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Journal articles on the topic 'Neutrosophic Crisp Set'

Author: Grafiati

Published: 2 June 2025

Last updated: 31 July 2025

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1

Al-Hamido, Riad K. Al. "New Operators Using Neutrosophic Crisp Open Set." International Journal of Neutrosophic Science 20, no. 1 (2023): 17–26. http://dx.doi.org/10.54216/ijns.200102.

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In this paper, we introduce new sets in neutrosophic crisp topology called neutrosophic crisp frontier, neutrosophic crisp border and neutrosophic crisp exterior with the help of neutrosophic crisp open sets in neutrosophic crisp topological space. Also, we discuss the basic and important properties of them and the relations between them. Finally, many examples are presented.

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2

Salama, A. A., Said Broumi, and Florentin Smarandache. "Neutrosophic Crisp Open Set and Neutrosophic Crisp Continuity via Neutrosophic Crisp Ideals." International Journal of Information Engineering and Electronic Business 6, no. 3 (2014): 1–8. http://dx.doi.org/10.5815/ijieeb.2014.03.01.

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3

A.A., Salama, K.F.Alhasan, A. Elagamy H., and Smarandache Florentin. "Neutrosophic Dynamic Set." Neutrosophic Knowledge 3, no. 1 (2021): 1–5. https://doi.org/10.5281/zenodo.5507522.

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In this paper, we introduced the concept of the dynamic set according to modern logic, is neutrosophic logic. We study the neutrosophic dynamic set according to time and random variable depended on dynamic set. Neutrosophic dynamic is a dynamic analysis of a sequence of data through of time. It used in many problems in life such as a mathematical statistic, philosophy, medicine, engineering. Some examples and notes are presented.

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4

Riad, K. Al-Hamido. "Neutrosophic Crisp Bi-Topological Spaces." Neutrosophic Sets and Systems 21 / 2018 (September 4, 2018): 66–73. https://doi.org/10.5281/zenodo.1408696.

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In this paper, neutrosophic crisp bi-topological spaces, new types of open and closed sets in neutrosophic crisp bitopological spaces, the closure and interior neutrosophic crisp set and a new concept of open and closed sets are introduced. The basic properties of these types of open and closed sets and their properties are studied.

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Doaa, Doaa, and L. A. A. Al Al-Swidi. "Stable Neutrosophic Crisp Topological Space." International Journal of Neutrosophic Science 24, no. 1 (2024): 154–59. http://dx.doi.org/10.54216/ijns.230411.

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The significance and influence of neutrosophic crisp set theory in numerous scientific domains, particularly topology, led us to construct a new definition of topology based on neutrosophic crisp sets, allowing us to regulate its key mathematical ideas. Therefore, we constructed this definition and dubbed it stable neutrosophic crisp topology, where we went over the key idea which is the interior with the vital features.

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6

Sabir majeed, Amir, and Nabeel Ezzulddin Arif. "Domination (set and Number) in Neutrosophic Soft over Graphs." Wasit Journal of Pure sciences 1, no. 3 (2022): 26–43. http://dx.doi.org/10.31185/wjps.65.

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By combining the ideas of neutrosophic soft sets and oversets in graphs and replacing each crisp or neutrosophic set by overset at each vertex and edge, we present a new framework for treating neutrosophic soft information (NSI) in this research.

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7

R, Hema, Sudharani R, and Kavitha M. "A Novel Approach on Plithogenic Interval Valued Neutrosophic Hypersoft Sets and its Application in Decision Making." Indian Journal of Science and Technology 16, no. 32 (2023): 2494–502. https://doi.org/10.17485/IJST/v16i32.1302.

