*4.2. Impact of Temporal Window over Linguistic Terms*

In this section, we describe an evaluation on the fuzzy temporal windows over linguistic terms which describe the heart rate stream during rehabilitation sessions. As we detailed previously, the theoretical thresholds of the heart range zones from CRP are defined theoretically missing the temporal permanence in OHRTZs. In some critical situations when patients develop the CRP, the evolution of heart rate between OHRTZs is prompt and inconstant. In those cases, the adherence and adequacy could not be just defined by the current value of HR.

In order to analyze the impact of the temporal windows, a survey with 15 key fragments of prompt and inconstant heart rate streams from the CRSs was designed to evaluate three temporal windows. The cardiac rehabilitation team from the Hospital Complex of Jaen (Spain) analyzed the impact of temporal windows for each term {*low*, *adequate*, *high*} based on their expert knowledge.

The temporal windows to evaluate are (*t*1): the last single sample; (*t*2): a 3–5 s window; and (*t*3): a 5–10 s window. In the two last cases (*t*<sup>2</sup> and *t*3), we have defined the next fuzzy temporal windows

*µt*2(∆*ti*) = *TS*(3*s*, 3*s*, 3*s*, 5*s*) and *µt*3(∆*ti*) = *TS*(5*s*, 5*s*, 5*s*, 10*s*) based on the temporal fuzzification described in Section 2.2.3. In Figure 6, we detail an example of the semantics and impact of the three temporal windows on a heart rate streams.

In Table 2, we show the results of the evaluation described by a 5-point Likert scale: *{value* −*2, value* −*1, value 0, value +1, value +2}*. We can observe that the short-term temporal window *t*<sup>1</sup> is more recommendable when evaluating the term *high* because of corresponding critical values of HR, which require an immediate response from the patient to decrease the heart rate, whereas the long-term window *t*<sup>3</sup> is strongly not recommended. On the other hand, the longer temporal window *t*<sup>2</sup> is more properly related to the temporal term *adequate* because of the correct adherence the HR stream needs for a temporary stabilization in OHRZs. Finally, the term *low* is more appropriate with the temporal window *t*2, and is adequate with other windows too.

**Table 2.** The columns are related in order of: (1) term; (2) model; and the percentage of responses for: (3) value −2; (4) value −1; (5) value 0; (6) value +1; and (7) value +2.


**Figure 6.** Impact of temporal windows on a case of prompt heart rate streams within the zones described by the linguistic terms {*low*, *adequate*, *high*}. Based on expert evaluation: Model A (short-term temporal window) suits in *high* zones detecting immediately critical HRs; Model B (middle-term temporal window) suits in *adequate* zone requiring a minimal permanence within; and Model B suits in the *low* zone without critical differences with regard to other models.
