Nothing Special   »   [go: up one dir, main page]
Skip to main content
Springer Nature Link
Log in

Theory and Applications of Non-additive Measures and Corresponding Integrals

  • Conference paper
Modeling Decisions for Artificial Intelligence (MDAI 2013)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 8234))

Abstract

It is given an short overview of some recent results in the theory of non-additive measures and corresponding integrals. It is presented the universal integral, which include among others, Lebesgue, Choquet, Sugeno, pseudo–additive, Shilkret integrals. Related pseudo-integral a generalization of L p space is introduced. Many useful applications illustrate the power of non-additive measures and corresponding integrals.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Similar content being viewed by others

References

  1. Agahi, H., Mesiar, R., Ouyang, Y.: General Minkowski type inequalities for Sugeno integrals. Fuzzy Sets and Systems 161, 708–715 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  2. Agahi, H., Mesiar, R., Ouyang, Y.: New general extensions of Chebyshev type inequalities for Sugeno integrals. Int. J. of Approximate Reasoning 51, 135–140 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  3. Agahi, H., Mesiar, R., Ouyang, Y.: Chebyshev type inequalities for pseudo-integrals. Nonlinear Analysis: Theory, Methods and Applications 72, 2737–2743 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  4. Agahi, H., Mesiar, R., Ouyang, Y., Pap, E., Štrboja, M.: Hölder and Minkowski type inequalities for pseudo-integral. Applied Mathematics and Computation 217(21), 8630–8639 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  5. Agahi, H., Mesiar, R., Ouyang, Y., Pap, E., Štrboja, M.: Berwald type inequality for Sugeno integral. Applied Mathematics and Computation 217, 4100–4108 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  6. Akian, M.: Densities of idempotent measures and large deviations. Transactions of the American Mathematical Society 351(11), 4515–4543 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  7. Bede, B., O’Regan, D.: The theory of pseudo-linear operators. Knowledge Based Systems 38, 19–26 (2013)

    Article  Google Scholar 

  8. Del Moral, P.: Résolution particulaire des problèmes d’estimation et d’optimisation non-linéaires. Thesis dissertation, Université Paul Sabatier, Toulouse (1994)

    Google Scholar 

  9. Denneberg, D.: Non-additive measure and integral. Kluwer Academic Publishers, Dordrecht (1994)

    Book  MATH  Google Scholar 

  10. Dubois, D., Pap, E., Prade, H.: Hybrid probabilistic-possibilistic mixtures and utility functions. In: Fodor, J., de Baets, B., Perny, P. (eds.) Preferences and Decisions under Incomplete Knowledge. STUDFUZZ, vol. 51, pp. 51–73. Springer, Heidelberg (2000)

    Chapter  Google Scholar 

  11. Falconer, K.: Fractal Geometry. John Wiley and Sons, Chichester (1990)

    MATH  Google Scholar 

  12. Flores-Franulič, A., Román-Flores, H., Chalco-Cano, Y.: Markov type inequalities for fuzzy integrals. Applied Mathematics and Computation 207, 242–247 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  13. Grabisch, M., Marichal, J.L., Mesiar, R., Pap, E.: Aggregation Functions. Encyclopedia of Mathematics and Its Applications, vol. 127. Cambridge University Press (2009)

    Google Scholar 

  14. Grabisch, M., Murofushi, T., Sugeno, M. (eds.): Fuzzy Measures and Integrals. Theory and applications. Physica-Verlag, Heidelberg (2000)

    MATH  Google Scholar 

  15. Grbić, T., Pap, E.: Generalization of the Portmanteau theorem with respect to the pseudo-weak convergence of random closed sets (Veroyatnost i Primenen.). SIAM Theory of Probability and Its Applications 54(1), 51–67 (2010)

    Article  Google Scholar 

  16. Klement, E.P., Mesiar, R., Pap, E.: Triangular norms. In: Trends in Logic. Studia Logica Library, vol. 8. Kluwer Academic Publishers, Dodrecht (2000)

    Google Scholar 

  17. Klement, E.P., Mesiar, R., Pap, E.: Integration with respect to decomposable measures, based on a conditionally distributive semiring on the unit interval. Internat. J. Uncertain. Fuzziness Knowledge-Based Systems 8, 701–717 (2000)

    MathSciNet  MATH  Google Scholar 

  18. Klement, E.P., Mesiar, R., Pap, E.: A Universal Integral as Common Frame for Choquet and Sugeno Integral. IEEE Transactions on Fuzzy Systems 18(1), 178–187 (2000)

    Article  Google Scholar 

  19. Kolokoltsov, V.N., Maslov, V.P.: Idempotent Analysis and Its Applications. Kluwer Academic Publishers, Dordrecht (1997)