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Abstract <strong>Objectives:</strong> In problem solving process, we have advanced the study of plithogenic interval valued neutrosophic hypersoft set, to analyse with all the appendages and traits under consideration for getting the better accuracy for the multi criterion decision making environment. <strong>Methods:</strong> Based on the combination of hypersoft sets, plithogenic sets and neutrosophic fuzzy sets, a plithogenic interval valued neutrosophic hypersoft set has been proposed. <strong>Findings:</strong> The tnorm , tconorm, accuracy function and plithogeni

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8

D. Sasikala. "On Determining Shortest Path Problem under Pentagonal Neutrosophic Fuzzy Number." Communications on Applied Nonlinear Analysis 31, no. 2s (2024): 09–16. http://dx.doi.org/10.52783/cana.v31.588.

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Neutrosophic sets is the generalization of fuzzy set theory. In this discipline the crucial situation are widely explained in three components appear in it in distinct fields. The study of Neutrosophy deals with the interactions of different ideational spectra. And also the shortest path method is one of the important tool in network analysis. In this approach the pentagonal neutrosophic fuzzy number is applied to determine the shortest path. A score function is used to defuzzify the number into crisp number. The new algorithm evaluates the shortest path for pentagonal neutrosophic fuzzy envir

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9

A. Soliman, Entesar. "Basic concepts of neutrosophic crisp sets." Libyan Journal of Science &Technology 12, no. 1 (2024): 187–93. https://doi.org/10.37376/ljst.v12i1.7057.

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The world around us is characterized by specificity, ambiguity, and contradiction, which led to a lack of our full knowledge of its facts and events. Therefore, we became in need of a new vision and a logical system that fits our incomplete information. In 1965, the American scientist F. Smarandache presented neutrosophic logic as a generalization of fuzzy logic and intuitive fuzzy logic. He added a new component to the degrees of a membership function and a non-membership function, which is the degree of indeterminacy. The crispneutrosophic sets presented by Ahmed Salama is considered a gener

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10

Surya, V., and R. Sophia Porchelvi. "Evaluation of Vital Parameters Influencing Oxygen Demand with Pythagorean Neutrosophic-Fuzzy Cognitive Map." Indian Journal Of Science And Technology 17, no. 29 (2024): 3018–25. http://dx.doi.org/10.17485/ijst/v17i29.1734.

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Objectives: The primary goal is to provide a novel idea known as the Pythagorean neutrosophic fuzzy cognitive map. A multi-objective goal programming issue with a set of objectives and constraints is solved using PNCM. Methods: Linguistic variables are transformed into crisp values using a score function and the Pythagorean neutrosophic quantification scale. The linear combinations of crisp values and factors yield the goal and constraint equations. Findings: To enhance decision-making in emergency situations like COVID-19, the implications of the novel PNCM concept were utilized to examine th

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11

Florentin, Smarandache. "Plithogenic Set, an Extension of Crisp, Fuzzy, Intuitionistic Fuzzy, and Neutrosophic Sets - Revisited." Neutrosophic Sets and Systems 21 / 2018 (September 4, 2018): 153–66. https://doi.org/10.5281/zenodo.1408741.

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In this paper, we introduce the plithogenic set (as generalization of crisp, fuzzy, intuitionistic fuzzy, and neutrosoph-ic sets), which is a set whose elements are characterized by many attributes’ values. An attribute value <em>v</em> has a corresponding (fuzzy, intuitionistic fuzzy, or neutrosophic) degree of appurtenance d(<em>x,v</em>) of the element <em>x</em>, to the set <em>P</em>, with respect to some given criteria. In order to obtain a better accuracy for the plithogenic aggregation operators in the plithogenic set, and for a more exact inclusion (partial order), a (fuzzy, int

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12

V, Surya, and Sophia Porchelvi R. "Evaluation of Vital Parameters Influencing Oxygen Demand with Pythagorean Neutrosophic-Fuzzy Cognitive Map." Indian Journal of Science and Technology 17, no. 29 (2024): 3018–25. https://doi.org/10.17485/IJST/v17i29.1734.

