Abstract
Single-valued neutrosophic sets (SVNSs) handling the uncertainties characterized by truth, indeterminacy, and falsity membership degrees, are a more flexible way to capture uncertainty. In this paper, some new types of distance measures, overcoming the shortcomings of the existing measures, for SVNSs with two parameters are proposed along with their proofs. The various desirable relations between the proposed measures have also been derived. A comparison between the proposed and the existing measures has been performed in terms of counter-intuitive cases for showing its validity. The proposed measures have been illustrated with case studies of pattern recognition as well as medical diagnoses, along with the effect of the different parameters on the ordering of the objects.
Highlights
The classical measure theory has been widely used to represent uncertainties in data.these measures are valid only for precise data, and they may be unable to give accurate judgments for data uncertain and imprecise in nature
The gap in the research motivates us to develop some families of the distance measures of the single-valued NS (SVNS) to solve the decision-making problem, for which preferences related to different alternatives are taken in the form of neutrosophic numbers
SVNSs are applied to problems with imprecise, uncertain, incomplete and inconsistent information existing in the real world
Summary
The classical measure theory has been widely used to represent uncertainties in data. A particular case of the NS called a single-valued NS (SVNS) has been proposed by Smarandache [17], Wang et al [18] After this pioneering work, researchers have been engaged in extensions and applications to different disciplines. Information 2017, 8, 162 distance for comparing the SVNSs. Ye [21] presented the concept of correlation for single-valued neutrosophic numbers (SVNNs). Garg and Nancy [25] presented the entropy measure of order α and applied them to solve decision-making problems. The gap in the research motivates us to develop some families of the distance measures of the SVNS to solve the decision-making problem, for which preferences related to different alternatives are taken in the form of neutrosophic numbers.
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