Assessment of functional impairment in human locomotion: A fuzzy-motivated approach

Abstract

Abstract-Many neurological disorders result in disordered motion. The effects of a disorder can be decrease by an appropriate rehabilitation. To make rehabilitation efficient, we need to monitor the patient and check how well he or she improves. In our previous papers, we proposed a fuzzy-based semi-heuristic method of gauging how well a patient improved. Surprisingly, this semi-heuristic method turned out to be more efficient that we expected. In this paper, we provide a justification for this efficiency.

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…”

“…(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.…”