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Issue:About the Lp space of intuitionistic fuzzy observables: Difference between revisions

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  | format          = PDF
  | format          = PDF
  | size            = 220
  | size            = 220
  | abstract        = The aim of this paper is to define an $L^p$ space of intuitionistic fuzzy observables. We~work in an intuitionistic fuzzy space $({\mathcal F}, {\bf m})$ with product, where $\mathcal F$ is a family of intuitionistic fuzzy events and ${\bf m}$ is an intuitionistic fuzzy state. We prove that the space $L^p$ with corresponding intuitionistic fuzzy pseudometric $\rho_{IF}$ is a pseudometric space.
  | abstract        = The aim of this paper is to define an <math>L^p</math> space of intuitionistic fuzzy observables. We work in an intuitionistic fuzzy space <math>({\mathcal F}, {\bf m})</math> with product, where <math>\mathcal F</math> is a family of intuitionistic fuzzy events and <math>{\bf m}</math> is an intuitionistic fuzzy state. We prove that the space <math>L^p</math> with corresponding intuitionistic fuzzy pseudometric <math>\rho_{IF}</math> is a pseudometric space.
  | keywords        = Intuitionistic fuzzy observable, Intuitionistic fuzzy state, Joint intuitionistic fuzzy observable, Function of several intuitionistic fuzzy observables, Product, ''L<sup>p</sup>'' space, Pseudometric space, Intuitionistic fuzzy pseudometric.
  | keywords        = Intuitionistic fuzzy observable, Intuitionistic fuzzy state, Joint intuitionistic fuzzy observable, Function of several intuitionistic fuzzy observables, Product, ''L<sup>p</sup>'' space, Pseudometric space, Intuitionistic fuzzy pseudometric.
  | ams            = 03B52, 60A86.
  | ams            = 03B52, 60A86.
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# Čunderlíková, K. (2019). [[Issue:m-almost everywhere convergence of intuitionistic fuzzy observables induced by Borel measurable function|'''m'''-almost everywhere convergence of intuitionistic fuzzy observables induced by Borel measurable function]]. Notes on Intuitionistic Fuzzy Sets, 25(2), 29–40.
# Čunderlíková, K. (2019). [[Issue:m-almost everywhere convergence of intuitionistic fuzzy observables induced by Borel measurable function|'''m'''-almost everywhere convergence of intuitionistic fuzzy observables induced by Borel measurable function]]. Notes on Intuitionistic Fuzzy Sets, 25(2), 29–40.
# Lendelová, K. (2006). Conditional IF-probability.  ''Lawry, J. et al. (Eds.). Soft Methods for Integrated Uncertainty Modelling. Advances in Soft Computing'', Vol. 37, Springer-Verlag Berlag Heidelberg, 275–283.
# Lendelová, K. (2006). Conditional IF-probability.  ''Lawry, J. et al. (Eds.). Soft Methods for Integrated Uncertainty Modelling. Advances in Soft Computing'', Vol. 37, Springer-Verlag Berlag Heidelberg, 275–283.
# Riečan, B. (1999). On the $L^p$ space of observables. Fuzzy Sets and Systems, 105(2), 299–306.
# Riečan, B. (1999). On the <math>L^p</math> space of observables. Fuzzy Sets and Systems, 105(2), 299–306.
# Riečan, B. (2000). On the $L^p$ space of observables on product MV algebras. International Journal of Theoretical Physics, 39(3), 851–858.
# Riečan, B. (2000). On the <math>L^p</math> space of observables on product MV algebras. International Journal of Theoretical Physics, 39(3), 851–858.
# Riečan, B. (2006). On a problem of Radko Mesiar: General form of IF-probabilities. Fuzzy Sets and Systems, 157(11), 1485–1490.
# Riečan, B. (2006). On a problem of Radko Mesiar: General form of IF-probabilities. Fuzzy Sets and Systems, 157(11), 1485–1490.
# Riečan, B. (2006). On the probability and random variables on IF events. In: Ruan, D. et al.  (Eds.). Applied Artificial Intelligence, Proceedings of the 7th FLINS Conference, Genova, 138–145.
# Riečan, B. (2006). On the probability and random variables on IF events. In: Ruan, D. et al.  (Eds.). Applied Artificial Intelligence, Proceedings of the 7th FLINS Conference, Genova, 138–145.

