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One of the toughest challenges in medical diagnosis is the handling of uncertainty. Since medical diagnosis with respect to the symptoms uncertain, they will be assumed to have an intuitive nature. Thus, to obtain the uncertain optimism degree of the doctor, fuzzy linguistic quantifiers will be used. The aim of this article is to provide an improved nonprobabilistic entropy approach to support doctors examining the work of the preliminary diagnosing. The proposed entropy measure is based on intuitionistic fuzzy sets, extrainformation regarding hesitation degree, and an intuitive and mathematical connection between the notions of entropy in terms of fuzziness and intuitionism has been revealed. An illustrative example for medical pattern recognition demonstrates the usefulness of this study. Furthermore, in order to make computing and ranking results easier and to increase the recruiting productivity, a computer-based interface system has been developed to support doctors in making more efficient judgments.

Medical diagnostic investigations are very important and complex. Uncertainty is an inseparable aspect of medical diagnosis problems. A symptom is an uncertain indication of a disease as it may or may not occur with or as a result of the disease. Uncertainty characterizes a relation between symptoms and diseases [

The fuzzy set framework has been utilized in several different approaches to model the diagnostic process. In the approach formulated by Sanchez [

With

Furthermore, based on the concepts of fuzzy sets (FSs) theory, numerous fuzzy approaches to medical diagnosis have been addressed, and the readers can refer to [

In addition, several investigations in medical diagnosis have addressed these issues based on intuitionistic fuzzy sets (IFSs), such as Shannon et al. [

Furthermore, Vlachos and Sergiadis [

Among the IFCE approach, this paper also provides an improvement to examine their capabilities to cope with uncertainty in the medical pattern recognition.

The remainder of this study is organized as follows. In Section

Fuzzy sets theory, proposed by Zadeh [

The IFSs is as an extension of fuzzy sets. An IFSs

For each IFSs

The illustration of these degrees has been exhibited in Figure

The descriptions of membership, nonmembership and hesitation degree.

Therefore, to describe an intuitionistic fuzzy set completely, we need at least two functions from the triplet [

Let us recall the definition of the cross-entropy by Kullback [

Based on (

Let

Let us consider two sets

For two sets

However, one can observe that

For two sets

It can easily be verified that

It is easy to see that cross-entropy proposed by Vlachos and Sergiadis [

Furthermore, Szmidt and Kacprzyk [

Motivated by the idea of Szmidt and Kacprzyk [

Following (

We will illustrate an application using the improved IFCE approach for medical pattern recognition problem.

Let us consider the same example in De et al. [

Symptoms characteristic for the diagnoses considered.

Viral fever | Malaria | Typhoid | Stomach problem | Chest problem | |
---|---|---|---|---|---|

Temperature | (0.4, 0.0, 0.6) | (0.7, 0.0, 0.3) | (0.3, 0.3, 0.4) | (0.1, 0.7, 0.2) | (0.1, 0.8, 0.1) |

Headache | (0.3, 0.5, 0.2) | (0.2, 0.6, 0.2) | (0.6, 0.1, 0.3) | (0.2, 0.4, 0.4) | (0.0, 0.8, 0.2) |

Stomach pain | (0.1, 0.7, 0.2) | (0.0, 0.9, 0.1) | (0.2, 0.7, 0.1) | (0.8, 0.0, 0.2) | (0.2, 0.8, 0.0) |

Cough | (0.4, 0.3, 0.3) | (0.7, 0.0, 0.3) | (0.2, 0.6, 0.2) | (0.2, 0.7, 0.1) | (0.2, 0.8, 0.0) |

Chest pain | (0.1, 0.7, 0.2) | (0.1, 0.8, 0.1) | (0.1, 0.9, 0.0) | (0.2, 0.7, 0.1) | (0.8, 0.1, 0.1) |

Symptoms characteristic for the patients considered.

Temperature | Headache | Stomach pain | Cough | Chest pain | |
---|---|---|---|---|---|

Al | (0.8, 0.1, 0.1) | (0.6, 0.1, 0.3) | (0.2, 0.8, 0.0) | (0.6, 0.1, 0.3) | (0.1, 0.6, 0.3) |

Bob | (0.0, 0.8, 0.2) | (0.4, 0.4, 0.2) | (0.6, 0.1, 0.3) | (0.1, 0.7, 0.2) | (0.1, 0.8, 0.1) |

Joe | (0.8, 0.1, 0.1) | (0.8, 0.1, 0.1) | (0.0, 0.6, 0.4) | (0.2, 0.7, 0.1) | (0.0, 0.5, 0.5) |

Ted | (0.6, 0.1, 0.3) | (0.5, 0.4, 0.1) | (0.3, 0.4, 0.3) | (0.7, 0.2, 0.1) | (0.3, 0.4, 0.3) |

In order to find a proper diagnosis, we calculate for each patient

The diagnosed results by the improved IFCE approach.

Viral fever | Malaria | Typhoid | Stomach problem | Chest problem | |
---|---|---|---|---|---|

Al | 0.7885 | 0.8902 | 2.1573 | 2.5384 | |

Bob | 1.6195 | 2.6886 | 0.9896 | 1.8327 | |

Joe | 1.5938 | 1.0668 | 2.2708 | 2.8497 | |

Ted | 0.8992 | 0.9952 | 1.4273 | 1.9536 |

According to Table

Through this study, some issues can be raised and depicted as follows.

From the practical case of medical diagnosis study, the proposed method can provide a useful way to help doctors perform preliminary diagnosis. The proposed method differs from previous methods for medical diagnosis decision making due to the fact that the proposed method considers the degree of hesitation compared to other existing approaches. In the future, the proposed method may be a merit for the preliminary diagnosed models to solve the medical diagnosis problem using IFSs.

Sometimes, the difference between two adjacent ranking scores is very close. Observing Table

As more and more decisions in real organizational settings are made, applying IFSs into medical diagnosis analysis to deal with imprecision, uncertainty, and fuzziness in decision making may become a popular research topic in the current uncertain environment. The application of IFSs in supporting doctors can provide a useful way to help the decision analyzer make his/her decisions efficiently.

In this paper, in order to make computing and ranking the results much easier and to increase the recruiting productivity, we have developed an information system called intuitionistic fuzzy sets medical diagnosis system (IFSMDS) as shown in Figure

The functional interface of IFSMDS.

Input intuitionistic diagnosed value on each symptom for patient.

The outcomes and ranking of medical diagnosis.

In this paper, an improved IFCE approach is presented based on IFSs. The idea of improvement is to add the hesitation degree and reveal an intuitive and mathematical connection between the notions of entropy for IFSs in terms of fuzziness and intuitionism based on this entropy measure. Illustrative examples have demonstrated the usefulness of the proposed discrimination information measure for medical diagnosis. In addition, in order to prevent misjudgment, we have suggested that when the diagnosed results between the diseases are very close, an advanced diagnosis is necessary to avoid some error risks of the medical diagnosis.

The author would like to express appreciation to the anonymous reviewers for their very helpful comments on improving this paper. This research is partially supported by the National Science Council of the Republic of China, Taiwan with Grant no. NSC 100-2410-H-606-002-MY2.