Hausdorff Distance and Similarity Measures for Single-Valued Neutrosophic Sets with Application in Multi-Criteria Decision Making
Title | Hausdorff Distance and Similarity Measures for Single-Valued Neutrosophic Sets with Application in Multi-Criteria Decision Making PDF eBook |
Author | Mehboob Ali |
Publisher | Infinite Study |
Pages | 17 |
Release | 2022-01-01 |
Genre | Mathematics |
ISBN |
Hausdorff distance is one of the important distance measures to study the degree of dissimilarity between two sets that had been used in various fields under fuzzy environments. Among those, the framework of single-valued neutrosophic sets (SVNSs) is the one that has more potential to explain uncertain, inconsistent and indeterminate information in a comprehensive way. And so, Hausdorff distance for SVNSs is important. Thus, we propose two novel schemes to calculate the Hausdorff distance and its corresponding similarity measures (SMs) for SVNSs. In doing so, we firstly develop the two forms of Hausdorff distance between SVNSs based on the definition of Hausdorff metric between two sets. We then use these new distance measures to construct several SMs for SVNSs. Some mathematical theorems regarding the proposed Hausdorff distances for SVNSs are also proven to strengthen its theoretical properties. In order to show the exact calculation behavior and distance measurement mechanism of our proposed methods in accordance with the decorum of Hausdorff metric, we utilize an intuitive numerical example that demonstrate the novelty and practicality of our proposed measures. Furthermore, we develop a multi-criteria decision making (MCDM) method under single-valued neutrosophic environment using the proposed SMs based on our defined Hausdorff distance measures, called as a single-valued neutrosophic MCDM (SVN-MCDM) method. In this connection, we employ our proposed SMs to compute the degree of similarity of each option with the ideal choice to identify the best alternative as well as to perform an overall ranking of the alternatives under study. We then apply our proposed SVN-MCDM scheme to solve two real world problems of MCDM under single-valued neutrosophic environment to show its effectiveness and application.
MULTI-CRITERIA DECISION MAKING METHOD BASED ON SIMILARITY MEASURES UNDER SINGLE VALUED NEUTROSOPHIC REFINED AND INTERVAL NEUTROSOPHIC REFINED ENVIRONMENTS
Title | MULTI-CRITERIA DECISION MAKING METHOD BASED ON SIMILARITY MEASURES UNDER SINGLE VALUED NEUTROSOPHIC REFINED AND INTERVAL NEUTROSOPHIC REFINED ENVIRONMENTS PDF eBook |
Author | FARUK KARAASLAN |
Publisher | Infinite Study |
Pages | 15 |
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In this paper, we propose three similarity measure methods for single valued neutrosophic refined sets and interval neutrosophic refined sets based on Jaccard, Dice and Cosine similarity measures of single valued neutrosophic sets and interval neutrosophic sets.
Similarity Measures of Quadripartitioned Single Valued Bipolar Neutrosophic Sets and Its Application in Multi-Criteria Decision Making Problems
Title | Similarity Measures of Quadripartitioned Single Valued Bipolar Neutrosophic Sets and Its Application in Multi-Criteria Decision Making Problems PDF eBook |
Author | Subhadip Roy |
Publisher | Infinite Study |
Pages | 17 |
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Genre | Mathematics |
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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.
Some new operations on single-valued neutrosophic matrices and their applications in multi-criteria group decision making
Title | Some new operations on single-valued neutrosophic matrices and their applications in multi-criteria group decision making PDF eBook |
Author | Faruk Karaaslan |
Publisher | Infinite Study |
Pages | 21 |
Release | |
Genre | Mathematics |
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The single-valued neutrosophic set plays a crucial role to handle indeterminant and inconsistent information during decision making process. In recent research, a development in neutrosophic theory is emerged, called single-valued neutrosophic matrices, are used to address uncertainties. The beauty of single-valued neutrosophic matrices is that the utilizing of several fruitful operations in decision making.
New distance and similarity measures of single value neutrosophic sets with application in multi-criteria decision-making
Title | New distance and similarity measures of single value neutrosophic sets with application in multi-criteria decision-making PDF eBook |
Author | Yameng Wang |
Publisher | Infinite Study |
Pages | 16 |
Release | |
Genre | Mathematics |
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The processing of uncertainty information has gradually became one of the hot issues in arti cial intelligence eld, and the infor- mation measures of uncertainty information processing are of importance. Single value neutrosophic sets (SVNSs) provide us a exible 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.
A Novel Single-Valued Neutrosophic Set Similarity Measure and Its Application in Multicriteria Decision-Making
Title | A Novel Single-Valued Neutrosophic Set Similarity Measure and Its Application in Multicriteria Decision-Making PDF eBook |
Author | Wen Jiang |
Publisher | Infinite Study |
Pages | 14 |
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The single-valued neutrosophic set is a subclass of neutrosophi cset, and has been proposed in recent years. An important application for single-valued neutrosophic sets is to solve multicriteria decision-making problems.
Several Similarity Measures of Neutrosophic Sets
Title | Several Similarity Measures of Neutrosophic Sets PDF eBook |
Author | Said Broumi |
Publisher | Infinite Study |
Pages | 9 |
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Smarandache (1995) defined the notion of neutrosophic sets, which is a generalization of Zadeh's fuzzy set and Atanassov's intuitionistic fuzzy set. In this paper, we first develop some similarity measures of neutrosophic sets.