Latest revision as of 15:37, 3 July 2023

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http://ifigenia.org/wiki/issue:nifs/29/2/90-98
Title of paper: About the Lp space of intuitionistic fuzzy observables
Author(s):
Katarína Čunderlíková
Mathematical Institute, Slovak Academy of Sciences, Štefánikova 49, 814 73 Bratislava, Slovakia
cunderlikova.lendelova@gmail.com
Presented at: 26th International Conference on Intuitionistic Fuzzy Sets, Sofia, 26—27 June 2023
Published in: Notes on Intuitionistic Fuzzy Sets, Volume 29 (2023), Number 2, pages 90–98
DOI: https://doi.org/10.7546/nifs.2023.29.2.90-98
Download:  PDF (220  Kb, Info)
Abstract: The aim of this paper is to define an [math]\displaystyle{ L^p }[/math] space of intuitionistic fuzzy observables. We work in an intuitionistic fuzzy space [math]\displaystyle{ ({\mathcal F}, {\bf m}) }[/math] with product, where [math]\displaystyle{ \mathcal F }[/math] is a family of intuitionistic fuzzy events and [math]\displaystyle{ {\bf m} }[/math] is an intuitionistic fuzzy state. We prove that the space [math]\displaystyle{ L^p }[/math] with corresponding intuitionistic fuzzy pseudometric [math]\displaystyle{ \rho_{IF} }[/math] is a pseudometric space.
Keywords: Intuitionistic fuzzy observable, Intuitionistic fuzzy state, Joint intuitionistic fuzzy observable, Function of several intuitionistic fuzzy observables, Product, Lp space, Pseudometric space, Intuitionistic fuzzy pseudometric.
AMS Classification: 03B52, 60A86.
References:
  1. Atanassov, K. T. (1983). Intuitionistic fuzzy sets, VII ITKR Session, Sofia, 20-23 June 1983 (Deposed in Centr. Sci.-Techn. Library of the Bulg. Acad. of Sci., 1697/84) (in Bulgarian). Reprinted: Int. J. Bioautomation, 2016, 20(S1), S1–S6.
  2. Atanassov, K. T. (1999). Intuitionistic Fuzzy Sets: Theory and Applications, Physica Verlag, New York.
  3. Atanassov, K. T. (2012). On Intuitionistic Fuzzy Sets, Springer, Berlin.
  4. Bartková, R., & Čunderlíková, K. (2018). About Fisher–Tippett–Gnedenko Theorem for Intuitionistic Fuzzy Events. In: Kacprzyk, J., et al. (eds) Advances in Fuzzy Logic and Technology 2017. IWIFSGN 2017, EUSFLAT 2017. Advances in Intelligent Systems and Computing, Vol. 641, Springer, Cham, 125–135.
  5. Čunderlíková, K. (2019). m-almost everywhere convergence of intuitionistic fuzzy observables induced by Borel measurable function. Notes on Intuitionistic Fuzzy Sets, 25(2), 29–40.
  6. Lendelová, K. (2006). Conditional IF-probability. Lawry, J. et al. (Eds.). Soft Methods for Integrated Uncertainty Modelling. Advances in Soft Computing, Vol. 37, Springer-Verlag Berlag Heidelberg, 275–283.
  7. Riečan, B. (1999). On the [math]\displaystyle{ L^p }[/math] space of observables. Fuzzy Sets and Systems, 105(2), 299–306.
  8. Riečan, B. (2000). On the [math]\displaystyle{ L^p }[/math] space of observables on product MV algebras. International Journal of Theoretical Physics, 39(3), 851–858.
  9. Riečan, B. (2006). On a problem of Radko Mesiar: General form of IF-probabilities. Fuzzy Sets and Systems, 157(11), 1485–1490.
  10. Riečan, B. (2006). On the probability and random variables on IF events. In: Ruan, D. et al. (Eds.). Applied Artificial Intelligence, Proceedings of the 7th FLINS Conference, Genova, 138–145.
  11. Riečan, B. (2007). Probability theory on intuitionistic fuzzy events. In: Aguzzoli, D. et al. (eds) A volume in honour of Daniele Mundici’s 60th birthday. Lecture Notes in Computer Science, Springer, 290–308.
  12. Riečan, B. (2012). Analysis of fuzzy logic models. In: Koleshko, V. (Ed.). Intelligent Systems, INTECH, 219–244.
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