New Distance Measure Of Single Valued Neutrosophic Sets And Its Application
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| Author | : Han-Liang Huang |
| Publisher | : Infinite Study |
| Total Pages | : 12 |
| Release | : |
| Genre | : |
| ISBN | : |
A single-valued neutrosophic set (SVNS) is an instance of a neutrosophic set, which can be used to handle uncertainty, imprecise, indeterminate, and inconsistent information in real life. In this paper, a new distance measure between two SVNSs is defined by the full consideration of truthmembership function, indeterminacy-membership function, and falsity-membership function for the forward and backward differences. Then the similarity measure, the entropy measure, and the index of distance are also presented. Finally, two illustrative examples are given to demonstrate the effectiveness of the proposed clustering method and multicriteria decision-making method based on the distance (similarity) measure between SVNSs.
| Author | : Florentin Smarandache |
| Publisher | : Infinite Study |
| Total Pages | : 10 |
| Release | : 2010-08-23 |
| Genre | : Mathematics |
| ISBN | : |
In this paper one generalizes the intuitionistic fuzzy set (IFS), paraconsistent set, and intuitionistic set to the neutrosophic set (NS). Many examples are presented. Distinctions between NS and IFS are underlined.
| Author | : Yameng Wang |
| Publisher | : Infinite Study |
| Total Pages | : 16 |
| Release | : |
| Genre | : Mathematics |
| ISBN | : |
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.
| Author | : Donghai Liu |
| Publisher | : Infinite Study |
| Total Pages | : 10 |
| Release | : |
| Genre | : Mathematics |
| ISBN | : |
Similarity measure is an important tool in multiple criteria decision-making problems, which can be used to measure the difference between the alternatives. In this paper, some new similarity measures of single-valued neutrosophic sets (SVNSs) and interval-valued neutrosophic sets (IVNSs) are defined based on the Euclidean distance measure, respectively, and the proposed similarity measures satisfy the axiom of the similarity measure. Furthermore, we apply the proposed similarity measures to medical diagnosis decision problem; the numerical example is used to illustrate the feasibility and effectiveness of the proposed similarity measures of SVNSs and IVNSs, which are then compared to other existing similarity measures.
| Author | : Harish Garg and Nancy |
| Publisher | : Infinite Study |
| Total Pages | : 20 |
| Release | : |
| Genre | : |
| ISBN | : |
Single-valued neutrosophic sets (SVNSs) handling the uncertainties characterized by truth, indeterminacy, and falsity membership degrees, area more flexible way to capture uncertainty.
| Author | : Subhadip Roy |
| Publisher | : Infinite Study |
| Total Pages | : 17 |
| Release | : |
| Genre | : Mathematics |
| ISBN | : |
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.
| Author | : Florentin Smarandache |
| Publisher | : Infinite Study |
| Total Pages | : 970 |
| Release | : 2022-09-01 |
| Genre | : Mathematics |
| ISBN | : |
| Author | : Florentin Smarandache |
| Publisher | : Infinite Study |
| Total Pages | : 168 |
| Release | : 2018 |
| Genre | : Mathematics |
| ISBN | : 1599735814 |
“Neutrosophic Sets and Systems” has been created for publications on advanced studies in neutrosophy, neutrosophic set, neutrosophic logic, neutrosophic probability, neutrosophic statistics that started in 1995 and their applications in any field, such as the neutrosophic structures developed in algebra, geometry, topology, etc.
| Author | : Ji Chen |
| Publisher | : Infinite Study |
| Total Pages | : 15 |
| Release | : |
| Genre | : |
| ISBN | : |
This paper presents a technique based on the ordered weighted averaging (OWA) distance for the single-valued neutrosophic linguistic (SVNL) technique for order preference by similarity to an ideal solution (TOPSIS). First, the inadequacies of the existing SVNL TOPSIS are analyzed in detail.
| Author | : Harish Garg |
| Publisher | : Infinite Study |
| Total Pages | : 23 |
| Release | : |
| Genre | : Mathematics |
| ISBN | : |
Single-valued neutrosophic set (SVNS) is an important contrivance for directing the decision-making queries with unknown and indeterminant data by employing a degree of “acceptance”, “indeterminacy”, and “non-acceptance” in quantitative terms. Under this set, the objective of this paper is to propose some new distance measures to find discrimination between the SVNSs. The basic axioms of the measures have been highlighted and examined their properties. Furthermore, to examine the relevance of proposed measures, an extended TOPSIS (“technique for order preference by similarity to ideal solution”) method is introduced to solve the group decision-making problems. Additionally, a new clustering technique is proposed based on the stated measures to classify the objects. The advantages, comparative analysis as well as superiority analysis is given to shows its influence over existing approaches.
