New distance and similarity measures of single value neutrosophic sets with application in multi-criteria decision-making
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The processing of uncertainty information has gradually became one of the hot issues in artificial intelligence field, and the information measures of uncertainty information processing are of importance. Single value neutrosophic sets (SVNSs) provide us a flexible mathematical framework to process uncertainty information. In this paper, we mainly consider the measures of SVNSs. The existing information measures mostly are constructed based on the two typical inclusion relations about single value neutrosopgic sets. However, there exist some practical problems that do not apply to the two typical inclusion relations. Therefore, there exists another inclusion relation which is called the type-3 inclusion relation about SVNSs. This inclusion relation can help us to process some uncertain information in a new way. It is noteworthy that the existing information measures are not suitable for the type-3 inclusion about SVNSs. In this case, we proposed the new distance measure based on the cross-entropy about SVNSs, then the corresponding similarity measure is proposed according to the matching function between distance and similarity. Finally, the new distance measure is applied to decision-making problem with a illustrative example. The verification result show that the new distance is favorable for dealing with some practical problems.
Abstract
The processing of uncertainty information has gradually became one of the hot issues in artificial intelligence field, and the information measures of uncertainty information processing are of importance. Single value neutrosophic sets (SVNSs) provide us a flexible mathematical framework to process uncertainty information. In this paper, we mainly consider the measures of SVNSs. The existing information measures mostly are constructed based on the two typical inclusion relations about single value neutrosopgic sets. However, there exist some practical problems that do not apply to the two typical inclusion relations. Therefore, there exists another inclusion relation which is called the type-3 inclusion relation about SVNSs. This inclusion relation can help us to process some uncertain information in a new way. It is noteworthy that the existing information measures are not suitable for the type-3 inclusion about SVNSs. In this case, we proposed the new distance measure based on the cross-entropy about SVNSs, then the corresponding similarity measure is proposed according to the matching function between distance and similarity. Finally, the new distance measure is applied to decision-making problem with a illustrative example. The verification result show that the new distance is favorable for dealing with some practical problems.
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