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Journal articles on the topic 'Neutrosophic entropy'

Author: Grafiati

Published: 2 June 2025

Last updated: 31 July 2025

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1

Ye, Jun. "Improved Cross Entropy Measures of Single Valued Neutrosophic Sets and Interval Neutrosophic Sets and Their Multicriteria Decision Making Methods." Cybernetics and Information Technologies 15, no. 4 (2015): 13–26. http://dx.doi.org/10.1515/cait-2015-0051.

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Abstract Due to some drawbacks of the cross entropy between Single Valued Neutrosophic Sets (SVNSs) in dealing with decision-making problems, the existing single valued neutrosophic cross entropy indicates an asymmetrical phenomenon or may produce an undefined (unmeaningful) phenomenon in some situations. In order to overcome these disadvantages, this paper proposes an improved cross entropy measure of SVNSs and investigates its properties, and then extends it to a cross entropy measure between interval neutrosophic sets (INSs). Furthermore, the cross entropy measures are applied to multicrite

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2

Cui, Wen-Hua, and Jun Ye. "Generalized Distance-Based Entropy and Dimension Root Entropy for Simplified Neutrosophic Sets." Entropy 20, no. 11 (2018): 844. http://dx.doi.org/10.3390/e20110844.

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In order to quantify the fuzziness in the simplified neutrosophic setting, this paper proposes a generalized distance-based entropy measure and a dimension root entropy measure of simplified neutrosophic sets (NSs) (containing interval-valued and single-valued NSs) and verifies their properties. Then, comparison with the existing relative interval-valued NS entropy measures through a numerical example is carried out to demonstrate the feasibility and rationality of the presented generalized distance-based entropy and dimension root entropy measures of simplified NSs. Lastly, a decision-making

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3

Kandasamy, Ilanthenral, and Florentin Smarandache. "Multicriteria Decision Making Using Double Refined Indeterminacy Neutrosophic Cross Entropy and Indeterminacy Based Cross Entropy." Applied Mechanics and Materials 859 (December 2016): 129–43. http://dx.doi.org/10.4028/www.scientific.net/amm.859.129.

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Double Refined Indeterminacy Neutrosophic Set (DRINS) is an inclusive case of the refined neutrosophic set, defined by Smarandache (2013), which provides the additional possibility to represent with sensitivity and accuracy the uncertain, imprecise, incomplete, and inconsistent information which are available in real world. More precision is provided in handling indeterminacy; by classifying indeterminacy (I) into two, based on membership; as indeterminacy leaning towards truth membership (IT) and indeterminacy leaning towards false membership (IF). This kind of classification of indeterminacy

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4

Abu Qamar, Majdoleen, and Nasruddin Hassan. "Entropy, Measures of Distance and Similarity of Q-Neutrosophic Soft Sets and Some Applications." Entropy 20, no. 9 (2018): 672. http://dx.doi.org/10.3390/e20090672.

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The idea of the Q-neutrosophic soft set emerges from the neutrosophic soft set by upgrading the membership functions to a two-dimensional entity which indicate uncertainty, indeterminacy and falsity. Hence, it is able to deal with two-dimensional inconsistent, imprecise, and indeterminate information appearing in real life situations. In this study, the tools that measure the similarity, distance and the degree of fuzziness of Q-neutrosophic soft sets are presented. The definitions of distance, similarity and measures of entropy are introduced. Some formulas for Q-neutrosophic soft entropy wer

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Tan, Ruipu, Wende Zhang, and Shengqun Chen. "Some Generalized Single Valued Neutrosophic Linguistic Operators and Their Application to Multiple Attribute Group Decision Making." Journal of Systems Science and Information 5, no. 2 (2017): 148–62. http://dx.doi.org/10.21078/jssi-2017-148-15.

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Abstract This paper proposes a group decision making method based on entropy of neutrosophic linguistic sets and generalized single valued neutrosophic linguistic operators. This method is applied to solve the multiple attribute group decision making problems under single valued neutrosophic liguistic environment, in which the attribute weights are completely unknown. First, the attribute weights are obtained by using the entropy of neutrosophic linguistic sets. Then three generalized single valued neutrosophic linguistic operators are introduced, including the generalized single valued neutro

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Mourad, Nahia. "Assessment of Structural Cracks in Aircraft Using a Decision-Making Approach Based on Enhanced Entropy and Single-Valued Neutrosophic Sets." International Journal of Neutrosophic Science 19, no. 04 (2022): 49–57. http://dx.doi.org/10.54216/ijns.190404.