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Abstract <strong>Objectives:</strong> The primary goal is to provide a novel idea known as the Pythagorean neutrosophic fuzzy cognitive map. A multi-objective goal programming issue with a set of objectives and constraints is solved using PNCM. <strong>Methods:</strong> Linguistic variables are transformed into crisp values using a score function and the Pythagorean neutrosophic quantification scale. The linear combinations of crisp values and factors yield the goal and constraint equations. <strong>Findings:</strong> To enhance decision-making in emergency situations

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13

Salama, A. A., and Elghawalby Hewayda. "Neutrosophic Crisp Set & Neutrosophic Crisp relations." July 1, 2015. https://doi.org/10.5281/zenodo.22579.

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Since the world is full of indeterminacy, the neutrosophics found their place into contemporary research. The purpose of this paper is to introduce a new type of neutrosophic crisp set as the *- neutrosophic crisp sets as a generalization to star intuitionistic set due to Indira et al.[4 ], and study some of its properties. Finally we introduce and study the notion of *- neutrosophic relation and some of its properties. .

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14

Eman.M.El-Nakeeb, ElGhawalby Hewayda, A.A.Salama, and S.A.El-Hafeez. "Neutrosophic Crisp Mathematical Morphology." June 19, 2017. https://doi.org/10.5281/zenodo.831937.

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In this paper, we aim to apply the concepts of the neutrosophic crisp sets and its operations to the classical mathematical morphological operations, introducing what we call "Neutrosophic Crisp Mathematical Morphology". Several operators are to be developed, including the neutrosophic crisp dilation, the neutrosophic crisp erosion, the neutrosophic crisp opening and the neutrosophic crisp closing.

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15

A., A. Salama. "Basic Structure of Some Classes of Neutrosophic Crisp Nearly Open Sets & Possible Application to GIS Topology." July 1, 2015. https://doi.org/10.5281/zenodo.22438.

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Since the world is full of indeterminacy, the neutrosophics found their place into contemporary research. The fundamental concepts of neutrosophic set, introduced by Smarandache and Salama. In Geographical information systems (GIS) there is a need to model spatial regions with indeterminate boundary and under indeterminacy. In this paper the structure of some classes of neutrosophic crisp nearly open sets are investigated and some applications are given. Finally we generalize the crisp topological and intuitioistic studies to the notion of neutrosop

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16

Ahmed, B. AL-Nafee, Smarandache Florentin, and A. Salama A. "New Types of Neutrosophic Crisp Closed Sets." October 4, 2020. https://doi.org/10.5281/zenodo.4065428.

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  "The neutrosophic sets were known since 1999, and because of their wide applications and their great flexibility to solve the problems, we used these the concepts to define a new types of neutrosophic crisp closed sets and limit points in neutrosophic crisp topological space, namly [neutrosophic crisp Gem sets and neutrosophic crisp Turig points ] respactvely, we stady their properties in details and join it with topological concepts. Finally we used [neutrosophic crisp Gem sets and neutrosophic crisp Turig points] to introduce the some of topological concepts as : neutrosophic cri

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17

A.A.SALAMA, I.M.HANAFY, ELGHAWALBY HEWAYDA, and M.S.DABASH. "Neutrosophic Crisp Closed Region and Neutrosophic Crisp Continuous Functions." December 10, 2016. https://doi.org/10.5281/zenodo.200048.

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18

A., A. Salama, Broumi Said, and Smarandache Florentin. "Some Types of Neutrosophic Crisp Sets and Neutrosophic Crisp Relations." October 6, 2014. https://doi.org/10.5281/zenodo.49159.

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The purpose of this paper is to introduce a new types of crisp sets are called the neutrosophic crisp set with three types 1, 2, 3. After given the fundamental definitions and operations, we obtain several properties, and discussed the relationship between neutrosophic crisp sets and others. Finally, we introduce and study the notion of neutrosophic crisp relations.

