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Journal articles on the topic 'Complex neutrosophic sets'

Author: Grafiati

Published: 5 June 2025

Last updated: 1 August 2025

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1

Gulistan, Muhammad, Florentin Smarandache, and Amir Abdullah. "An application of complex neutrosophic sets to the theory of groups." International Journal of Algebra and Statistics 7, no. 1-2 (2018): 94–112. http://dx.doi.org/10.20454/ijas.2018.1455.

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In this article we introduce the concept of complex neutrosophıc subgroups (normal subgroups). We define the notion of alpha-cut of complex neutrosophıc set, give examples and study some of its related results. We also define the Cartesian product of complex neutrosophic subgroups. Furthermore, we introduce the concept of image and preimage of complex neutrosophic set and prove some of its properties.

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Al-Sharqi, Faisal Al, Abd Ghafur Ahmad, and Ashraf Al Al-Quran. "Mapping on Interval Complex Neutrosophic Soft Sets." International Journal of Neutrosophic Science 19, no. 4 (2022): 77–85. http://dx.doi.org/10.54216/ijns.190406.

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The neutrosophic idea is a fertile environment adaptable to different mathematical tools. This paper aims to introduce the mapping of complex interval neutrosophic soft sets (MI-CNSSs). Further, the images and inverse images of complex interval neutrosophic soft sets and their properties are explored. These will be supported by concrete examples, and this paper will present some theorems about complex interval neutrosophic soft images and inverse images.

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Gulistan, Muhammad, and Salma Khan. "Extentions of neutrosophic cubic sets via complex fuzzy sets with application." Complex & Intelligent Systems 6, no. 2 (2019): 309–20. http://dx.doi.org/10.1007/s40747-019-00120-8.

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Abstract In this paper, we propose that the complex neutrosophic cubic set (internal and external) show, which is a blend of complex fuzzy sets, neutrosophic sets, and cubic sets. We characterize a few set theoretic activities of internal complex neutrosophic sets, for example, union, intersection and complement, and a while later the operational principles. A few ideas identified with the structure of this model are clarified. We present some accumulation administrators and talk about some basic leadership issue with genuine model.

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Saeed, Maha Mohammed, Sami Ullah Khan, Fatima Suriyya, Arif Mehmood, and Jamil J. Hamja. "Interval-Valued Complex Neutrosophic Sets and Complex Neutrosophic Soft Topological Spaces." International Journal of Analysis and Applications 23 (June 9, 2025): 132. https://doi.org/10.28924/2291-8639-23-2025-132.

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Network performance is the evaluation and assessment of collective network statistics, to define the quality of services offered by the computer network. It is a qualitative and quantitative technique that measures and defines the performance level for a network. Networking provides a link between different factors (bandwidth, number of devices, network traffic and latency) for performing multiple tasks. These factors affect the network speed and quality. Some errors occur due to network traffic and latency can produce uncertain results. These results provide low quality and speed in the netwo

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Omaima, Omaima, and Omaima alshanqiti. "Algebraic properties applied to sin trigonometric complex neutrosophic sets." International Journal of Neutrosophic Science 23, no. 4 (2024): 206–23. http://dx.doi.org/10.54216/ijns.230416.

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This article presents a new way of analyzing multiple attribute decision-making (MADM) using (♭1, ♭2, ♭3) sin trigonometric complex neutrosophic sets (ST-CNS). Complex neutrosophic weighted averaging (ST-CNWA), sin trigonometric complex neutrosophic weighted geometric (ST-CNWG), sin trigonometric complex generalized neutrosophic weighted averaging (ST-CGNWA), and sin trigonometric complex generalized neutrosophic weighted geometric (ST-CGNWG). During our discussion, we presented an algorithm that utilized these operators. There are extensive numerical illustrations of score values. Furthermore

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Al-Quran, Ashraf Al, Abd Ghafur .., Faisal Al Al-Sharqi, and Abdalwali Lutfi. "Q-Complex Neutrosophic Set." International Journal of Neutrosophic Science 20, no. 2 (2023): 08–19. http://dx.doi.org/10.54216/ijns.200201.