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Structural health monitoring (SHM) tries to determine the status of substances, elements, and the life expectancy of any aircraft building. It also serves as a vital tool for ensuring the structural integrity and safety of the aircraft. This research used a neutrosophic-Entropy model to assess the structural cracks in the reinforced concrete aircraft to evaluate its structural performance. For example, Entropy may be used in the civil engineering profession to pick subcontractors, manage traffic, and monitor the structural integrity of a structure, among other things. SHM in reinforced concret

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Bian, Xiaofei, Haiwei Pan, Kejia Zhang, Chunling Chen, Peng Liu, and Kun Shi. "NeDSeM: Neutrosophy Domain-Based Segmentation Method for Malignant Melanoma Images." Entropy 24, no. 6 (2022): 783. http://dx.doi.org/10.3390/e24060783.

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Skin lesion segmentation is the first and indispensable step of malignant melanoma recognition and diagnosis. At present, most of the existing skin lesions segmentation techniques often used traditional methods like optimum thresholding, etc., and deep learning methods like U-net, etc. However, the edges of skin lesions in malignant melanoma images are gradually changed in color, and this change is nonlinear. The existing methods can not effectively distinguish banded edges between lesion areas and healthy skin areas well. Aiming at the uncertainty and fuzziness of banded edges, the neutrosoph

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R., Sarannya Kumari, Sunny Joseph Kalayathankal, Mathews M. George, and Florentin Smarandache. "An Entropy Measure for n-Cylindrical Fuzzy Neutrosophic Sets." Neutrosophic Optimization and Intelligent Systems 3 (May 5, 2024): 23–31. http://dx.doi.org/10.61356/j.nois.2024.3220.

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n-Cylindrical fuzzy neutrosophic set (n-CyFNS) is a new variant of fuzzy neutrosophic sets. In this paper, our aim is to introduce an entropy measure for n-CyFNS. Here, we explained its properties along with examples. Two real life applications, one on better way of shopping and the second on teacher evaluation, based on this proposed entropy measure are also illustrated.

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CHENG, H. D., and YANHUI GUO. "A NEW NEUTROSOPHIC APPROACH TO IMAGE THRESHOLDING." New Mathematics and Natural Computation 04, no. 03 (2008): 291–308. http://dx.doi.org/10.1142/s1793005708001082.

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A neutrosophic set (Ns), a part of neutrosophy theory, studies the origin, nature, and scope of neutralities, as well as their interactions with different ideational spectra. The neutrosophic set is a powerful general formal framework that has been recently proposed. However, the neutrosophic set needs to be specified from a technical point of view. We apply the neutrosophic set in image domain and define some concepts and operations for image thresholding. The image G is transformed into Ns domain, which is described using three subsets T, I and F. The entropy in neutrosophic set is defined a

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GUO, YANHUI, H. D. CHENG, and YINGTAO ZHANG. "A NEW NEUTROSOPHIC APPROACH TO IMAGE DENOISING." New Mathematics and Natural Computation 05, no. 03 (2009): 653–62. http://dx.doi.org/10.1142/s1793005709001490.

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A neutrosophic set (NS), a part of neutrosophy theory, studies the origin, nature, and scope of neutralities, as well as their interactions with different ideational spectra. The neutrosophic set is a general formal framework that has been recently proposed. However, the neutrosophic set needs to be specified from a technical point of view. Now, we apply the neutrosophic set into image domain and define some concepts and operators for image denoising. The image G is transformed into NS domain, which is described using three membership sets: T, I and F. The entropy of the neutrosophic set is de

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Yang, Han, Xiaoman Wang, and Keyun Qin. "New Similarity and Entropy Measures of Interval Neutrosophic Sets with Applications in Multi-Attribute Decision-Making." Symmetry 11, no. 3 (2019): 370. http://dx.doi.org/10.3390/sym11030370.

