Abstract:This article demonstrates that a normal fuzzy number can be constructed from earthquake waveform data. According to the RandomnessFuzziness Consistency Principle, two independent laws of randomness in [α, β] and [β, γ] are necessary and sufficient to define a normal fuzzy number [α, β, γ]. In this article, we have shown how to construct normal fuzzy numbers using data from earthquake waveform and have studied the pattern of the membership curve of the waveform.

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In this article, a method has been developed to construct the membership surface of imprecise vector based on Randomness-Impreciseness Consistency Principle. The Randomness-Impreciseness Consistency Principle leads to define a normal law of impreciseness using two different laws of randomness. The Dubois-Prade left and right reference functions of an imprecise number are distribution function and complementary distribution function respectively. In this article, based on the Randomness-Impreciseness Consistency Principle we have successfully obtained the membership surface of imprecise vector and demonstrated with the help of numerical examples.

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Abstract:A fuzzy real number [α, β, γ] is an interval around the real number β with the elements in the interval being partially present. Partial presence of an element in a fuzzy set is defined by the name membership function. According to the Randomness-Fuzziness Consistency Principle, two independent laws of randomness in [α, β] and [β, γ] are necessary and sufficient to define a normal fuzzy number [α, β, γ]. In this article, we have shown how to construct normal fuzzy number using daily temperature data.

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