Novel Divergence Measure Under Neutrosophic Environment and Its Utility in Various Problems of Decision Making

Novel Divergence Measure Under Neutrosophic Environment and Its Utility in Various Problems of Decision Making

Adeeba Umar, Ram Naresh Saraswat
Copyright: © 2020 |Pages: 23
DOI: 10.4018/IJFSA.2020100104
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This article develops a novel divergence measure for single valued neutrosophic sets with its validity proof to overcome the incapability of the existing divergence measures. The properties of proposed novel divergence measure for single valued neutrosophic sets are also discussed. Practical applications of proposed novel divergence measure for decision making in company selection and medical investigation are demonstrated through numerical illustrations. The comparison of novel divergence measure with the existing divergence measures under a neutrosophic environment is presented and the verification of validity test criteria is given to show that the proposed novel divergence measure is more intelligible and viable which works effectively than the other existing ones.
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1. Introduction

Zadeh (1965) introduced notion of fuzzy set theory to deal with uncertainty, vagueness, ambiguity and imprecision. After that, Atanassov (1986) introduced theory of intuitionistic fuzzy set, which is the generalization of fuzzy set. Adlassnig (1986) implemented fuzzy set theory to formulate medical relations and fuzzy logic to make the diagnostic process and presented a computerized diagnostic system. There are many applications and developments of medical systems exist in the literature (Innocent and John, 2004; Pramanik and Mondal, 2015; Saitta and Torasso, 1981) which are based on fuzzy set theory. First De et al (2001) introduced the application of intuitionistic fuzzy set in medical diagnosis. Many researchers implemented fuzzy set theory in medical diagnosis, but Hung and Tuan (2013) exhibited that the approach which was discussed in (De et al., 2001) shows questionable results which may falsely diagnose the disease. It is widely known that the information which is available to the doctor and medical practitioners about a patient and its medical relationships are inherently uncertain because information is partially known or incomplete as it continuously gets changed. Florentin Smarandache (Wang et al., 2010) introduced neutrosophic set which deals with the uncertainty, inconsistency and incompleteness in medical diagnosis problem. Neutrosophic set comprises three parameters called as truth-membership, indeterminacy-membership and falsity-membership, which are independent of one another and lies in ]0-,1+[. As it is hard to implement notion of neutrosophic set to the practical problems, hence (Wang et al., 2010) gave the theory of single valued neutrosophic set, which is a branch of neutrosophic sets. The concept of single valued neutrosophic relation which is based on single valued neutrosophic sets was introduced by Yang et al (2016). The idea of similarity is necessarily important in every scientific region. Many different methods have been introduced (Chen et al., 1995; Hyung et al., 1994; Pappis and Karacapilidis, 1993; Wang, 1997) to measure the similarity between two fuzzy sets but these measures are not appropriate for dealing with similarity measures of neutrosophic sets. Ye (2014) introduced similarity measures between interval neutrosophic set based on Euclidean distance and Hamming distance and demonstrated the application of these measures in decision making problems. Furthermore, Pramanik et al. (2017) discussed hybrid vector similarity measures for interval neutrosophic sets and single valued neutrosophic sets. Ye (2015) discussed the improved cosine similarity measures of simplified neutrosophic sets and interval neutrosophic sets and implemented them to medical diagnosis problems. Mondal and Pramanik (2015) introduced neutrosophic tangent similarity measure and neutrosophic weighted tangent similarity measure and implemented them in medical diagnosis. Ye (2016) introduced multi-period medical diagnosis method based on tangent function under neutrosophic environment. Nguyen et al. discussed a survey of state of the arts on neutrosophic sets for biomedical diagnoses. Under single valued neutrosophic environment, (Biswas et al., 2016; Ye, 2015) introduced TOPSIS method in decision making based on distance measure to give preference and rank to the alternatives. Abdel-Basset (2019) introduced a powerful framework which is based on neutrosophic sets to treat cancer patients. He also proposed a neutrosophic multi criteria decision making technique to assist health care professionals so that they can predict whether the patient is suffering from cancer disease. Wang et al. (2019) considered the relation between the distance measures and the discrimination measures of fuzzy sets and found that cross-entropy satisfied the conditions of distance measure. Li et al. (2019) introduced a multi attribute decision making method based on neutrosophic information measures and constructed some information measures on the basis of cosine function.

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