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The canonical representation of multiplication operation on triangular fuzzy numbers. (English) Zbl 1044.03534

Summary: The representation of the multiplication operation on fuzzy numbers is very useful and important in fuzzy systems such as fuzzy decision making. In this paper, we propose a new arithmetical principle and a new arithmetical method for the arithmetical operations on fuzzy numbers. The new arithmetical principle is the \(L^{-1}\)-\(R^{-1}\) inverse function arithmetic principle. Based on the \(L^{-1}\)-\(R^{-1}\) inverse function arithmetic principle, it is easy to interpret the multiplication operation with the membership functions of fuzzy numbers. The new arithmetical method is the graded multiple integrals representation method. Based on the graded multiple integrals representation method, it is easy to compute the canonical representation of the multiplication operation on fuzzy numbers. Finally, the canonical representation is applied to a numerical example of fuzzy decision.

MSC:

03E72 Theory of fuzzy sets, etc.
91B06 Decision theory
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References:

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