Properties of Fuzzy Arithmetic Based on Triangular Norms

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  • t-ノルムに基づくファジィ算法に関する諸性質

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The aim of this paper is to clarify the properties of fuzzy arithmetic based on a generalized extension principle and consider the possibility of its applications. The generalized extension principle corresponding to sup-(t-norm) convolution enables us to control the growth of fuzziness in calculation by choosing an adequate t-norm. In this paper, it was made clear that the family of fuzzy numbers forms commutative monoids concerning addition and multiplication, respectively. Also, the authors found some new properties on the distribution of multiplication on addition, and showed their differences from those of the ordinary fuzzy arithmetic based on sup-min convolution.

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