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19

A., A. Salama, Smarandache Florentin, and Kroumov Valeri. "Neutrosophic Crisp Sets & Neutrosophic Crisp Topological Spaces." March 1, 2015. https://doi.org/10.5281/zenodo.30216.

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In this paper, we generalize the crisp topological space to the notion of neutrosophic crisp topological space, and we construct the basic concepts of the neutrosophic crisp topology. In addition to these, we introduce the de nitions of neutrosophic crisp continuous function and neutrosophic crisp compact spaces. Finally, some characterizations concerning neutrosophic crisp compact spaces are presented and one obtains several properties. Possible application to GIS topology rules are touched upon.

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20

Xiaohong, Zhang, Li Mengyuan, and Lei Tao. "On Neutrosophic Crisp Sets and Neutrosophic Crisp Mathematical Morphology." June 8, 2021. https://doi.org/10.5281/zenodo.4914794.

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In this paper, we analyze the basic algebraic operations of neutrosophic crisp sets and their properties, show that some operations of neutrosophic crisp sets with type 2 and type 3 are not closed by counter examples, and give some new operations. Then, discuss some morphological operators in neutrosophic crisp mathematical morphology, and study the application to edge extraction of color images, and give some Python programs and related experimental results.

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21

A., A. Salama, Broumi Said, and Smarandache Florentin. "Neutrosophic Crisp Open Set and Neutrosophic Crisp Continuity via Neutrosophic Crisp Ideals." February 19, 2013. https://doi.org/10.5281/zenodo.30215.

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The focus of this paper is to propose a new notion of neutrosophic crisp sets via neutrosophic crisp ideals and to study some basic operations and results in neutrosophic crisp topological spaces. Also, neutrosophic crisp L-openness and neutrosophic crisp L- continuity are considered as a generalizations for a crisp and fuzzy concepts. Relationships between the above new neutrosophic crisp notions and the other relevant classes are investigated. Finally, we define and study two different types of neutrosophic crisp functions.

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22

Salama, A. A., and Florentin Smarandache. "Neutrosophic Crisp Set Theory." Neutrosophic Sets and Systems 5, 2014 (May 4, 2014). https://doi.org/10.5281/zenodo.571506.

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The purpose of this paper is to introduce new types of neutrosophic crisp sets with three types 1, 2, 3. After given the fundamental definitions and operations, we obtain several properties, and discussed the relationship between neutrosophic crisp sets and others. Also, we introduce and study the neutrosophic crisp point and neutrosophic crisp relations. Possible applications to database are touched upon.

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23

HEWAYDA, ELGHAWALBY, and A. SALAMA A. "Ultra neutrosophic crisp sets and relations." December 10, 2016. https://doi.org/10.5281/zenodo.200102.

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In this paper we present a new neutrosophic crisp family generated from the three components’ neutrosophic crisp sets presented by Salama [4]. The idea behind Salam’s neutrosophic crisp set was to classify the elements of a universe of discourse with respect to an event ”A” into three classes: one class contains those elements that are fully supportive to A, another class contains those elements that totally against A, and a third class for those elements that stand in a distance from being with or against A. Our aim here is to study the elements of the universe of discourse which their existe

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K., Tharani, та Kokilavani V. "On Neutrosophic Crisp g#α Closed Set Operators". 10 вересня 2024. https://doi.org/10.5281/zenodo.13989234.

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The concept of g#α closed set in general topological spaces was first introduced by MuthukumaraswamyK et. al.,. Recently, kokilavani V, Tharani K et. al., introduced neutrosophic crisp g#α closed setin neutrosophic crisp topological space. Now, in this present paper, we introduced and study the neutrosophiccrisp topological properties of neutrosophic crisp g#α interior, neutrosophic crisp g#α closure, neutrosophiccrisp g#α frontier, neutrosophic crisp g#α border, neutrosophic crisp g#α exterior via the concept of neutrosophiccrisp g#α open set.

