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On the Correlations between Fuzzy Variables

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Advances in Swarm Intelligence (ICSI 2010)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6146))

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Abstract

The expected value and variance of a fuzzy variable have been well studied in the literature, and they provide important characterizations of the possibility distribution for the fuzzy variable. In this paper, we seek a similar characterization of the joint possibility distribution for a pair of fuzzy variables. In view of the success of introducing the expected value and variance as fuzzy integrals of appropriate functions of single fuzzy variable, it is natural to look to fuzzy integrals of appropriate functions of a pair of fuzzy variables. We consider one such function to obtain the covariance of the pair fuzzy variables and focus on its computation for common possibility distributions. Under mild assumptions, we derive several useful covariance formulas for triangular and trapezoidal fuzzy variables, which have potential applications in quantitative finance problems when we consider the correlations among fuzzy returns.

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Authors and Affiliations

  1. College of Mathematics and Computer Science, Hebei University, Baoding, 071002, Hebei, China

    Yankui Liu & Xin Zhang

Authors
  1. Yankui Liu
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  2. Xin Zhang
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Editor information

Editors and Affiliations

  1. Key Laboratory of Machine Perception (MOE), Department of Machine Intelligence, Peking University, 100871, Beijing, China

    Ying Tan

  2. Research and Postgraduate Office, Xi’an Jiaotong-Liverpool University, 215123, Suzhoum, China

    Yuhui Shi

  3. Department of Electrical and Computer Engineering, Engineering Drive 3, 4 Engineering Drive 3, National University of Singapore, 117576, Singapore

    Kay Chen Tan

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© 2010 Springer-Verlag Berlin Heidelberg

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Liu, Y., Zhang, X. (2010). On the Correlations between Fuzzy Variables. In: Tan, Y., Shi, Y., Tan, K.C. (eds) Advances in Swarm Intelligence. ICSI 2010. Lecture Notes in Computer Science, vol 6146. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-13498-2_1

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  • DOI: https://doi.org/10.1007/978-3-642-13498-2_1

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-13497-5

  • Online ISBN: 978-3-642-13498-2

  • eBook Packages: Computer ScienceComputer Science (R0)

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