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Information measures play an important role in the interval neutrosophic sets (INS) theory. The main purpose of this paper is to study the similarity and entropy of INS and its application in multi-attribute decision-making. We propose a new inclusion relation between interval neutrosophic sets where the importance of the three membership functions may be different. Then, we propose the axiomatic definitions of the similarity measure and entropy of the interval neutrosophic set (INS) based on the new inclusion relation. Based on the Hamming distance, cosine function and cotangent function, som

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12

Alias, Suriana, Daud Mohamad, and Adibah Shuib. "The entropy of rough neutrosophic multisets." Journal of Physics: Conference Series 1988, no. 1 (2021): 012079. http://dx.doi.org/10.1088/1742-6596/1988/1/012079.

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13

Rogulj, Katarina, Jelena Kilić Pamuković, and Majda Ivić. "Hybrid MCDM Based on VIKOR and Cross Entropy under Rough Neutrosophic Set Theory." Mathematics 9, no. 12 (2021): 1334. http://dx.doi.org/10.3390/math9121334.

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Problems in real life usually involve uncertain, inconsistent and incomplete information. An example of such problems is strategic decision making with respect to remediation planning of historic pedestrian bridges. The multiple decision makers and experts, as well as the various mutually conflicting criteria, unknown criteria weights, and vagueness and duality in final decisions, provide motivation to develop a methodology that is able to resist the challenges implicit in this problem. Therefore, the aim of this research was to propose an algorithm based on the theory of rough neutrosophic se

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Mohan, J., V. Krishnaveni, and Yanhui Guo. "A New Neutrosophic Approach of Wiener Filtering for MRI Denoising." Measurement Science Review 13, no. 4 (2013): 177–86. http://dx.doi.org/10.2478/msr-2013-0027.

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In this paper, a new filtering method based on neutrosophic set (NS) approach of wiener filter is presented to remove Rician noise from magnetic resonance image. A neutrosophic set, a part of neutrosophy theory, studies the origin, nature and scope of neutralities, as well as their interactions with different ideational spectra. Now, we apply the neutrosophic set into image domain and define some concepts and operators for image denoising. The image is transformed into NS domain, described using three membership sets: True (T), Indeterminacy (I) and False (F). The entropy of the neutrosophic s

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Sinha, Kalyan, and Pinaki Majumdar. "Bipolar quadripartitioned single valued neutrosophic sets." Proyecciones (Antofagasta) 39, no. 6 (2020): 1597–614. http://dx.doi.org/10.22199/issn.0717-6279-2020-06-0095.

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The notion of simple bipolar quadripartition is presented valuable neutrosophic set. Some basic set theoretic terminologies, operations and properties of bipolar quadripartitioned single valued neutrosophic set are given here. Also different types of distances, similarity measures and entropy measure are discussed. Finally a decision making problem using the similarity measure technique of bipolar quadripartitioned single valued neutrosophic sets has been solved.

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16

Li, Qiaoyan, Yingcang Ma, Florentin Smarandache, and Shuangwu Zhu. "Single-Valued Neutrosophic Clustering Algorithm Based on Tsallis Entropy Maximization." Axioms 7, no. 3 (2018): 57. http://dx.doi.org/10.3390/axioms7030057.

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Data clustering is an important field in pattern recognition and machine learning. Fuzzy c-means is considered as a useful tool in data clustering. The neutrosophic set, which is an extension of the fuzzy set, has received extensive attention in solving many real-life problems of inaccuracy, incompleteness, inconsistency and uncertainty. In this paper, we propose a new clustering algorithm, the single-valued neutrosophic clustering algorithm, which is inspired by fuzzy c-means, picture fuzzy clustering and the single-valued neutrosophic set. A novel suitable objective function, which is depict

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Quek, Shio Gai, Ganeshsree Selvachandran, Florentin Smarandache, et al. "Entropy Measures for Plithogenic Sets and Applications in Multi-Attribute Decision Making." Mathematics 8, no. 6 (2020): 965. http://dx.doi.org/10.3390/math8060965.

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Plithogenic set is an extension of the crisp set, fuzzy set, intuitionistic fuzzy set, and neutrosophic sets, whose elements are characterized by one or more attributes, and each attribute can assume many values. Each attribute has a corresponding degree of appurtenance of the element to the set with respect to the given criteria. In order to obtain a better accuracy and for a more exact exclusion (partial order), a contradiction or dissimilarity degree is defined between each attribute value and the dominant attribute value. In this paper, entropy measures for plithogenic sets have been intro

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18

Wang, Yi, Xiao-Kang Wang, and Jian-Qiang Wang. "Cloud service reliability assessment approach based on multi-valued neutrosophic cross-entropy and entropy measures." Filomat 32, no. 8 (2018): 2793–812. http://dx.doi.org/10.2298/fil1808793w.

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Cloud service reliability assessment is a vital decision-making activity for companies and individuals. In this assessment, the evaluation information can be represented by multi-valued neutrosophic numbers (MVNNs). MVNNs are regarded as an integration of single-valued neutrosophic numbers (SVNNs) and hesitant fuzzy numbers (HFNs); therefore, considering the defects of entropy and crossentropy measures for SVNNs and HFNs, we first define a framework of entropy measures and a family of cross-entropy measures for MVNNs in this paper. Second, a novel extended VIKOR (VlseKriterijumska Optimizacija

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19

Majumdar, Pinaki, and Syamal Kumar Samanta. "On similarity and entropy of neutrosophic sets." Journal of Intelligent & Fuzzy Systems 26, no. 3 (2014): 1245–52. http://dx.doi.org/10.3233/ifs-130810.

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Wang, Yameng, Han Yang, and Keyun Qin. "The Consistency between Cross-Entropy and Distance Measures in Fuzzy Sets." Symmetry 11, no. 3 (2019): 386. http://dx.doi.org/10.3390/sym11030386.

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The processing of uncertain information is increasingly becoming a hot topic in the artificial intelligence field, and the information measures of uncertainty information processing are also becoming of importance. In the process of decision-making, decision-makers make decisions mostly according to information measures such as similarity, distance, entropy, and cross-entropy in order to choose the best one. However, we found that many researchers apply cross-entropy to multi-attribute decision-making according to the minimum principle, which is in accordance with the principle of distance mea

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21

Sharma, Sonam, and Surender Singh. "A Complementary Dual of Single-Valued Neutrosophic Entropy with Application to MAGDM." Mathematics 10, no. 20 (2022): 3726. http://dx.doi.org/10.3390/math10203726.

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A single-valued neutrosophic set (SVNS) is a subcategory of neutrosophic set that is used to represent uncertainty and fuzziness in three tiers, namely truthfulness, indeterminacy, and falsity. The measure of entropy of a SVNS plays an important role to determine the ambiguity in a variety of situations. The knowledge measure is a dual form of entropy and is helpful in certain counterintuitive situations. In this paper, we introduce a knowledge measure for the SVNS and contrast the same with existing measures. The comparative study reveals that the proposed knowledge measure is more effective

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Şahin, Rıdvan, and Ahmet Küçük. "On similarity and entropy of neutrosophic soft sets." Journal of Intelligent & Fuzzy Systems 27, no. 5 (2014): 2417–30. http://dx.doi.org/10.3233/ifs-141211.

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airaju, A. Sol, and M. Shaj ahan. "Neutrosophic Fuzzy MAGDM using Maximal Entropy OWA Weights." International Journal of Mathematics Trends and Technology 60, no. 3 (2018): 173–79. http://dx.doi.org/10.14445/22315373/ijmtt-v60p527.

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Alias, Suriana, Daud Mohamad, Adibah Shuib, et al. "Rough Neutrosophic Multisets Geometric Aggregation Operator with Entropy Weight Combined Roughness Dice Similarity Measure and Its Application." ITM Web of Conferences 67 (2024): 01026. http://dx.doi.org/10.1051/itmconf/20246701026.

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Rough neutrosophic multisets (RNM) is an uncertainty set theory generalized from the rough neutrosophic set. In the same equivalence relation, the universal set is a neutrosophic multisets with boundary regions involving lower and upper approximation. To date, to handle the multiplicity of information collected, the rough neutrosophic multisets geometric aggregation operator (RNMGAO) is introduced. The algebraic operations of RNM used in the derivation of RNMGAO are defined. The entropy measure of RNM is also discussed as a weighted assign for each criterion simultaneously with the geometric a

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Gulistan, Muhammad, Hafiz Wahab, Florentin Smarandache, Salma Khan, and Sayed Shah. "Some Linguistic Neutrosophic Cubic Mean Operators and Entropy with Applications in a Corporation to Choose an Area Supervisor." Symmetry 10, no. 10 (2018): 428. http://dx.doi.org/10.3390/sym10100428.

