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On a New Generalization of Decomposition Integrals

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Modeling Decisions for Artificial Intelligence (MDAI 2023)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 13890))

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Abstract

In the few past years, decomposition integrals show a prolific interest of researchers. Some modifications and generalizations of these integrals were proposed, including the so-called minimax integrals. In the presented work, we introduce a new generalization of decomposition integrals based on set-based extended aggregation functions, which unifies the classical decomposition integrals and the minimax integrals into one framework of integrals called S-decomposition integrals. Some examples are given and future research outlined.

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References

  1. Choquet, G.: Theory of capacities. Annales de l’Institut Fourier 5, 131–295 (1954). https://doi.org/10.5802/aif.53

    Article  MathSciNet  MATH  Google Scholar 

  2. Even, Y., Lehrer, E.: Decomposition-integral: unifying Choquet and the concave integrals. Econ. Theor. 56(1), 33–58 (2013). https://doi.org/10.1007/s00199-013-0780-0

    Article  MathSciNet  MATH  Google Scholar 

  3. Fodor, J.C.: An extension of Fung-Fu’s theorem. Internat. J. Uncertain. Fuzziness Knowl.-Based Syst. 4(3), 235–243 (1996). https://doi.org/10.1142/S0218488596000147

    Article  MathSciNet  MATH  Google Scholar 

  4. Fung, L.W., Fu, K.S.: An axiomatic approach to rational decision making in a fuzzy environment. In: Zadeh, L.A., Fu, K.S., Tanaka, K., Shimura, M. (eds.) Fuzzy Sets and Their Applications to Cognitive and Decision Processes, pp. 227–256. Academic Press, New York (1975). https://doi.org/10.1016/B978-0-12-775260-0.50015-3

  5. Grabisch, M., Marichal, J.-L., Mesiar, R., Pap, E.: Aggregation functions. Encyclopedia of Mathematics and Its Applications 127. Cambridge University Press (2009). ISBN 978-0-521-51926-7

    Google Scholar 

  6. Honda, A., James, S., Rajasegarar, S.: Orness and cardinality indices for averaging inclusion-exclusion integrals. In: Torra, V., Narukawa, Y., Honda, A., Inoue, S. (eds.) MDAI 2017. LNCS (LNAI), vol. 10571, pp. 51–62. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-67422-3_6

    Chapter  MATH  Google Scholar 

  7. Honda, A., Okazaki, Y.: Theory of inclusion-exclusion integral. Inf. Sci. 376, 136–147 (2017). https://doi.org/10.1016/j.ins.2016.09.063

    Article  MathSciNet  MATH  Google Scholar 

  8. Horanská, Ľ, Bustince, H., Fernandez, J., Mesiar, R.: Generalized decomposition integral. Inf. Sci. 538, 415–427 (2020). https://doi.org/10.1016/j.ins.2020.05.081

    Article  MathSciNet  MATH  Google Scholar 

  9. Klement, E.P., Mesiar, R., Pap, E.: A universal integral as common frame for Choquet and Sugeno integral. IEEE Trans. Fuzzy Syst. 18(1), 178–187 (2010). https://doi.org/10.1109/TFUZZ.2009.2039367

    Article  Google Scholar 

  10. Lehrer, E.: A new integral for capacities. Econ. Theor. 39, 157–176 (2009). https://doi.org/10.1007/s00199-007-0302-z

    Article  MathSciNet  MATH  Google Scholar 

  11. Mesiar, R., Kolesárová, A., Gómez, D., Montero, J.: Set-based extended aggregation functions. Int. J. Intell. Syst. 34(9), 2039–2054 (2019). https://doi.org/10.1002/int.22128

    Article  Google Scholar 

  12. Mesiar, R., Kolesárová, A., Stupňanová, A.: Quo vadis aggregation? Int. J. Gen. Syst. 47(2), 97–117 (2018). https://doi.org/10.1080/03081079.2017.1402893

    Article  MathSciNet  Google Scholar 

  13. Mesiar, R., Li, J., Pap, E.: Superdecomposition integrals. Fuzzy Sets Syst. 259, 3–11 (2015). https://doi.org/10.1016/j.fss.2014.05.003

    Article  MathSciNet  MATH  Google Scholar 

  14. Mesiar, R., Stupňanová, A.: Decomposition integrals. Int. J. Approximate Reasoning 54(8), 1252–1259 (2013). https://doi.org/10.1016/j.ijar.2013.02.001

    Article  MathSciNet  MATH  Google Scholar 

  15. Šeliga, A.: Decomposition integral without alternatives, its equivalence to Lebesgue integral, and computational algorithms. J. Automation Mob. Robot. Intell. Syst. 13(3), 41–48 (2019). https://doi.org/10.14313/JAMRIS/3-2019/26

  16. Šeliga, A.: Decomposition integrals for interval-valued functions. In: Cornejo, M.E., Kóczy, L.T., Medina-Moreno, J., Moreno-García, J. (eds.) Computational Intelligence and Mathematics for Tackling Complex Problems 2. SCI, vol. 955, pp. 183–189. Springer, Cham (2022). https://doi.org/10.1007/978-3-030-88817-6_21

    Chapter  MATH  Google Scholar 

  17. Šeliga, A., Mesiar, R., Ouyang, Y., Li, J.: Minimax decomposition integrals. Submitted

    Google Scholar 

  18. Shilkret, N.: Maxitive measure and integration. Indag. Math. 33, 109–116 (1971). https://doi.org/10.1016/S1385-7258(71)80017-3

    Article  MathSciNet  MATH  Google Scholar 

  19. Wang, Z., Klir, G.J.: Generalized Measure Theory. Springer (2009). ISBN 9780387768526

    Google Scholar 

  20. Yang, Q.: The PAN-integral on the fuzzy measure space. Fuzzy Math. 3, 107–114 (1985). In Chinese

    MathSciNet  MATH  Google Scholar 

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Acknowledgements

The author was supported by the Slovak Research and Development Agency under the contract no. APVV-18-0052. Also the support of the grant VEGA 1/0036/23 is kindly announced.

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Authors and Affiliations

  1. Department of Mathematics and Descriptive Geometry, Faculty of Civil Engineering, Slovak University of Technology in Bratislava, Radlinského 11, 810 05, Bratislava, Slovakia

    Adam Šeliga

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  1. Adam Šeliga
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Correspondence to Adam Šeliga .

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Editors and Affiliations

  1. Umeå University, Umeå, Sweden

    Vicenç Torra

  2. Tamagawa University, Tokyo, Japan

    Yasuo Narukawa

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Šeliga, A. (2023). On a New Generalization of Decomposition Integrals. In: Torra, V., Narukawa, Y. (eds) Modeling Decisions for Artificial Intelligence. MDAI 2023. Lecture Notes in Computer Science(), vol 13890. Springer, Cham. https://doi.org/10.1007/978-3-031-33498-6_6

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  • DOI: https://doi.org/10.1007/978-3-031-33498-6_6

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-031-33497-9

  • Online ISBN: 978-3-031-33498-6

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