# The Open Cybernetics & Systemics Journal

(Discontinued)

ISSN: 1874-110X ― Volume 12, 2018
RESEARCH ARTICLE

# Medical Decision Making via the Arithmetic of Generalized Triangular Fuzzy Numbers

Palash Dutta1, *, Satya Ranjan Dash2
1 Department of Mathematics, Dibrugarh University, Dibrugarh, Assam, India
2 School of Computer Application, KIIT University, Bhubaneswar, India

## Abstract

### Background:

When patient(s) approach to a medical expert to explain their problems, they often explain their conditions through vague linguistic expression [1]. Medical expert needs to prepare a list of potential symptoms for the particular diseases of the patients based on their vague linguistic statements. Together with the vagueness in medical documents and imprecise information gathered for decision making makes the medical experts’ job more complex. Due to the occurrence of uncertainty in medical decision making exploitation of the Fuzzy Set (FST) is required. Generally in literature, type-I fuzzy set, Intuitionistic Fuzzy Sets (IFSs), Interval Valued Fuzzy Sets (IVFSs), and Picture Fuzzy Sets (PFSs) are extensively applied in medical decision making.

### Objective:

Although different approaches have been used in medical decision making, no single evidence has been observed in use of Generalized Fuzzy Numbers (GFNs) in medical decision making. GFN has the ability to deal with vague/imprecise information in a supple way. Basically, the parameter height of GFN characterizes the grade of buoyancy of judgments of decision takers in a very specific comportment. Therefore, a maiden effort has been made to study medical diagnosis using arithmetic of GFNs, and finally to exhibit the techniques a case study has been carried out under this setting.

### Method:

To achieve the proposed goal an algorithm is being formulated and to obtain patients-diseases relationship the arithmetic of GFNs is used as the composition of fuzzy relations.

### Results:

In this study, two scenarios are taken into considerations. In scenario-I, TFNs are used while in scenario-II, GFNs are taken to characterize uncertainty and medical decision making has been carried out. The advantages of GFNs over the TFNs are observed through the comparison of both the approaches in medical decision making. Major advantage GFNs here is that it makes it possible to compare various diseases against each other’s in a more acceptable manner and accordingly diseases of the patients can be detected directly.

### Conclusion:

The advantage of the GFN approach has been observed from the case study where it is found that existing TFN approach provides illogical results while proposed one gives a rational result. Also, it has been established that proposed approach is efficient, simple, logical, technically sound and general enough for implementation.

Keywords: Uncertainty, Imprecision, Fuzzy numbers, Generalized fuzzy numbers, Fuzzy arithmetic, Medical decision making.

### Article Information

#### Identifiers and Pagination:

Year: 2018
Volume: 12
First Page: 1
Last Page: 19
Publisher Id: TOCSJ-12-1
DOI: 10.2174/1874110X01812010001

#### Article History:

Revision Received Date: 28/12/2017
Acceptance Date: 30/01/2018
Electronic publication date: 22/02/2018
Collection year: 2018

© 2018 Dutta and Dash.

open-access license: This is an open access article distributed under the terms of the Creative Commons Attribution 4.0 International Public License (CC-BY 4.0), a copy of which is available at: (https://creativecommons.org/licenses/by/4.0/legalcode). This license permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

Correspondence: Address correspondence to this author at the Department of Mathematics, Dibrugarh University, Dibrugarh, Assam, India; Tel:+919435184995; E-mails: palash.dtt@gmail.com, palashdutta@dibru.ac.in

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