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In this paper, we combined entropy with linguisti neutrosophic cubic numbers and used it in daily life problems related to a corporation that is going to choose an area supervisor, which is the main target of our proposed model. For this, we first develop the theory of linguistic neutrosophic cubic numbers, which explains the indeterminate and incomplete information by truth, indeterminacy and falsity linguistic variables (LVs) for the past, present, as well as for the future time very effectively. After giving the definitions, we initiate some basic operations and properties of linguistic neu

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Guan, Hongjun, Zongli Dai, Shuang Guan, and Aiwu Zhao. "A Forecasting Model Based on High-Order Fluctuation Trends and Information Entropy." Entropy 20, no. 9 (2018): 669. http://dx.doi.org/10.3390/e20090669.

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Most existing high-order prediction models abstract logical rules that are based on historical discrete states without considering historical inconsistency and fluctuation trends. In fact, these two characteristics are important for describing historical fluctuations. This paper proposes a model based on logical rules abstracted from historical dynamic fluctuation trends and the corresponding inconsistencies. In the logical rule training stage, the dynamic trend states of up and down are mapped to the two dimensions of truth-membership and false-membership of neutrosophic sets, respectively. M

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Zhang, Haibo, Zhimin Mu, and Shouzhen Zeng. "Multiple Attribute Group Decision Making Based on Simplified Neutrosophic Integrated Weighted Distance Measure and Entropy Method." Mathematical Problems in Engineering 2020 (July 20, 2020): 1–10. http://dx.doi.org/10.1155/2020/9075845.

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Simplified neutrosophic set (SNS) is a popular tool in modelling potential, imprecise, and uncertain information within complex environments. In this paper, a method based on the integrated weighted distance measure and entropy weight is proposed for handling SNS multiple attribute group decision-making (MAGDM) problems. To this end, the simplified neutrosophic (SN) integrated weighted distance (SVNIWD) measure is first developed for overcoming the limitations of the existing methods. Afterward, the proposed SNIWD’s several properties and particular status are studied. Moreover, a flexible and

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Wang, Tongjuan. "The Projection Model with Unknown Weight Information under Interval Neutrosophic Environment and Its Application to Software Quality-in-Use Evaluation." Mathematical Problems in Engineering 2020 (February 24, 2020): 1–11. http://dx.doi.org/10.1155/2020/7279420.

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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 attitud

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Mustapha, Norzieha, Suriana Alias, Roliza Md Yasin, Nurnisa Nasuha Mohd Yusof, Nurul Najiha Fakhrarazi, and Nik Nur Aisyah Nik Hassan. "New Entropy Measure Concept for Single Value Neutrosophic Sets with Application in Medical Diagnosis." International Journal of Neutrosophic Science 19, no. 1 (2022): 375–83. http://dx.doi.org/10.54216/ijns.190118n.

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This study aims to propose a new entropy weight on the distance measure of single value neutrosophic set (SVNS) to analyse medical diagnosis patient’s risk. Four distance measures will be integrated with three entropy weight concepts and applied to medical diagnosis. A new entropy weight measure integrated with the four distance measures are calculated using the medical data of one patient with five symptoms and five diseases. The calculated new entropy and its associated distance measures give consistent finding with the existing entropy weight measures. However, all the values are even small

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R. Ramesh. "Application of Neutrosophic Sets in Multi Attribute Decision Making." Communications on Applied Nonlinear Analysis 32, no. 9s (2025): 2635–49. https://doi.org/10.52783/cana.v32.4545.

