Journal of Modern Medical

Introduction
In recent years, fuzzy systems have been successfully used in different fields of science, especially medical sciences [1, 2]. They use linguistic rules to describe systems that are easily interpreted and checked by the user [3, 4]. Therefore, one of their applications of interest is in clinical decision support systems, where the discovery of rules hidden in the data and the interpretability of these rules are of great importance. The extraction of these rules with two indicators of accuracy and high interpretability helps specialists in increasing the accuracy and speed of disease diagnosis [5, 6, 7].
In the studies that have been conducted so far, attention to the extraction of single rules with high positive predictive value (PPV) and negative predictive value (NPV) has been neglected [8, 9, 10]. Due to the interest of specialists in diagnostic rules that are capable of quick evaluation and are easy to remember, and because many medical data sets, including the Pima diabetes dataset, contain clinical parameters resulting from tests, it is important to design a model for extracting single rules with high efficiency in terms of PPV and NPV. In this paper, we aim to propose a hybrid genetic-fuzzy classification system that automatically extracts the rules hidden in the data. Then, by evaluating each of the extracted rules, we provide the best single rule for diagnosis of disease and absence of disease. In addition, a new self-organizing chromosomal structure is proposed to eliminate the effect of the selection of genetic algorithm operators on the efficiency of the model. The Pima diabetes dataset was finally used to evaluate the proposed model.
Methods
In this study, the rule base of retrospective Mamdani fuzzy systems is designed using PIMA data. One of the problems of PIMA dataset is the presence of missing values and outliers. In this study, KNNi method was used to remove missing values and K-means was applied to remove outliers [2, 9]. At the beginning, there are no rules in the rule base and no membership functions are assigned to the fuzzy variables. They are generated and optimized using the genetic algorithm [2]. To eliminate the effect of the type of mutation and recombination operators on the efficiency of the model and reduce the time of setting the parameters of the genetic algorithm by trial and error, a new chromosomal structure was proposed which, while producing the fuzzy rule base, provides the best mutation and recombination operators among the existing methods for each dataset. In this proposed chromosomal structure, as generations pass and the results converge, the recombination operator corresponding to individuals with the highest fitness is selected more than others. In this way, the optimal recombination operator for the examined data set is automatically selected. The same process is done for the mutation operator. Then, each rule was evaluated on the dataset and their accuracy was measured. Finally, the best single rules with the highest PPV for detecting people with diabetes and the highest NPV for people without diabetes were determined. Afterwards, the diagnostic rules of having and not having the disease were combined and a set of two diagnostic rules was presented as the output of the model.
Results
The result of implementing the proposed model was the presentation of 81 single rules. Among the rules for diagnosing diabetes, those with PPV >70% were selected, and among the rules for diagnosing the absence of diabetes, those with NPV >80% were selected. Four single rules were finally determined which are listed in Table 1.


Table 2 presents the result of combining the best single rules and the output of the proposed model.


Table 3 compares the efficiency of the proposed method with some existing methods in terms of the number of rules selected in the final rule base, the number of linguistic terms to describe each variable, the fuzzy membership function, the total number of conditions in the rules, the number of records used to build the model, and accuracy.


Discussion
In this study, due to the importance of extracting precise rules and their interpretability in medical assistant systems, a rule extraction model using a hybrid genetic-fuzzy algorithm with high accuracy was presented for determining the most compact set of rules and benchmarked on the PIMA diabetes dataset. In addition, Also, to avoid the complexity of setting genetic algorithm parameters and remove their effect on model efficiency, a new chromosomal structure with automatic adjustment of mutation and recombination operators was presented. The best set of rules according to the two criteria of interpretability and high accuracy, was the set with 2 rules, 4 sets of fuzzy terms per each prefix, and an average length of 2 per each rule, which achieved 79.05% accuracy. The used membership function was a symmetric triangular function, which makes it easier for human users to understand the concepts due to the constant width of all functions.
Based on the rule length criteria, the number of rules and membership functions, which are the most important indicators of the interpretability of rules by human users [10, 11, 12, 13], the proposed model could provide an effective rule set with high interpretability to distinguish diabetic and non-diabetic people including only one diagnostic rule for diabetic people and one diagnostic rule for non-diabetic people.
Conclusion
Rule extraction from datasets in medical diagnosis is an important area for knowledge discovery. Fuzzy systems are known as a popular tool in this application to rules that can be interpreted by humans. For the automatic design of fuzzy systems from the data, the genetic algorithm has shown a high ability. In this study, a self-organizing rule extraction model using genetic-fuzzy system was proposed for diagnostic goals. The PIMA diabetes dataset was used to evaluate the proposed model. Based on this model, the best single diagnostic rules for people without and with diabetes were presented.
Based on the results, it can be concluded that the proposed model with accuracy of 79.05, PPV of 70.83 and NPV of 81.41% can be used as a promising general model in medical data classification and diagnosis. The small number of rules and their shortness are among the important features of the proposed rules, which can be easily evaluated and remembered by experts, along with quick implementation.
One of the limitations of the study was the use of public data and not evaluation of the proposed rules by clinical experts. It is suggested that the proposed model be implemented on local data and each of the extracted rules be evaluated by clinical experts.
Ethical Considerations
Compliance with ethical guidelines
In this study, no experiment on human or animal samples were conducted. Therefore, there as no need for obtaining ethical code.
Funding
This study was extracted from a research project (Code: 400-01-00) in Behbahan Khatam Alanbia University of Technology. It was not funded by any organization.
Authors' contributions
Conceptualization: Amin Golabpour; Writing: Fatemeh Ahouz; Methodology, model implementation and analysis: All authors
Conflicts of interest
The authors declared no conflict of interest.

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