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Most complex problems in the real-world typically involve uncertain,incomplete and indeterminate two-dimen sional data i.e. information pertaining to the attributes and the periodicity of the problem parameters. To meet the demand for models that has the ability to handle these information with these characteristics, the introduction of neutrosophic sets (NSs) was followed by their extension to the complex neutrosophic sets (CNSs). In this paper, we introduce the concept of Q- complex neutrosophic set (Q-CNS) by extending the ranges of the membership functions in Q-neutrosophic set (Q-NS) from

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M., M., Abdallah Al Al-Husban, Lejo J. Manavalan, Jamil J. Jaber, M. Palanikumar, and G. Balaji. "Selection process real-life application for new type complex neutrosophic sets using various aggregation operators." International Journal of Neutrosophic Science 23, no. 4 (2024): 136–53. http://dx.doi.org/10.54216/ijns.230410.

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A new approach to multiple attribute decision-making (MADM) is presented in this article, which is based on (ȷ1, ȷ2, ȷ3) complex neutrosophic sets (CNS). We are extending the CNS in this way. Complex neutrosophic weighted averaging (CNWA), complex neutrosophic weighted geometric (CNWG), complex generalized neutrosophic weighted averaging (CGNWA), and complex generalized neutrosophic weighted geometric (CGNWG). An algorithm utilizing these operators was presented during our discussion. Extensive score and accuracy values are illustrated numerically. We will also discuss idempotency, boundedness

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8

S. Sathishkumar. "An In-Depth Exploration of The Properties and Theoretical Foundations of Neutrosophic Generalized Semipreclosed Sets in Neutrosophic Topological Spaces." Communications on Applied Nonlinear Analysis 31, no. 8s (2024): 272–81. http://dx.doi.org/10.52783/cana.v31.1482.

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This paper goes deeply into various intrinsic characteristics of Neutrosophic generalized semipre closed sets. By meticulously investigating these sets, we hope to identify their essential traits and behaviors within the larger context of Neutrosophic set theory. Furthermore, our research looks at the complex linkages and interactions between Neutrosophic generalized semipre closed sets and other forms of Neutrosophic sets. Through this comparative research, we hope to highlight the links and distinctions that exist across these diverse types of Neutrosophic sets, thus contributing to a more t

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Khan, Madad, Saima Anis, Kainat Bibi, Sohail Iqbal, and Florentin Smarandache. "Complex Neutrosophic Soft Matrices Framework: An Application in Signal Processing." Journal of Mathematics 2021 (September 15, 2021): 1–10. http://dx.doi.org/10.1155/2021/8887824.

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In this paper, we introduce the concept of complex neutrosophic soft matrices. We define some basic operations including complement, union, and intersection on these matrices. We extend the concept of complex neutrosophic soft sets to complex neutrosophic soft matrices and prove related properties. Moreover, we develop an algorithm using complex neutrosophic soft matrices and apply it in signal processing.

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10

Malath., F. Aswad. "A Study of n-Refined Neutrosophic Complex Numbers and Their Properties." Neutrosophic Knowledge 3, no. 3 (2021): 14–22. https://doi.org/10.5281/zenodo.5507551.

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This paper is dedicated to define for the first time the concept of complex n-refined neutrosophic number as a direct application of n-refined neutrosophic sets and as a new generalization of neutrosophic complex numbers. Also, it presents some of their elementary properties such as, conjugates, absolute values, invertibility, and algebraic operations.

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11

Jo, Dongsik, S. Saleh, Jeong-Gon Lee, Kul Hur, and Chen Xueyou. "Topological Structures via Interval-Valued Neutrosophic Crisp Sets." Symmetry 12, no. 12 (2020): 2050. http://dx.doi.org/10.3390/sym12122050.

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In this paper, we introduce the new notion of interval-valued neutrosophic crisp sets providing a tool for approximating undefinable or complex concepts in real world. First, we deal with some of its algebraic structures. We also define an interval-valued neutrosophic crisp (vanishing) point and obtain some of its properties. Next, we define an interval-valued neutrosophic crisp topology, base (subbase), neighborhood, and interior (closure), respectively and investigate some of each property, and give some examples. Finally, we define an interval-valued neutrosophic crisp continuity and quotie

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Mahizha, Mahizha, and Immaculate Mary M. "A Comprehensive Approach to Solid Waste Management Site Selection Using Simplified Neutrosophic Distance-Based Similarity Measures with N-Valued T-Spherical Fuzzy Neutrosophic Sets." International Journal of Neutrosophic Science 26, no. 1 (2025): 293–310. https://doi.org/10.54216/ijns.260125.