    Book  MATH  Google Scholar 

  20. Mesiar, R., Pap, E.: Idempotent integral as limit of g -integrals. Fuzzy Sets and Systems 102, 385–392 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  21. Mesiar, R., Li, J., Pap, E.: The Choquet integral as Lebesgue integral and related inequalities. Kybernetika 46, 1098–1107 (2010)

    MathSciNet  MATH  Google Scholar 

  22. Mesiar, R., Li, J., Pap, E.: Discrete pseudo-integrals. Int. J. of Approximative Reasoning 54, 357–364 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  23. Pap, E.: g-calculus. Univ. u Novom Sadu Zb. Rad. Prirod.-Mat. Fak. Ser. Mat. 23(1), 145–156 (1993)

    MathSciNet  MATH  Google Scholar 

  24. Pap, E.: Null-Additive Set Functions. Kluwer Academic Publishers, Dordrecht (1995)

    MATH  Google Scholar 

  25. Pap, E. (ed.): Handbook of Measure Theory. Elsevier, Amsterdam (2002)

    MATH  Google Scholar 

  26. Pap, E.: Pseudo-Additive Measures and Their Aplications. Handbook of Measure Theory. In: Pap, E. (ed.) Handbook of Measure Theory, vol. II, pp. 1403–1465. Elsevier (2002)

    Google Scholar 

  27. Pap, E., Štrboja, M.: Generalization of the Jensen inequality for pseudo-integral. Information Sciences 180, 543–548 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  28. Pap, E., Štrboja, M.: Generalizations of Integral Inequalities for Integrals Based on Nonadditive Measures. In: Pap, E. (ed.) Intelligent Systems: Models and Applications. TIEI, vol. 3, pp. 3–22. Springer, Heidelberg (2013)

    Chapter  Google Scholar 

  29. Pap, E., Štrboja, M.: Pseudo-L p space and convergence. Fuzzy Sets and Systems (in print)

    Google Scholar 

  30. Puhalskii, A.: Large deviations and idempotent probability. Chapman, Hall/CRC (2001)

    Google Scholar 

  31. Rudas, I.J., Pap, E., Fodor, J.: Information aggregation in intelligent systems: an application oriented approach. Knowledge Based Systems 38, 3–13 (2013)

    Article  Google Scholar 

  32. Sugeno, M.: Theory of fuzzy integrals and its applications. Ph.D. Dissertation, Tokyo Institute of Technology (1974)

    Google Scholar 

  33. Sugeno, M., Murofushi, T.: Pseudo-additive measures and integrals. J. Math. Anal. Appl. 122, 197–222 (1987)

    Article  MathSciNet  MATH  Google Scholar 

  34. Torra, V., Narukawa, Y.: Modeling Decisions: Information Fusion and Aggregation Operators. Cognitive Technologies. Springer (2007)

    Google Scholar 

  35. Wang, Z., Klir, G.J.: Generalized measure theory. Springer, Boston (2009)

    Book  MATH  Google Scholar 

  36. Wang, R.S.: Some inequalities and convergence theorems for Choquet integrals. J. Appl. Comput. 35(1-2), 305–321 (2011)

    Article  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. University of Novi Sad, 21000, Novi Sad, Serbia

    Endre Pap

  2. Óbuda University, H-1034, Budapest, Hungary

    Endre Pap

  3. Singidunum University, 11000, Belgrade, Serbia

    Endre Pap

Authors
  1. Endre Pap
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. IIIA-CSIC, Campüus UAB s/n, 08193, Bellaterra, Catalonia, Spain

    Vicenç Torra

  2. Toho Gakuen, 3-1-10, Naka, 186-0004, Kunitachi, Tokyo, Japan

    Yasuo Narukawa

  3. Departament d’Enginyeria de la Informació i de les Comunicacions, Universitat Autonoma de Barcelona, 08193, Bellaterra, Catalonia, Spain

    Guillermo Navarro-Arribas

  4. Internet Interdisciplinary Institute (IN3); Estudis d’Informàtica, Multimèdia i Telecomunicació, Universitat Oberta de Catalunya, Rambla del Poblenou, 156, 08018, Barcelona, Catalonia, Spain

    David Megías

Rights and permissions

Reprints and permissions

Copyright information

© 2013 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Pap, E. (2013). Theory and Applications of Non-additive Measures and Corresponding Integrals. In: Torra, V., Narukawa, Y., Navarro-Arribas, G., Megías, D. (eds) Modeling Decisions for Artificial Intelligence. MDAI 2013. Lecture Notes in Computer Science(), vol 8234. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-41550-0_1

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-41550-0_1

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-41549-4

  • Online ISBN: 978-3-642-41550-0

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation