On entropy, similarity measure and cross-entropy of single-valued neutrosophic sets and their application in multi-attribute decision making

Due to more or less deviations in the imaging system, there will be noise in the image, which makes the image segmentation inaccurate. To divide a natural image into a more accurate binary image, the target and background of the image are effectively separated to achieve a more effective segmentation result. Therefore, this paper proposes an image segmentation algorithm combining a saliency map and neutrosophic set (NS) theory. First, to overcome the problem of weak edges in the image, we highlight the details and use the guided filter to filter the various channels of the natural image. Then, the initial saliency map is generated. After the weighted superposition of the initial saliency map, the local entropy map and the gray scale map, the final saliency map can be generated using the nonlinear function, and it can effectively highlight the foreground information of the image. Second, the saliency map is transformed to the NS domain and interpreted by three subsets: true (T), indeterminate (I), and false (F). According to NS theory, the indeterminacy is reduced, and the segmentation results are finally obtained by using the method of threshold. Various experiments were done and compared with other state-of-the-art approaches. These experiments demonstrate the effect of the proposed work, which is fast and effective for de-noising.

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“…To fuse the three subsets of T, I and F together, the new entropy formula [32] was selected in this paper, which is defined as follows:…”

Section: Neutrosophic Set Theorymentioning

confidence: 99%

A Fast Image Segmentation Algorithm Based on Saliency Map and Neutrosophic Set Theory

et al. 2020

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“…Each element contained in IFS was depicted by an ordered pair including the degree of membership µ and non-membership v, and the sum of them is limited to 1. Since IFS theory was proposed, a variety of similarity measures between intuitionistic fuzzy sets (IFSs) have been studied in the document [3][4][5][6]. Based on IFS and theories of similarity measures, Li and Cheng [7] presented appropriate similarity measure and gave a numerical example of pattern recognition problems to illustrate the effective of this method.…”

Section: Introductionmentioning

confidence: 99%

Similarity Measures of q-Rung Orthopair Fuzzy Sets Based on Cosine Function and Their Applications

et al. 2019

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In this article, we propose another form of ten similarity measures by considering the function of membership degree, non-membership degree, and indeterminacy membership degree between the q-ROFSs on the basis of the traditional cosine similarity measures and cotangent similarity measures. Then, we utilize our presented ten similarity measures and ten weighted similarity measures between q-ROFSs to deal with multiple attribute decision-making (MADM) problems including pattern recognition and scheme selection. Finally, two numerical examples are provided to illustrate the scientific and effective of the similarity measures for pattern recognition and scheme selection.

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“…e other is to combine new concepts with more mature MCDM methods and further innovate and apply these methods. Among them, the research on the single value neutrosophic set mainly includes basic concepts, operational rules, similarity measurement, distance measurement, entropy measurement, definition of cross entropy [13,14], aggregation operator [15][16][17][18], and decision method [19,20]. INS adopts the form of the interval number to represent the truth information, indeterminacy information, and falsity information, which can effectively catch and express more information in case of uncertainty [21].…”

Section: Introductionmentioning

confidence: 99%

The Projection Model with Unknown Weight Information under Interval Neutrosophic Environment and Its Application to Software Quality-in-Use Evaluation

Wang

2020

Mathematical Problems in Engineering

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Interval neutrosophic sets (INSs) provide us with a more flexible and effective way to express incomplete, indeterminate, and inconsistent information. The purpose of this paper is to introduce the new multicriteria decision-making (MCDM) method based on the improved projection model under the interval neutrosophic environment. In this paper, we investigated the basic concepts and operational rules of interval neutrosophic numbers (INNs), then proposed the projection of two INNs and improved the entropy formula of the INNs. Furthermore, this paper took account into the decision maker’s attitude towards the indeterminacy and risk and proposed two different methods to determine the ideal solutions. Based on this, we presented an improved MCDM method based on the projection model under the interval neutrosophic environment. Finally, the practicability and reliability of the proposed method were explained by the example of software quality-in-use evaluation.

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On entropy, similarity measure and cross-entropy of single-valued neutrosophic sets and their application in multi-attribute decision making

Cited by 41 publications

References 36 publications

A Fast Image Segmentation Algorithm Based on Saliency Map and Neutrosophic Set Theory

A Fast Image Segmentation Algorithm Based on Saliency Map and Neutrosophic Set Theory

Similarity Measures of q-Rung Orthopair Fuzzy Sets Based on Cosine Function and Their Applications

The Projection Model with Unknown Weight Information under Interval Neutrosophic Environment and Its Application to Software Quality-in-Use Evaluation

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