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Arithmetics of Vectors of Fuzzy Sets

Author

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  • Hsien-Chung Wu

    (Department of Mathematics, National Kaohsiung Normal University, Kaohsiung 802, Taiwan)

Abstract

The arithmetic operations of fuzzy sets are completely different from the arithmetic operations of vectors of fuzzy sets. In this paper, the arithmetic operations of vectors of fuzzy intervals are studied by using the extension principle and a form of decomposition theorem. These two different methodologies lead to the different types of membership functions. We establish their equivalences under some mild conditions. On the other hand, the α -level sets of addition, difference and scalar products of vectors of fuzzy intervals are also studied, which will be useful for the different usage in applications.

Suggested Citation

  • Hsien-Chung Wu, 2020. "Arithmetics of Vectors of Fuzzy Sets," Mathematics, MDPI, vol. 8(9), pages 1-42, September.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:9:p:1614-:d:415629
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    References listed on IDEAS

    as
    1. Hsien-Chung Wu, 2019. "Generalized extension principle for non-normal fuzzy sets," Fuzzy Optimization and Decision Making, Springer, vol. 18(4), pages 399-432, December.
    2. Barnab?s Bede & Luciano Stefanini, 2012. "Generalized Differentiability of Fuzzy-valued Functions," Working Papers 1209, University of Urbino Carlo Bo, Department of Economics, Society & Politics - Scientific Committee - L. Stefanini & G. Travaglini, revised 2012.
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