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The selection of an optimal hospital for healthcare services is a complex decision-making problem due to the involvement of multiple, often conflicting, criteria such as quality of care, infrastructure, staff expertise, cost, and patient satisfaction. This paper presents an innovative approach for hospital selection using a hybrid decision-making framework combining neutrosophic sets, entropy weight, and the Multi-Attribute Decision-Making (MADM) method. Neutrosophic sets are employed to handle the inherent uncertainty and indeterminacy in hospital evaluation criteria, allowing for more flexib

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Vasile, Patrascu. "Entropy, Neutro-Entropy and Anti-Entropy for Neutrosophic Information." April 30, 2018. https://doi.org/10.5281/zenodo.1237879.

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This article shows a deca-valued representation of neutrosophic information. For this representation the following neutrosophic features were defined and used: truth, falsity, weak truth, weak falsity, ignorance, contradiction, saturation, neutrality, ambiguity and hesitation. In the context created by these ten features emerged the possibility but also the necessity of defining three neutrosophic concepts: entropy, neutro-entropy and anti-entropy. Possibility appeared due to the refining of neutrosophic representation. The necessity appeared because all of these features cannot be classified

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Vasile, Patrascu. "Shannon Entropy for Neutrosophic Information." May 22, 2019. https://doi.org/10.5281/zenodo.3131095.

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The paper presents an extension of Shannon entropy for neutrosophic information. This extension uses a new formula for distance between two neutrosophic triplets. In addition, the obtained results are particularized for bifuzzy, intuitionistic and paraconsistent fuzzy information.

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Mohan, J., V. Krishnaveni, and Guo Yanhui. "A Neutrosophic Approach of MRI Denoising." November 5, 2011. https://doi.org/10.5281/zenodo.34759.

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In this paper, a new filtering method to remove Rician noise from magnetic resonance image is presented. This filter is based on Neutrosophic set (NS) approach of median filtering. A Neutrosophic set, a part of neutrosophy theory, studies the origin, nature and scope of neutralities, as well as their interactions with different ideational spectra. Here the MRI image is transformed into NS domain, which is described using three membership sets: T, I, F.

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Majdoleen, Abu Qamar, and Hassan Nasruddin. "Entropy, Measures of Distance and Similarity of Q-Neutrosophic Soft Sets and Some Applications." May 20, 2019. https://doi.org/10.5281/zenodo.3053717.

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The idea of the Q-neutrosophic soft set emerges from the neutrosophic soft set by upgrading the membership functions to a two-dimensional entity which indicate uncertainty, indeterminacy and falsity. Hence, it is able to deal with two-dimensional inconsistent, imprecise, and indeterminate information appearing in real life situations.

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Jin, Feifei, Hao Jiang, and Lidan Pei. "Exponential function-driven single-valued neutrosophic entropy and similarity measures and their applications to multi-attribute decision-making." Journal of Intelligent & Fuzzy Systems, October 19, 2022, 1–10. http://dx.doi.org/10.3233/jifs-220566.

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Single-valued neutrosophic set is an important tool for describing fuzzy information and solving fuzzy decision problems. It is known that entropy can be applied to measure the degree of uncertainty of evaluation information and determine the important degree of objects, similarity is mainly used to capture the internal relationship of the evaluation objects. Therefore, single-valued neutrosophic entropy and single-valued neutrosophic similarity are two important topics in multi-attribute decision-making (MADM) problems. In this paper, some new single-valued neutrosophic entropy and similarity

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Vasile, Pătraşcu. "The Neutrosophic Entropy and its Five Components." July 1, 2015. https://doi.org/10.5281/zenodo.22655.

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This paper presents two variants of pentavalued representation for neutrosophic entropy. The first is an extension of Kaufman's formula and the second is an extension of Kosko's formula. Based on the primary three-valued information represented by the degree of truth, degree of falsity and degree of neutrality there are built some penta-valued representations that better highlights some specific features of neutrosophic entropy. Thus, we highlight five features of neutrosophic uncertainty such as ambiguity, ignorance, contradiction, neutrality an

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Wen-Hua, Cui, and Ye Jun. "Generalized Distance-Based Entropy and Dimension Root Entropy for Simplified Neutrosophic Sets." May 20, 2019. https://doi.org/10.5281/zenodo.3051831.

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In order to quantify the fuzziness in the simplified neutrosophic setting, this paper proposes a generalized distance-based entropy measure and a dimension root entropy measure of simplified neutrosophic sets (NSs) (containing interval-valued and single-valued NSs) and verifies their properties.