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A.A., Salama, I.M.Hanafy та S. Dabash M. "Semi-Compact and Semi-Lindelӧf Spaces via Neutrosophic Crisp Set Theory". 22 травня 2019. https://doi.org/10.5281/zenodo.3130970.

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The aim of this paper is devoted to introduce and study the concepts of semi-compact (resp. semi-Lindelӧf, locally semi-compact) spaces in a neutrosophic crisp topological space. Several properties, functions properties of neutrosophic crisp semi-compact spaces are studied. In addition to these, we introduce and study the definition of neutrosophic crisp semi-Lindelӧf spaces and neutrosophic crisp locally semi-compact spaces. We show that neutrosophic crisp semi-compact spaces is preserved under neutrosophic crisp irresolute function and neutrosophic crisp pre-semi-closed function with neutros

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A., A. Salama, and Smarandache Florentin. "Filters via Neutrosophic Crisp Sets." April 2, 2013. https://doi.org/10.5281/zenodo.30168.

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In this paper we introduce the notion of filter on the neutrosophic crisp set, then we consider a generalization of the filter’s studies. Afterwards, we present the important neutrosophic crisp filters. We also study several relations between different neutrosophic crisp filters and neutrosophic topologies. Possible applications to database systems are touched upon.

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27

A., A. SALAMA, and SMARANDACHE FLORENTIN. "Neutrosophic Crisp Probability Theory & Decision Making Process." December 10, 2016. https://doi.org/10.5281/zenodo.200051.

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Since the world is full of indeterminacy, the neutrosophics found their place into contemporary research. In neutrosophic set, indeterminacy is quantified explicitly and truth-membership, indeterminacy-membership and falsity-membership are independent. So it is natural to adopt for that purpose the value from the selected set with highest degree of truth-membership, indeterminacy membership and least degree of falsity-membership on the decision set. These factors indicate that a decision making process takes place in neutrosophic environment. In this paper, we introduce and study the probabili

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28

Al-Hamido, Riad K. Al. "ON Neutrosophic Crisp Supra Bi-Topological Spaces." International Journal of Neutrosophic Science, 2020, 36–46. http://dx.doi.org/10.54216/ijns.040104.

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In this paper, neutrosophic crisp supra bi-topological structure, which is a more general structure than neutrosophic crisp supra topological spaces, is built on neutrosophic crisp sets. The necessary arguments which are pairwise neutrosophic crisp supra open set, pairwise neutrosophic crisp supra closed set, pairwise neutrosophic crisp supra closure, pairwise neutrosophic crisp supra interior is defined, and their basic properties are presented. Finally, many examples are presented.

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29

Salama, A. A., and Hewayda ElGhawalby. "Neutrosophic Crisp Set & relations." Neutrosophic Sets and Systems 6, 2014 (May 4, 2014). https://doi.org/10.5281/zenodo.571501.

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In a world full of indeterminacy, traditional crisp set with its boundaries of truth and false has not infused itself with the ability of reflecting the reality. Therefore, neutrosophic found its place into contemporary research as an alternative representation of the real world. In this paper, we aim to develop a new type of neutrosophic crisp sets called the *-Neutrosophic crisp sets as a generalization of the star intuitionistic set introduced by Indira et al.[4] , and hence studying some of its properties. To this end we will investigate the notion of *-Neutrosophic relation and some of it

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30

A.A.Salama, Broumi Said, and Smarandache Florentin. "Some Types of Neutrosophic Crisp Sets and Neutrosophic Crisp Relations." February 3, 2014. https://doi.org/10.5281/zenodo.30330.

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The purpose of this paper is to introduce a new types of crisp sets are called the neutrosophic crisp set with three types 1, 2, 3. After given the fundamental definitions and operations, we obtain several properties,  and discussed the relationship between neutrosophic crisp sets and others. Finally, we introduce and study the notion of neutrosophic crisp relations.

