Construction of normal fuzzy numbers: A case study with earthquake waveform data

Abstract

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.

The exact definition of fuzzy randomness: An application of the mathematics of partial presence

“…When we say that a normal fuzzy number is of the triangular type, it actually means that we have assumed that the left reference function is a uniform distribution function and the right reference function is a uniform complementary distribution function. We have actually found that the triangular fuzzy number appears very naturally in defining fuzziness (Das, 2013).…”

“…With reference to testing of statistical hypotheses, Goswami et al (1997) and Talukdar and Baruah ( , 2010aBaruah ( , 2010bBaruah ( , 2010cBaruah ( , 2011 have studied randomness with fuzzy observations. Goswami and Baruah (2008a) studied the effect of fuzziness on the binomial probability law. Fuzzy time series analysis was studied by Goswami and Baruah ( , 2008b.…”

“…Goswami and Baruah (2008a) studied the effect of fuzziness on the binomial probability law. Fuzzy time series analysis was studied by Goswami and Baruah ( , 2008b. In all these cases, the parameters concerned were taken to be fuzzy numbers, and the statistical analytical matters were dealt with accordingly.…”

Construction of the membership function of normal fuzzy numbers

“…We collected daily temperature data in the city of Guwahati, India for the month of Now, using the operation of set superimposition defined by Baruah (2010Baruah ( , 2011aBaruah ( , 2011bBaruah ( , 2011cBaruah ( , 2012 we may proceed to construct normal fuzzy numbers as discussed in (Das et al, 2013a(Das et al, , 2013b, which would define the uncertainty associated with temperature variations. Here, the data should must satisfy the condition max (a i ) ≤ min (b i ).…”

“…In this article we shall show how to construct normal fuzzy numbers (Das et al, 2013a(Das et al, , 2013b using the data of minimum and maximum temperature in Guwahati city for the month of December 2012 and up to 30 th January 2013. Partial presence of an element in a set is expressed in terms of the fuzzy membership function.…”