Abstract
A set of perceived random events is given by a fuzzy random variable, and its estimation is represented by a functional on real random variables. The estimation of the perception regarding random events is obtained, extending the functional to a functional of fuzzy random variables. This paper discusses conditions and various properties of perception-based extension of estimations with randomness, and several examples of the perception-based extension are investigated. The results can be applied other estimations in engineering, economics and so on.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Carlsson, C., Fullér, R.: On Possibilistic Mean Value and Variance of Fuzzy Numbers. Fuzzy Sets and Systems 122, 315–326 (2001)
López-DÃaz, M., Gil, M.A., Ralescu, D.A.: Overview on the Development of Fuzzy Random Variables. Fuzzy Sets and Systems 147, 2546–2557 (2006)
Feng, Y., Hu, L., Su, H.: The Variance and Covariance of Fuzzy Random Variables. Fuzzy Sets and Systems 120, 487–497 (2001)
Körner, R.: On the Variance of Fuzzy Random Variables. Fuzzy Sets and Systems 92, 83–93 (1997)
Kruse, R., Meyer, K.D.: Statistics with Vague Data. Riedel Publ. Co., Dortrecht (1987)
Kurano, M., Yasuda, M., Nakagami, J., Yoshida, Y.: A Fuzzy Stopping Problem with the Concept of Perception. Fuzzy Optimization and Decision Making 3, 367–374 (2004)
Kwakernaak, H.: Fuzzy Random Variables. Part I: Definitions and Theorem. Information Sciences 15, 1–29 (1978)
Kwakernaak, H.: Fuzzy Random Variables. Part II: Algorithms and Examples for the Discrete Case. Information Sciences 17, 253–278 (1979)
Meucci, A.: Risk and Asset Allocation. Springer, Heidelberg (2005)
Ohtsubo, Y.: Optimal Threshold Probability in Undiscounted Markov Decision Processes with a Target Set. Applied Math. and Computation 149, 519–532 (2004)
Puri, M.L., Ralescu, D.A.: Fuzzy Random Variables. J. Math. Anal. Appl. 114, 409–422 (1986)
Rockafellar, R.T., Uryasev, S.P.: Optimization of Conditional Value-at-Risk. Journal of Risk 2, 21–42 (2000)
Tasche, D.: Expected Shortfall and Beyond. Journal of Banking Finance 26, 1519–1533 (2002)
Yoshida, Y.: The Valuation of European Options in Uncertain Environment. European J. Oper. Res. 145, 221–229 (2003)
Yoshida, Y.: Mean Values, Measurement of Fuzziness and Variance of Fuzzy Random Variables for Fuzzy Optimization. In: Proceedings of SCIS & ISIS 2006 (Joint 3rd Intern. Conf. on Soft Comp. and Intell. Sys. and 7th Intern. Symp. on Advanced Intell. Sys.) Tokyo in Japan, pp. 2277–2282 (2006)
Zadeh, L.A.: Fuzzy Sets. Inform. and Control 8, 338–353 (1965)
Zadeh, L.A.: Toward a Perception-Based Theory of Probabilistic Reasoning with Imprecise Probabilities. J. of Statistical Planning and Inference 105, 233–264 (2002)
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 2007 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Yoshida, Y. (2007). Fuzzy Extension of Estimations with Randomness: The Perception-Based Approach. In: Torra, V., Narukawa, Y., Yoshida, Y. (eds) Modeling Decisions for Artificial Intelligence. MDAI 2007. Lecture Notes in Computer Science(), vol 4617. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-73729-2_28
Download citation
DOI: https://doi.org/10.1007/978-3-540-73729-2_28
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-73728-5
Online ISBN: 978-3-540-73729-2
eBook Packages: Computer ScienceComputer Science (R0)