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31

Atiqa, Siraj, Naeem Khalid, and Said Broumi. "Pythagorean m-polar Fuzzy Neutrosophic Metric Spaces." January 14, 2023. https://doi.org/10.5281/zenodo.7536088.

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Neutrosophy deals with the study of neutrosophic logic, set and probability. A Pythagorean mpolar neutrosophic set is indeed an expansion of crisp, fuzzy, intuitionistic fuzzy, neutrosophic and Pythagorean m-polar fuzzy sets. In this paper, we develop the perception of Pythagorean m-polar fuzzy neutrosophic metric space defined over Pythagorean m-polar fuzzy neutrosophic set relying on the classical definition of metric spaces defined on a crisp set. We present some related results and illustrations to perceive the conceptions. We present many examples of metrics which hold true for classical

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32

Pranab, Biswas, Pramanik Surapati, and C. Giri Bibhas. "TOPSIS method for multi-attribute group decision making under single-valued neutrosophic environment." December 6, 2013. https://doi.org/10.5281/zenodo.34915.

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A single-valued neutrosophic set is a special case of neutrosophic set. It has been proposed as a generalization of crisp sets, fuzzy sets, and intuitionistic fuzzy sets in order to deal with incomplete information.

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33

C., Antony Crispin Sweety, and Arockiarani I. "Rough sets in Fuzzy Neutrosophic approximation spase." October 11, 2015. https://doi.org/10.5281/zenodo.32273.

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Pranab, Biswas, Pramanik Surapati, and C. Giri Bibhas. "TOPSIS method for multi-attribute group decision-making under single-valued neutrosophic environment." March 19, 2015. https://doi.org/10.5281/zenodo.23173.

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A single-valued neutrosophic set is a special case of neutrosophic set. It has been proposed as a generalization of crisp sets, fuzzy sets, and intuitionistic fuzzy sets in order to deal with incomplete information. In this paper, a new approach for multi-attribute group decisionmaking problems is proposed by extending the technique for order preference by similarity to ideal solution to single-valued neutrosophic environment.

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C., Maheswari, Sathyabama M., and S.Chandrasekar. "Neutrosophic generalized b-closed sets in Neutrosophic topological spaces." May 21, 2019. https://doi.org/10.5281/zenodo.3077761.

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Smarandache introduced and developed the new concept of Neutrosophic set from the Intuitionistic fuzzy sets. A.A. Salama introduced Neutrosophic topological spaces by using the Neutrosophic crisp sets. Aim of this paper is we introduce and study about Neutrosophic generalized b closed sets in Neutrosophic topological spaces and its properties are discussed details.

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Al-Hamido, Riad K. Al, Luai Salha, and Taleb Gharibah. "Pre Separation Axioms In Neutrosophic Crisp Topological Spaces." International Journal of Neutrosophic Science, 2020, 72–79. http://dx.doi.org/10.54216/ijns.080201.

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In this paper, A new type of separation axioms in the neutrosophic crisp Topological space named neutrosophic crisp pre separation axioms is going to be defined , in which neutrosophic crisp pre open set and neutrosophic crisp point are to be depended on. Also, relations among them and the other type are going to be found.

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NGUYEN, XUAN THAO, CONG CUONG BUI, and Smarandache Florentin. "Rough Standard Neutrosophic Sets: an Application on standard Neutrosophic Information Systems." May 16, 2019. https://doi.org/10.5281/zenodo.2863295.

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A rough fuzzy set is the result of approximation of a fuzzy set with respect to a crisp approximation space. It is mathematical tool for the knowledge discovery in the fuzzy information systems. In this paper, we introduce the concepts of rough standard neutrosophic sets, standard neutrosophic information system and give the knowledge discovery on standard neutrosophic information system based on rough standard neutrosophic sets.

