1 Distance and Similarity Measures of Interval Neutrosophic Soft Sets Said Broumi 1 ,Irfan Deli 2 and Florentin Smarandache 3 1 Faculty of Arts and Humanities, Hay El Baraka Ben M'sik Casablanca B.P. 7951, Hassan II University Mohammedia-Casablanca , Morocco [email protected]2 Kilis 7 Aralık University, 79000 Kilis, Turkey, [email protected]3 Department of Mathematics, University of New Mexico,705 Gurley Avenue, Gallup, NM 87301, USA [email protected]Abstract:In this paper several distance and similarity measures of interval neutrosophic soft sets are introduced. The measures are examined based on the geometric model, the set theoretic approach and the matching function.Finally,we have successfully shown an application of this similarity measure of interval neutrosophic soft sets. Keywords: Distance, Similarity Measure, Neutrosophic set, Interval Neutrosohic sets, Interval Neutrosohic Soft sets. 1. Introdction In 1965, fuzzy set theory was firstly given by Zadeh [2] which is applied in many real applications to handle uncertainty.Then,interval-valued fuzzy set [3],intuitionisticfuzzy set theory[4] and interval valued intuitionistic fuzzy sets[5] was introduced by Türkşen, Atanassov and Atanassov and Gargov, respectively. This theories can only handle incomplete information not the indeterminate information and inconsistent information which exists commonly in belief systems. So, Neutrsophic sets, founded by F.Smarandache [1], has capapility to deal with uncertainty, imprecise, incomplete and inconsistent information which exist in real world from philosophical point of view. The theory is a powerful tool formal framework which generalizes the concept of the classic set, fuzzy set [2], interval-valued fuzzy set [3], intuitionistic fuzzy set [4] interval-valued intuitionistic fuzzy set [5], and so on. In the actual applications, sometimes, it is not easy to express the truth-membership, indeterminacy-membership and falsity-membership by crisp value, and they may be easier to expressed by interval numbers. The neutrosophic set and their operators need to be specified from scientific or engineering point of view. So, after the pioneering work of Smarandache, in 2005, Wang [6] proposed the notion of interval neutrosophic set ( INS for short) which is another extension of neutrosophic sets. INS can be described by a membership interval, a non-membership interval and indeterminate interval, thus the interval value (INS) has the virtue of complementing NS, which is more flexible and practical than neutrosophic set. The sets provides a more reasonable mathematical framework to deal with indeterminate and inconsistent information.A lot of works about neutrosophic set theory have been studied by several researches [7,11,13,14,15,16,17,18,19,20 ].
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Distance and Similarity Measures of Interval Neutrosophic Soft Sets
In this paper several distance and similarity measures of interval neutrosophic soft sets are introduced. The measures are examined based on the geometric model, the set theoretic approach and the matching function.Finally,we have successfully shown an application of this similarity measure of interval neutrosophic soft sets.
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1
Distance and Similarity Measures of Interval
Neutrosophic Soft Sets
Said Broumi1,Irfan Deli 2 and Florentin Smarandache3
1 Faculty of Arts and Humanities, Hay El Baraka Ben M'sik Casablanca B.P. 7951, Hassan II University Mohammedia-Casablanca , Morocco
Here the two ivn-soft sets, i.e. two symptoms Υ and Ω are significantly similar. Therefore, we
conclude that the person is possibly suffering from pneumonia. This is only a simple example
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to show the possibility of using this method for diagnosis of diseases which could be
improved by incorporating clinical results and other competing diagnosis.
Conclusions
In this paper we have defined, for the first time, the notion of distance and similarity measures
between two interval neutrosophic soft sets. We have studied few properties of distance and
similarity measures. The similarity measures have natural applications in the field of pattern
recognition, feature extraction, region extraction, image processing, coding theory etc. The
results of the proposed similarity measure and existing similarity measure are compared. We
also give an application for similarity measures of interval neutrosophic soft sets.
Acknowledgements
The authors are very grateful to the anonymous referees for their insightful and constructive
comments and suggestions, which have been very helpful in improving the paper.
References
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