}\). This example shows that the proposed distance measure can correctly classify different IFSs compared with other distance measures.

Example 4

(The example is from [46]) Three known patterns \({A_1}\), \({A_2}\), and \({A_2}\) are shown as follows:

$${{A_1} = \{< {x}_1 ,0.2,0.3> ,< {x}_2 ,0.1,0.4> , < {x}_3 ,0.2,0.6 > \} }{{A_2} = \{< {x}_1 ,0.3,0.2> ,< {x}_2 ,0.4,0.01> , < {x}_3 ,0.5.0.3 > \} } {{A_3} = \{< {x}_1 ,0.2,0.3> ,< {x}_2 ,0.4,0.1> , < {x}_3 ,0.5,0.3 > \} }$$

The pattern B needs to be classified into one of \({A_1}\),\({A_2}\),\({A_3}\) using the distance measures, where

$${{B} = \{< {x}_1 ,0.1,0.2> ,< {x}_2 ,0.4,0.5> , < {x}_3 ,0.0,0.0 > \} }$$

The classification results for different measures are shown in Table 10.

Table 10 Comparison results for distance measures in Example 4
Full size table

It can be observed that pattern B is classified to \({A_1}\) by the proposed distance measure \({d_{mn}}\). Most of measures cannot classify the sample B. For example, the sample B cannot be classified by the distance \({d_c}\) and \({d_{HY}^{pk2}}\) since \({d({A}_1 ,B)}={d({A}_3 ,B)}\). The distance measures \({d_{VS}}\) also cannot classify B because the antilogarithm of natural log is zero. It is obvious that the proposed distance measure can improve the performance of classification.

Example 5

(This example is from [15, 45, 47]) In order to make the diagnosis more accurate and reliable, doctors usually determine the patients’ diseases by distance measures or similar measures of IFSs. There are five criteria in the universe of disease X, that is,

$${X = \{ {x}_1 (Character~of~ stool), {x}_2 (Bellyache), {x}_3 (Ictusileus), {x}_4 (Chronics{-}ileus), {x}_5 (Anemia)\} }$$

The patient may fall into any of the following states by medical diagnosis:

$${A = \{ {A}_1 (metastasis), {A}_2 (recurrence),} {{A}_3 (bad), {A}_4 (well)\} }$$

which are represented as below:

$${{A}_1 (metastasis) = \{< {x}_1 ,0.4,0.4> ,< {x}_2 ,0.3,0.3> , < {x}_3 ,0.5,0.1 > , }{< {x}_4 ,0.5,0.2> , < {x}_5 ,0.6,0.2 > \} } {{A}_2 (recurrence) = \{< {x}_1 ,0.2,0.6> ,< {x}_2 ,0.3,0.5> , < {x}_3 ,0.2,0.3 > , } {< {x}_4 ,0.7,0.1> , < {x}_5 ,0.8,0.0 > \} } {{A}_3 (bad) = \{< {x}_1 ,0.1,0.9> ,< {x}_2 ,0.0,0.1> , < {x}_3 ,0.2,0.7 > , } {< {x}_4 ,0.1,0.8> , < {x}_5 ,0.2,0.8 > \} } {{A}_4 (well) = \{< {x}_1 ,0.8,0.2> ,< {x}_2 ,0.9,0.0> , < {x}_3 ,1.0,0.0 > , } {< {x}_4 ,0.7,0.2> , < {x}_5 ,0.6,0.4 > \} }$$

The pattern B needs to be classified into one of \({A_1}\), \({A_2}\), \({A_3}\) and \({A_4}\) using the distance measures, where

$${{B} = \{< {x}_1 ,0.3,0.5> ,< {x}_2 ,0.4,0.4> ,< {x}_3 ,0.6,0.2> \} < {x}_4 ,0.5,0.1 > ,} { < {x}_5 ,0.9,0.0 > \} }.$$

The classification results for different measures are shown in Table 11. It can be observed that the sample is classified as the pattern \({A_1}\) by proposed distance measure \({d_{mn}}\), while most measures cannot classify the patient B. For example, for \({d_{HK}}\), \({d_{HY}^{pk2}}\)and \({d_{LS}^E}\), \({d({A}_1 ,B)}= {d({A}_2 ,B)}\). Therefore, the proposed distance measure can get better performance compared with other distance measures between IFSs.

Table 11 Comparison results for distance measures in Example 5
Full size table

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Xie, J., Xu, X. & Li, F. Novel Intuitionistic Fuzzy Distance Based on Tendency and Its Application in Emergency Decision-Making. Int. J. Fuzzy Syst. 25, 2295–2311 (2023). https://doi.org/10.1007/s40815-023-01503-3

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