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Riad, K. Al-Hamido, Salha Luai, and Gharibah Taleb. "Pre Separation Axioms In Neutrosophic Crisp Topological Spaces." August 19, 2020. https://doi.org/10.5281/zenodo.3991464.

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In this  paper, a new type of  separation axioms in the neutrosophic crisp Topological space named  neutrosophic crisp pre separation axioms is going to be defined , in which neutrosophic  crisp pre open set and  neutrosophic  crisp point are to be depended on. Also, relations among them and the other type are going to be found. 

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39

Suman, Das, Das Rakhal, and Pramanik Surapati. "Topology on Ultra Neutrosophic Set." December 12, 2021. https://doi.org/10.5281/zenodo.5775098.

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In this paper, we introduce the ultra neutrosophic set, and define some operations and establish a few properties of the ultra neutrosophic sets. Using the notion of topology on ultra neutrosophic sets, we introduce the concept of ultra neutrosophic topology. Further, we define the notion of ultra neutrosophic interior and ultra neutrosophic closure via ultra neutrosophic topological space

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40

AL-Nafee, Ahmed B. AL, Said Broumi, and Luay A. Al Al-Swidi. "n-Valued Refined Neutrosophic Crisp Sets." International Journal of Neutrosophic Science, 2021, 87–95. http://dx.doi.org/10.54216/ijns.170201.

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The main purpose of this manuscript is to expand the notion of neutrosophic crisp set (NCS) by presenting the notion of n-valued refined neutrosophic crisp set with some illustration examples. We also establish some of its set-theoretical operations.

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41

Ummey, Habiba, and Quddoos Abdul. "Pentagonal Neutrosophic Transportation Problems with Interval Cost." October 2, 2022. https://doi.org/10.5281/zenodo.7135436.

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The present paper aims to deal with a new variant of uncertain classical transportation problem namely ‘Interval Pentagonal Neutrosophic Transportation Problem’ (IPNTP) in which the uncertainty of source & destination parameters are described by pentagonal neutrosophic numbers while an estimated range (interval number) is used to represent uncertain cost of transportation. The objective consisting interval cost has been splitted into two equivalent crisp objectives using the concept of expected value & uncertainty of interval number. The constraints containing pentagonal ne

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42

C., Antony Crispin Sweety, and Arockiarani I. "Rough sets in Fuzzy Neutrosophic approximation space." May 16, 2015. https://doi.org/10.5281/zenodo.23178.

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A rough set is a formal approximation of a crisp set which gives lower and upper approximation of original set to deal with uncertainties. The concept of neutrosophic set is a mathematical tool for handling imprecise, indeterministic and inconsistent data. In this paper, we introduce the concepts of Rough Fuzzy Neutrosophic Sets and Fuzzy Neutrosophic Rough Sets and investigate some of their properties. Further as the characterisation of fuzzy neutrosophic rough approximation operators, we introduce various notion of cut sets of neutrosophic fuzzy sets.

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Henry, Garrett. "Some Polynomials Related to Numbers in Classes of (Strong) Neutrosophic Graphs." March 29, 2022. https://doi.org/10.13140/RG.2.2.36280.83204.

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New setting is introduced to study girth polynomial and neutrosophic girth polynomial arising counting neutrosophic cycles and crisp cycles in strong neutrosophic graphs based on neutrosophic cycles and in neutrosophic graphs based on crisp cycles. Forming neutrosophic cycles from a sequence of consecutive vertices is key type of approach to have these notions namely girth polynomial and neutrosophic girth polynomial arising from counting neutrosophic cycles and crisp cycles in strong neutrosophic graphs based on neutrosophic cycles and in neutrosophic graphs based on crisp cycles. Two numbers

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44

Ye, Jun. "Exponential operations and aggregation operators of interval neutrosophic sets and their decision making methods." September 4, 2016. https://doi.org/10.5281/zenodo.235671.

