Medical Diagnosis Via Distances Measures Between Credibility Distributions

Medical Diagnosis Via Distances Measures Between Credibility Distributions

Palash Dutta (Dept. of Mathematics, Dibrugarh University, Dibrugarh, India)
Copyright: © 2018 |Pages: 16
DOI: 10.4018/IJDSST.2018100101
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The uncertain, vague, imprecise nature of medical documentation and information make the field of medical diagnosis is the most important and interesting area for applications of fuzzy variables. Furthermore, due to lots of factors to analyze for the diagnosis of the disease makes the doctor/physician's work complicated. In literature, most of medical diagnosis problems are fuzzy variables-based methods. However, no attempt has been seen using a credibility theory. This article presents a maiden effort to carry out medical diagnoses using distance measures between credibility distributions of fuzzy variables. Furthermore, some properties of distance measures on credibility distributions are also studied.
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1. Introduction

Real world problems are always tainted with uncertainty; to handle uncertainty Zadeh (1965) developed fuzzy set theory (FST). After the initiation of FST various direct/indirect extensions such as intuitionistic fuzzy set (IFS), interval valued fuzzy set (IVFS), picture fuzzy set (PFS) have been made and successfully applied in most of the problems of real world situation including medical diagnosis. Another representation of uncertainty is the credibility measure that is the average of the necessity measure and possibility measure developed by Liu (2004) and later redefined by Liu (2007).

Burillo and Bustine (1996) studied entropy and distances for IVFSs, Grzegorzewski (2004) proposed new distance measure based on Housdroff space which are straight forward generalization of Hamming distance, the Euclidean distance and their normal counter parts. Zeng and Guo (2008) studied the distances of IVFSs and relationship between entropy and similarity measure of IVFS. Park et al., (2008) proposed new distance measures for IVFS by incorporating amplitude of membership concept. Li (2009) discussed on distances of IVFS and some of its properties on metric space. Chetia and Das (2010) extended Sanchez’s approach for medical diagnosis using interval valued fuzzy soft sets and exhibited the technique with hypothetical case study. Ahn et al., (2011) presented a fuzzy diagnosis method based on the interval valued interview chart and the interval valued Intuitionistic fuzzy weighted arithmetic average operator and studied the occurrence information symptoms as the weights. Elizabeth and Sujatha (2014) discussed medical diagnosis based on IVFN matrices. Meenakshi and Kaliraja (2011) extended Sanchez’s approach for medical diagnosis using interval valued fuzzy matrix. De et al., (2001) studied Sanchez’s approach for medical diagnosis and extended the concept with the notion of IFS. Szmidt and Kacprzyk (2001) studied medical diagnosis using their proposed distance measures. Own (2009) studied advantages of type-2 fuzzy and switching relation between type-2 fuzzy sets and IFSs defined axiomatically and finally, switching results are applied in medical diagnosis. Samuel and Choi et al., (2012) proposed a fuzzy diagnosis method based on interval valued intuitionistic fuzzy sets, Samuel and Balamurngan (20012a, 2012b, 2013) studied medical diagnosis for IFSs and introduced a new concept of IFS with n parameters and applied in medical diagnosis. Davvaz and Sadrabadi (2016) verified some distance measures on IFSs by applying in medical. Some application of fuzzy set in medical diagnosis can be found in Azar AT, El-Said SA, Balas VE, Olariu T (2013), Banu PKN, Azar AT, Inbarani HH (2017) while application of neuro-fuzzy technique in medical diagnosis can be seen in Azar (2011), Azar, Hassanien, Kim (2012a), Azar, Hassanien &Kim (2012b), Azar (2013a), Azar (2013b), Azar (2014), Azar & Hassanien (2014)Mokeddem, Atmani, & Mokaddem (2014), Rodríguez-González et al (2013). Some other applications of fuzzy sets are seen in Abdel, Elsamahy, Hassan & Bendary (2017), Ismail (2012), Lin & Kuo (2012), Mahmoud, El-Araby, Shehata, AbouZaid, & El-Samie, (2015), Shereen, Ramadan & Ghali (2016).

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