1 Introduction

In recent decades, a healthy lifestyle has come into focus, and more and more devices are available, which ensure continuous control by measuring physiological parameters. In addition, due to the problem of an aging society, home patient monitoring devices have become necessary and therefore in demand.

At the same time, due to the technological development, the device background is also available due to the wide spread of the Internet of Things (IoT), so the development of a more functionally complex system covering a larger range is also possible [¹].

The pandemic of recent years has also highlighted the necessity and usefulness of remote diagnostics, since it was easier to prevent the spread of the virus if patients with less serious illnesses did not have to go to doctors' offices [²].

In medical-related applications, the need for a more flexible handling of data and evaluation often arises, since it is not possible to define sharp boundaries between normal and abnormal values. For this reason, fuzzy logic-based systems are very popular in dealing with these kinds of problems [³]. Fuzzy logic is able to handle uncertainties, imprecision and subjectivity in the data and in the evaluation adequately [⁴]. Interval Type-2 Fuzzy Logic can handle uncertainty even more effectively than traditional type-1 sets [⁵].

These systems are under continuous development, as personalized evaluation is of fundamental importance, but at the same time an extremely serious challenge for researchers [⁶]. In the literature, there are many solutions on how to define personalized value limits and how to personalize the evaluation.

Sieira et al. propose the definition of blood pressure values that can be considered abnormal in order to provide an alternative instead of different methods that contradict each other [⁷].

Based on the 24-hour recording of the patient's blood pressure, Guzman et al. implemented the classification of blood pressure values using a neuro-fuzzy model, in which the rule was optimized with the help of a genetic algorithm [⁸]. Ali et al. used type-2 fuzzy sets and fuzzy ontology together in their study in patient monitoring, thereby increasing the accuracy of prediction [⁹]. Miranda et al. proposed a new approach for evaluating the quality of photoplethysmographic (PPG) signals used in wearable cardiology measurement devices.

The proposed system tunes the interval of type-2 fuzzy sets to the unique characteristics of each person's PPG signals [¹⁰]. The main goal of this paper is to develop a personalized fuzzy-based model, which is able to take into account the patient’s usual reactions.

In order to achieve this goal, first a personal statistics-based function is created, which uses the measurement statistics made under the identical or nearly identical conditions. Then, this function serves the basis to convert the type-1 fuzzy sets to type-2 in the inference system.

The paper is organized as follows: In Section 2 the investigated original model is introduced. Section 3 describes how the statistics created from the results of previous measurements can be taken into account in the model.

In Section 4 the proposed method is presented in two subsections: Section 4.1 defines the type-1 and interval type-2 fuzzy sets, while in Section 4.2 the personalized interval type-2 membership function creation is illustrated.

In Section 5 a case study is presented: Section 5.1 describes the environment of the measurement, Section 5.2 illustrates the interval type-2 set generation in practice, and in Section 5.3 the measurement results are compared. Finally, Section 6 is devoted to the conclusions.

2 The Original Model

The original model is a hierarchical fuzzy inference structure, which is used to evaluate the current risk level of the patient’s activity taking into account the current physiological values, and the characteristics of the motion form (frequency, intensity, duration) and environmental conditions as well [¹¹].

This paper focuses on the subsystem, which is responsible for the evaluation of the physiological parameters (see Fig. 1). In order to ensure flexible, patient-specific measurement, the number and type of the input parameters can be adjusted depending on the current circumstances (current condition of the patient, available devices, medical recommendations, etc.). The dynamic choice of the number of parameters is indicated by their numbering in the diagram (param_1,..., param_i,..., param_n, where n is the number of the parameters to be measured).

Fig. 1 Structure of the subsystem Medical condition 

The original model under investigation is a Mamdani-type inference system in which the traditional type-1 membership functions are used throughout the system.

The personalized evaluation in the model is provided by a personal profile, which contains all the necessary information related to the patient. Among other things, it contains the characteristics of the parameters to be measured, the usual forms of activity, the value limits determined on the basis of medical recommendations for physiological characteristics, previous measurements, etc.

The parameters of the fuzzy sets that form the partition of the input parameters in the model can be adjusted individually based on the personal profile. This personalization can be further improved if the statistics available from previous measurements are used in membership function tuning.

3 Statistics-Based Function Creation

In order to make the personalized evaluation more effective, the basic idea is to take into account the results of the patient’s previous measurements under the same or nearly identical conditions (resting heart rate, intensity and duration of the activity, sampling frequency) [¹¹].