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An interval neutrosophic set (INS) is a subclass of a neutrosophic set and a generalization of an interval-valued intuitionistic fuzzy set, and then the characteristics of INS are independently described by the interval numbers of its truth-membership, indeterminacy-membership, and falsity-membership degrees. However, the exponential parameters (weights) of all the existing exponential operational laws of INSs and the corresponding exponential aggregation operators are crisp values in interval neutrosophic decision making problems.

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45

Rajesh, Kumar Saini, Sangal Atul, and Manisha. "Application of Single Valued Trapezoidal Neutrosophic Numbers in Transportation Problem." July 28, 2020. https://doi.org/10.5281/zenodo.3965004.

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Abstract: In the present paper, we introduced the concept of single valued trapezoidal neutrosophic number, which is generalization of single valued neutrosophic number. A generalization of crisp, fuzzy and intuitionistic fuzzy sets represents as neutrosophic sets, which have uncertainty, inconsistent, and incompleteness information in real world problem. De-neutrosophication is a process to convert neutrosophic number into a crisp number for practical applications. For unbalanced neutrosophic transportation problem, we also use here minimum row column method and set a compariso

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Florentin, Smarandache. "Extensión de Soft Set a Hypersoft Set, y luego a Plithogenic Hypersoft Set." January 1, 2023. https://doi.org/10.5281/zenodo.7519268.

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En este artículo, se generaliza el Soft Set al Hypersoft Set transformando la función F en una función multiatributo. Luego presentamos los híbridos de Crisp, Fuzzy, Intuitionistic Fuzzy, Neutrosophic y Plithogenic Hypersoft Set.

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47

C., Antony Crispin Sweety, and Arockiarani I. "Rough sets in Neutrosophic Approximation Space." December 6, 2013. https://doi.org/10.5281/zenodo.34888.

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Abstract:

A rough set is a formal approximation of a crisp set which gives lower and upper approximation of original set to deal with uncertainties. The concept of neutrosophic set is a mathematical tool for handling imprecise, indeterministic and inconsistent data. In this paper, we introduce the concepts of neutrosophic rough Sets and investigate some of its properties. Further as the characterisation of neutrosophic rough approxi- mation operators, we introduce various notions of cut sets of neutrosophic rough sets.

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48

Florentin, Smarandache. "Extension of Soft Set to Hypersoft Set, and then to Plithogenic Hypersoft Set." May 15, 2019. https://doi.org/10.5281/zenodo.2838716.

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In this paper, we generalize the soft set to the hypersoft set by transforming the function F into a multi-attribute function. Then we introduce the hybrids of Crisp, Fuzzy, Intuitionistic Fuzzy, Neutrosophic, and Plithogenic Hypersoft Set.

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49

Smarandache, Florentin. "Extension of Soft Set to Hypersoft Set, and then to Plithogenic Hypersoft Set." Neutrosophic Sets and Systems 22 (December 10, 2018). https://doi.org/10.5281/zenodo.2159755.

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Abstract:

In this paper, we generalize the soft set to the hypersoft set by transforming the function F into a multi-attribute function. Then we introduce the hybrids of Crisp, Fuzzy, Intuitionistic Fuzzy, Neutrosophic, and Plithogenic Hypersoft Set.

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50

Mouhammad, Bakro, Al-Kamha Reema, and Kanafani Qosai. "Neutrosophication Functions and their Implementation by MATLAB Program." February 18, 2021. https://doi.org/10.5281/zenodo.4549372.

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Neutrosophication is the process of converting crisp values into neutrosophic values, which is considered the first and basic step for any processing system that depends on the neutrosophic logical relationships and features, especially those that take into account indeterminacy values that result from ambiguity, noise, or inaccuracy. In this paper, we have presented a set of neutrosophication functions by modifying the functions used in fuzzy logic (trapezoid, triangle, gauss, bell-shaped, s-shaped, z-shaped) in a way that preserves the essence of the neutrosophic logic philosophy and the ind

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