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I., Arockiarani. "Entropy Measures on Neutrosophic Soft Sets and Its Application in Multi Attribute Decision Making." March 1, 2017. https://doi.org/10.5281/zenodo.1130009.

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The focus of the paper is to furnish the entropy measure for a neutrosophic set and neutrosophic soft set which is a measure of uncertainty and it permeates discourse and system. Various characterization of entropy measures are derived. Further we exemplify this concept by applying entropy in various real time decision making problems.

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Dalapati, Pramanik, Alam, Smarandache, and Roy. "IN-cross Entropy Based MAGDM Strategy under Interval Neutrosophic Set Environment." Neutrosophic Sets and Systems 18/2017 (February 18, 2018). https://doi.org/10.5281/zenodo.1175163.

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Cross entropy measure is one of the best way to calculate the divergence of any variable from the priori one variable. We define a new cross entropy measure under interval neutrosophic set (INS) environment, which we call IN-cross entropy measure and prove its basic properties. We also develop weighted IN-cross entropy measure and investigats its basic properties. Based on the weighted IN-cross entropy measure, we develop a novel strategy for multi attribute group decision making (MAGDM) strategy under interval neutrosophic environment. The proposed multi attribute group decision making strate

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Gandhi, C. P., Anil Kumar, Govind Vashishtha, Tang Hesheng, Akhand Rai, and Jiawei Xiang. "Maximal overlap discrete wavelet packet transform and variants of neutrosophic cubic cross entropy based identification of rotor defects." Measurement Science and Technology, March 22, 2022. http://dx.doi.org/10.1088/1361-6501/ac6001.

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Abstract The underlying study proposes a novel procedure for automated testimony of rotor defects through maximal overlap discrete wavelet packet transforms (MODWPT) and the proposed neutrosophic cubic cross measure, fuzzy cross entropy and single valued neutrosophic cross entropy measures consecutively. Discrete wavelet transform is an efficient data acquisition technique, but the technical barrier with this technique is that it can decompose only low frequency (approximate) signals and does not possess shift invariance property. MODWPT possesses shift invariance property and is highly capabl

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Yuan, Zhizhu, Lijuan Hou, Zihuan Gao, Meiqin Wu, and Jianping Fan. "Single-valued neutrosophic Schweizer-Sklar Hamy mean aggregation operators and their application in multi-attribute decision making." Journal of Intelligent & Fuzzy Systems, March 27, 2022, 1–19. http://dx.doi.org/10.3233/jifs-212818.

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Single-valued neutrosophic sets can efficiently depict a great deal of imprecise, uncertain and discordant information. Hamy mean operator can consider the interrelationships among multiple integrated arguments and Schweizer-Sklar operations express great flexibility in the process of information aggregation. To give full consideration to these advantages, we merge the Hamy mean operator with the Schweizer-Sklar operations in single-valued neutrosophic environment, proposing a single-valued neutrosophic Schweizer-Sklar Hamy mean operator and a single-valued neutrosophic Schweizer-Sklar weighte

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Surapati, Pramanik, and Mondal Kalyan. "Interval Neutrosophic Multi-Attribute Decision-Making Based on Grey Relational Analysis." May 17, 2015. https://doi.org/10.5281/zenodo.32259.

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This purpose of this paper is to introduce multi-attribute decision making based on the concept of interval neutrosophic sets. While the concept of neutrosophic sets is a powerful tool to deal with indeterminate and inconsistent data, the interval neutrosophic sets is also a powerful mathematical tool as well as more flexible to deal with incompleteness. The rating of all alternatives is expressed in terms of interval neutrosophic values characterized by interval truth-membership degree, interval indeterminacy-membership degree, and interval falsity-membership degree.

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Vasile, Patrascu. "The Neutrosophic Entropy and its Five Components." July 15, 2015. https://doi.org/10.5281/zenodo.32283.

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This paper presents two variants of pentavalued representation for neutrosophic entropy. The first is an extension of Kaufmann's formula and the second is an extension of Kosko's formula. Based on the primary three-valued information represented by the degree of truth, degree of falsity and degree of neutrality there are built some penta-valued representations that better highlights some specific features of neutrosophic entropy.

