Similarity Measures Of Quadripartitioned Single Valued Bipolar Neutrosophic Sets And Its Application In Multi Criteria Decision Making Problems
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Similarity Measures of Quadripartitioned Single Valued Bipolar Neutrosophic Sets and Its Application in Multi-Criteria Decision Making Problems
In this paper, a definition of quadripartitioned single valued bipolar neutrosophic set (QSVBNS) is introduced as a generalization of both quadripartitioned single valued neutrosophic sets (QSVNS) and bipolar neutrosophic sets (BNS). There is an inherent symmetry in the definition of QSVBNS. Some operations on them are defined and a set theoretic study is accomplished. Various similarity measures and distance measures are defined on QSVBNS. An algorithm relating to multi-criteria decision making problem is presented based on quadripartitioned bipolar weighted similarity measure. Finally, an example is shown to verify the flexibility of the given method and the advantage of considering QSVBNS in place of fuzzy sets and bipolar fuzzy sets.
Bipolar quadripartitioned single valued neutrosophic rough set
Here bipolar quadripartitioned single valued neutrosophic rough (BQSVNR) set is introduced. Some basic set theoretic terminologies like constant BQSVNR set, subsethood of two BQSVNR sets are shown. Algebraic operations like union, intersection and complement have also been defined. Different types of measure like similarity measure, quasi similarity measure and distance measures between two BQSVNR sets have been discussed with their properties. Again various measures of similarity namely distance based similarity measure, cosine similarity measure, membership function based similarity measure are introduced in this paper. A medical diagonasis problem has been solved using similarity measure at the end.
Bipolar quadripartitioned single valued neutrosophic sets
The notion of simple bipolar quadripartition is presented valuable neutrosophi set. Some basic theoretic terminologies, operations and properties of bipolar quadripartitioned single valued neutrosophic set are given here.