These measured values are stored together with all necessary parameters in a personal profile. First, based on these values, a histogram is created that represents the previous reactions of the patient under the specific conditions.

Then, a piecewise linear fuzzy function is fitted to this histogram in order to be able to tune the medical recommendation-based fuzzy sets. The function value of the breakpoints of the fitted fuzzy function is determined based on the histogram values using (1), and illustrated in Fig. 2.

Fig. 2 Structure of the subsystem Medical condition 

The resulting function still needs to be normalized, since the membership values must be kept in the universe, considering the maximum value as 1:

where i=1,…,n, n is the number of the histogram values; x _i, µ(x _i) and x _i+1, µ(x _i+1) are the coordinates of the adjacent breakpoints; normalized values are calculated by µ(x_i)=y_i/max(H(x)), and y _i denotes the histogram value belonging to interval i.

4 The Proposed Interval Type-2 Set-based Method

4.1 Type-1 and Interval Type-2 Fuzzy Sets

In the original system trapezoidal type-1 fuzzy sets are used as it is defined in (2) and illustrated in Fig. 3:

μAi(x)={0x≤aix−aibi−aiai≤x≤bi,1bi≤x≤cidi−xdi−cici≤x≤di0di≤x (2)

where a _i, b _i, c _i, d _i are the parameters of the fuzzy sets [¹²]. These parameters ensure the flexibility of the system, because they can be adjusted to the medical recommendations.

Fig. 3 Type-1 membership function 

In certain cases, type-1 sets prove to be insufficient for modeling uncertainty, because the uncertainty in the function value should also be modeled. In these cases, interval type-2 fuzzy sets are used, which are able to handle this issue.

With this approach, instead of an exact membership value, an interval can be assigned to each element, which represents the membership range of the given element, i.e., A:X→E([0,1]), where E([0,1]) denotes the set of closed intervals on the interval [0,1, ¹³].

Interval type-2 sets are represented by two curves, which define the lower and upper limits, as illustrated in Fig. 4. In the figure the lower fuzzy sets parameters are aL,bL,cL,dL, and the parameters of the upper membership function are aU,bU,cU,dU, respectively.

Fig. 4 Interval type-2 membership function 

In the proposed model the goal is to find the appropriate interval type-2 fuzzy sets to obtain a more realistic result.

5 Case Study

5.2 The Proposed Interval Type-2 Fuzzy Set Generation

As a first step of the transformation process, a histogram is generated from the previous measurement data before starting the measurement, as illustrated in Fig. 5.

Fig. 5 Histogram of the previous measurements [14] 

Based on the values of the histogram, a piecewise-linear function is created. The, values of this function must be normalized in accordance with the fuzzy membership functions so that they must fall into the range [0,1].

The input domain of the fuzzy function has to transform as well, it should be given as a percentage of the patient's maximum heart-rate value, instead of the exact heart-rate values. The resulting function is shown in Fig. 6.

Fig. 6 The fuzzy function fitted to the histogram [14] 

The evaluation is based on type-1 membership functions created on the basis of medical recommendations. For this 37 year old patient the Heart-rate functions are presented in Fig. 7, including the simplified statistics-based function (stat) as well, which is needed to transform these type-1 sets into interval type-2 sets.

Fig. 7 Medical recommendations and statistics-based membership function for Heart-rate values 

Based on the type-1 fuzzy sets and the simplified statistics-based function the new parameters of the type-2 fuzzy set can be determined using the method described in Section 3.2.

When the lower and upper membership function parameters of the type-2 set are available, the transformation can be performed. In the case of the examined patient, the functions shown in Fig. 8.

6 Conclusions

Nowadays, as a consequence of the increasingly common health-conscious life-style, patient monitoring devices based on wearable devices are gaining more and more attention. However, patient-specific assessment remains a serious issue for experts.

In this paper a possible solution for this problem is presented. The main idea is to incorporate statistics from the patient’s previous measurements into the evaluation model. These statistics are used to transform the type-1 fuzzy sets of the original Mamdani inference system to interval type-2 fuzzy sets, i.e., the type-1 sets representing medical recommendations can be converted into interval type-2 sets using the characteristic reactions of the patient as well.

As the results show, the proposed system is safer, as it estimates a higher risk level even when the measured value does not exceed the value limit specified in the medical recommendation, but the patient's typical reactions do.

In the presented case study, the subsystem Medical condition was in the focus, and the proposed statistics-based transformation is applied for the input Heart-rate. However, statistics-based transformation could be extend for the other inputs as well to improve the reliability of the system.