Application of wearable sensors for human gait analysis using fuzzy computational algorithm

Fuzzy (and Interval) Techniques in the Age of Big Data: An Overview with Applications to Environmental Science, Geosciences, Engineering, and Medicine

“…Empirical data shows that the fuzzy approach is in much better accordance with the doctor's evaluations 1,2,31,39 . This can be explained by the fact that -similarly to airplane maintenance -we want to make sure that the patient performs correctly under all possible circumstances before declaring the therapy a success.…”

“…For example, we can have two nearby towers, or we can bring additional sensors to the existing tower. In such a situation, instead of a single measurement result x, we have two different results x (1) and x (2) of measuring the same quantity x. Here, by definition of the measurement error, x…”

“…Thus, the standard deviation σ ′ of this difference is equal to √ 2 · σ. We can estimate this standard deviation σ ′ based on the observed differences x (1) − x (2) and therefore, we can estimate σ as σ…”

“…(1) = x + ∆x (1) and x (2) = x + ∆x (2) and therefore, (2) . Each of the random variables ∆x (1) and ∆x (2) is normally distributed with mean 0 and (unknown) standard deviation σ (i.e., variance σ 2 ).…”

“…Each of the random variables ∆x (1) and ∆x (2) is normally distributed with mean 0 and (unknown) standard deviation σ (i.e., variance σ 2 ). Since the two measuring instruments are independent, the corresponding random variables ∆x (1) and ∆x (2) are also independent, and so, the variance of their difference is equal to the sum of their variances σ 2 + σ 2 = 2σ 2 . Thus, the standard deviation σ ′ of this difference is equal to √ 2 · σ.…”