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Interval-Valued \(E_N\)-functions and Similarity Measures

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New Trends in Aggregation Theory (AGOP 2019)

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Abstract

In this work we introduce a definition of interval-valued similarity measures taking into account the width of the input intervals. We discuss a construction method based on the aggregation of interval-valued restricted equivalence functions.

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References

  1. Asiain, M.J., Bustince, H., Mesiar, R., Kolesárová, A., Takáč, Z.: Negations with respect to admissible orders in the interval-valued fuzzy set theory. IEEE Trans. Fuzzy Syst. 26, 556–568 (2018)

    Article  Google Scholar 

  2. Barrenechea, E., Bustince, H., De Baets, B., Lopez-Molina, C.: Construction of interval-valued fuzzy relations with application to the generation of fuzzy edge images. IEEE Trans. Fuzzy Syst. 19(5), 819–830 (2011)

    Article  Google Scholar 

  3. Barrenechea, E., Fernandez, J., Pagola, M., Chiclana, F., Bustince, H.: Construction of interval-valued fuzzy preference relations from ignorance functions and fuzzy preference relations. Appl. Decis. Making Knowl.-Based Syst. 58, 33–44 (2014)

    Article  Google Scholar 

  4. Bentkowska, U., Bustince, H., Jurio, A., Pagola, M., Pekala, B.: Decision making with an interval-valued fuzzy preference relation and admissible orders. Appl. Soft Comput. 35, 792–801 (2015)

    Article  Google Scholar 

  5. Burillo, P., Bustince, H.: Construction theorems for intuitionistic fuzzy sets. Fuzzy Sets Syst. 84, 271–281 (1996)

    Article  MathSciNet  MATH  Google Scholar 

  6. Bustince, H.: Indicator of inclusion grade for interval-valued fuzzy sets. Application to approximate reasoning based on interval-valued fuzzy sets. Int. J. Approx. Reason. 23(3), 137–209 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  7. Bustince, H., Barrenechea, E., Pagola, M.: Relationship between restricted dissimilarity functions, restricted equivalence functions and normal \(E_N\)-functions: image thresholding invariant. Pattern Recogn. Lett. 29(4), 525–536 (2008)

    Google Scholar 

  8. Bustince, H., Barrenechea, E., Pagola, M.: Image thresholding using restricted equivalence functions and maximizing the measure of similarity. Fuzzy Sets Syst. 128(5), 496–516 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  9. Bustince, H., Barrenechea, E., Pagola, M.: Restricted equivalence functions. Fuzzy Sets Syst. 157(17), 2333–2346 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  10. Bustince, H., Barrenechea, E., Pagola, M., Fernández, J., Xu, Z., Bedregal, B., Montero, J., Hagras, H., Herrera, F., De Baets, B.: A historical account of types of fuzzy sets and their relationship. IEEE Trans. Fuzzy Syst. 24(1), 179–194 (2016)

    Article  Google Scholar 

  11. Bustince, H., Fernandez, J., Kolesárová, A., Mesiar, R.: Generation of linear orders for intervals by means of aggregation functions. Fuzzy Sets Syst. 220, 69–77 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  12. Choi, H.M., Mun, G.S., Ahn, J.Y.: A medical diagnosis based on interval-valued fuzzy sets. Biomed. Eng. Appl. Basis Commun. 24(4), 349–354 (2012)

    Article  Google Scholar 

  13. Couto, P., Jurio, A., Varejao, A., Pagola, M., Bustince, H., Melo-Pinto, P.: An IVFS-based image segmentation methodology for rat gait analysis. Soft Comput. 15(10), 1937–1944 (2011)

    Article  Google Scholar 

  14. Deng, G., Song, L., Jiang, Y., Fu, J.: Monotonic similarity measures of interval-valued fuzzy sets and their applications. Int. J. Uncertainty Fuzziness Knowl. Based Syst. 25(4), 515–544 (2017)

    Article  MathSciNet  MATH  Google Scholar 

  15. Galar, M., Fernandez, J., Beliakov, G., Bustince, H.: Interval-valued fuzzy sets applied to stereo matching of color images. IEEE Trans. Image Process. 20(7), 1949–61 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  16. Heidarzade, A.: A new similarity measure for interval type-2 fuzzy sets: application in fuzzy risk analysis. Int. J. Appl. Decis. Sci. 9(4), 400–412 (2016)

    MathSciNet  Google Scholar 

  17. Jurio, A., Pagola, M., Mesiar, R., Beliakov, G., Bustince, H.: Image magnification using interval information. IEEE Trans. Image Process. 20(11), 3112–3123 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  18. Liu, X.: Entropy, distance measure and similarity measure of fuzzy sets and their relations. Fuzzy Sets Syst. 52, 305–318 (1992)

    Article  MathSciNet  MATH  Google Scholar 

  19. Lu, Z., Ye, J.: Logarithmic similarity measure between interval-valued fuzzy sets and its fault diagnosis method. Information (Switzerland) 9, 36 (2018)

    Google Scholar 

  20. Sanz, J.A., Fernandez, A., Bustince, H., Herrera, F.: IVTURS: a linguistic fuzzy rule-based classification system based on a new interval-valued fuzzy reasoning method with tuning and rule selection. IEEE Trans. Fuzzy Syst. 21(3), 399–411 (2013)

    Article  Google Scholar 

  21. Xu, Z.S., Yager, R.R.: Some geometric aggregation operators based on intuitionistic fuzzy sets. Int. J. Gen. Syst. 35, 417–433 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  22. Ye, J.: Multicriteria decision-making method based on cosine similarity measures between interval-valued fuzzy sets with risk preference. Econ. Comput. Econ. Cybern. Stud. Res. 50(4), 205–215 (2016)

    Google Scholar 

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Acknowledgement

This work was partially supported by project TIN2016-77356-P (MINECO, UE/AEI, FEDER) of the Spanish Government and by Project VEGA 1/0614/18.

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Correspondence to Zdenko Takáč .

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Takáč, Z., Bustince, H., Fernandez, J., Dimuro, G., Asmus, T., Castillo, A. (2019). Interval-Valued \(E_N\)-functions and Similarity Measures. In: Halaš, R., Gagolewski, M., Mesiar, R. (eds) New Trends in Aggregation Theory. AGOP 2019. Advances in Intelligent Systems and Computing, vol 981. Springer, Cham. https://doi.org/10.1007/978-3-030-19494-9_13

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