*4.1. Impact of Modifiers over Linguistic Terms*

In this section, we describe an evaluation of the linguistic modifiers for the terms defined in Section 2.2.1. As we detailed previously, the OHRTZs define the ranges where the values of HR are totally *adequate*, *VT*<sup>1</sup> defines the basal-aerobic threshold from which inferior values of HR are totally *low*, and *VT*<sup>2</sup> the aerobic-anaerobic threshold from which upper values of HR are totally *high*. However, the values of HR between these optimal zones need to change gradually. This progression between optimal zones has been modeled and evaluated using several modifiers.

In this work, we have evaluated three models using different modifiers to adjust the progression in the trapezoidal membership functions of the terms *low, adequate, and high* with regards to Section 2.2.1.

First, we have evaluated low–adequate values of the heart rate by means of three models: (A) a severe model, where the *low* term is strong and the *adequate* term is weak; (B) a neutral model, where neutral modifiers are applied to both terms; and (C) a yielding model, where the *adequate* term is stronger than the *low* term, which is weaker. The strong, neutral, and weak properties have been defined by the parameters *α* = 0.5, *α* = 1, and *α* = 2.0 of the modifier, respectively. In Figure 5, we show a representation of the impact of the modifiers on the degree of the linguistic terms in a HR stream.

To evaluate the impact of fuzzy modifiers, we have included a survey of 10 cases with key fragments of low values from the heart rate of a sessions, which were colored with blue and green, based on the degree of the terms low and adequate, respectively. In Figure 5, we show an example of a survey case. In a clinical session, the cardiac rehabilitation team evaluates them using a 5-point Likert scale: *{value -2, value -1, value 0, value +1, value +2}*, for which results are detailed in Table 1.

Second, in a similar way, high–adequate values of heart rate have been evaluated by means of three models: (A) a severe model; (B) a neutral model; and (C) a yielding model. A second survey, which contains 10 cases with key fragments of high values from the heart rate of sessions, was evaluated by the cardiac rehabilitation team using the 5-point Likert scale. Results are detailed in Table 1 and two examples of cases from the surveys are presented in Figure 5.


**Table 1.** The columns are related in order of: (1) survey; (2) model; (3) modifiers; and then percentages of responses for (4) value −2; (5) value −1; (6) value 0; (7) value +1; and (8) value +2.

**Figure 5.** Impact of the fuzzy modifiers on heart rate streams. Heart rate is plotted using gradually changing colors *blue, green, red* based on the degree of the terms {*low*, *adequate*, *high*}, respectively. Green dotted lines determine the OHRTZs of patient. Blue and red dotted lines determine aerobic thresholds *VT*<sup>1</sup> , *VT*<sup>2</sup> of the patient, respectively. The impact of the models A, B and C for a case of high–adequate HRs (**right**); and the impact of the models A, B, and C for a case of low–adequate HRs (**left**).