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C., P. Gandhi, Kaur Simerjit, Dev Rahul, and Bali Manoj. "Neutrosophic Entropy Based Fluoride Contamination Indices for Community Health Risk Assessment from Groundwater of Kangra County, North India." April 9, 2022. https://doi.org/10.5281/zenodo.6426391.

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The underlying study intends to evaluate community health risk assessment from fluoride contamination of groundwater samples employing the proposed entropy variants of single valued neutrosophic sets. The symmetric fuzzy cross entropy numbers, which can represent the macroscopic view of fluoride contamination more effectively, are constructed in this study and then deployed to rank the seasonal parameters (pre-monsoon, rainy season and pre-monsoon) responsible for fluoride contamination in the study area. To quantify the non-linear relationship between seasonal parameters and sampling spots, t

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Simerjit, Kaur, P. Gandhi C., and Singal Nidhi. "Neutrosophic Entropy Based Heavy Metal Contamination Indices for Impact Assessment of Sirsa River Water Quality Within County of District Baddi, India." February 11, 2022. https://doi.org/10.5281/zenodo.6041492.

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This study contributes a novel fuzzy and neutrosophic entropy-based procedure to identify the most contaminated sampling spot and to assess the impact of heavy metals concentration, before and after the amalgamation of pharmaceutical effluents treated in common effluent treatment plant. in river water samples. It is observed that the concentration of heavy metals, which were within permissible limits before amalgamation, dwindled gradually after amalgamation, owing to the decrease in fuzzy and neutrosophic entropy values. To identify the most contaminated sampling spot, responsible for heavy m

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Qaisar, Khan, Hassan Nasruddin, and Mahmood Tahir. "Neutrosophic Cubic Power Muirhead Mean Operators with Uncertain Data for Multi-Attribute Decision-Making." May 16, 2019. https://doi.org/10.5281/zenodo.2861852.

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The neutrosophic cubic set (NCS) is a hybrid structure, which consists of interval neutrosophic sets (INS) (associated with the undetermined part of information associated with entropy) and single-valued neutrosophic set (SVNS) (associated with the determined part of information).

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Ruipu, TAN, ZHANG Wende, and CHEN Shengqun. "Some Generalized Single Valued Neutrosophic Linguistic Operators and Their Application to Multiple Attribute Group Decision Making." April 3, 2017. https://doi.org/10.5281/zenodo.1041693.

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Jian-qiang, Wang, and Tian Zhang-peng. "Multi-criteria Decision Making Method Based on Cross-entropy with Interval Neutrosophic Sets." October 10, 2015. https://doi.org/10.5281/zenodo.32263.

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The main purpose of this paper is to provide a method of multi-criteria decision making that combines interval neutrosophic sets and TOPSIS involving the relative likelihood-based comparison relations of the performances of alternatives that are aggregated into interval numbers. A fuzzy cross-entropy approach is proposed to state the discrimination measure between alternatives and the absolute ideal solutions after a transformation operator has been developed to convert interval neutrosophic numbers to simplified neutrosophic numbers.

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Surapati, Pramanik, Pratim Dey Partha, SMARANDACHE FLORENTIN, and Ye Jun. "Cross Entropy Measures of Bipolar and Interval Bipolar Neutrosophic Sets and Their Application for Multi-Attribute Decision-Making." March 24, 2018. https://doi.org/10.5281/zenodo.1410233.

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The bipolar neutrosophic set is an important extension of the bipolar fuzzy set. The bipolar neutrosophic set is a hybridization of the bipolar fuzzy set and neutrosophic set. Every element of a bipolar neutrosophic set consists of three independent positive membership functions and three independent negative membership functions. In this paper, we develop cross entropy measures of bipolar neutrosophic sets and prove their basic properties.

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A., A. Salama, Smarandache Florentin, and Eisa Mohamed. "Introduction to Image Processing via Neutrosophic Techniques." May 3, 2014. https://doi.org/10.5281/zenodo.30198.

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This paper is an attempt of proposing the  processing approach of neutrosophic technique in image  processing. As neutrosophic sets is a suitable tool to cope with imperfectly defined images, the properties, basic operations distance measure, entropy measures, of the neutrosophic sets method are presented here.

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