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In a neutrosophic environment, a single-valued neutrosophic multi-set, and an intuitionistic fuzzy-valued neutrosophic multi-set are defined by sequences of acceptance, indeterminacy, and rejection grades. The structure of these sets enables the incorporation of multiple layers of information across acceptance, indeterminacy, and rejection grades, making them particularly valuable for multi-criteria decision-making processes. This paper presents the N-valued T-spherical fuzzy neutrosophic set as an advanced extension of neutrosophic sets, aimed at improving uncertainty management and imprecisi

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Alqahtani, Mohammed, M. Kaviyarasu, Anas Al-Masarwah, and M. Rajeshwari. "Application of Complex Neutrosophic Graphs in Hospital Infrastructure Design." Mathematics 12, no. 5 (2024): 719. http://dx.doi.org/10.3390/math12050719.

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Complex neutrosophic graphs are created by combining complex neutrosophic sets with graph theory ideas. This provides a flexible framework for tackling complex problem-solving circumstances. Various processes, such as union, join, and composition, are thoroughly investigated to improve the administration of complicated neutrosophic graphs. This research also looks into the area of complicated neutrosophic graph homeomorphisms, investigating the transformations and mappings that occur inside these structures. This investigation advances our knowledge of the intrinsic features and linkages found

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Luqman, Anam, Muhammad Akram, and Florentin Smarandache. "Complex Neutrosophic Hypergraphs: New Social Network Models." Algorithms 12, no. 11 (2019): 234. http://dx.doi.org/10.3390/a12110234.

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A complex neutrosophic set is a useful model to handle indeterminate situations with a periodic nature. This is characterized by truth, indeterminacy, and falsity degrees which are the combination of real-valued amplitude terms and complex-valued phase terms. Hypergraphs are objects that enable us to dig out invisible connections between the underlying structures of complex systems such as those leading to sustainable development. In this paper, we apply the most fruitful concept of complex neutrosophic sets to theory of hypergraphs. We define complex neutrosophic hypergraphs and discuss their

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15

Romdhini, Mamika Ujianita, Ashraf Al Al-Quran, Faisal Al Al-Sharqi, Mohammad K. Tahat, and Abdalwali Lutfi. "Exploring the Algebraic Structures of Q-Complex Neutrosophic Soft Fields." International Journal of Neutrosophic Science 22, no. 4 (2023): 93–105. http://dx.doi.org/10.54216/ijns.220408.

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A field is a fundamental algebraic structure that finds extensive applications in algebra and various mathematical domains. On the other hand, a Q-complex neutrosophic soft set (Q-CNSS) is a unique hybrid model that combines the characteristics of soft sets and neutrosophic sets within a complex number framework. It utilizes the effectiveness of Q-set as a powerful tool in the domain of this particular model. In this article, we leverage this model to define fields under uncertainty. We present the Q-complex neutrosophic soft field (Q-CNSF) and examine the unique algebraic properties associate

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Khalid, Neha Andaleeb, and Muhammad Saeed. "An Approach for Hybridizing N-Subalgebra with Quantified Neutrosophic Set using G-Algebra." Neutrosophic Systems with Applications 25 (January 1, 2025): 14–29. https://doi.org/10.61356/j.nswa.2025.25411.

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Neutrosophic sets are a generalized form of fuzzy sets as well as intuitionistic fuzzy sets, as they address the uncertainty factor as an independent component along with truthfulness and falsity. However, traditional neutrosophic approaches often struggle with effectively managing and quantifying indeterminate elements in complex algebraic structures. To address this limitation, this paper employs an expanded version of the neutrosophic set, incorporating a subalgebra. The proposed research is multifaceted: firstly, the new concept of N-Subalgebra (NSU) is proposed. This is the modified setti

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Al-Quran, Ashraf Al, Faisal Al Al-Sharqi, Zahari Md Rodzi, et al. "The Algebraic Structures of Q-Complex Neutrosophic Soft Sets Associated with Groups and Subgroups." International Journal of Neutrosophic Science 22, no. 1 (2023): 60–76. http://dx.doi.org/10.54216/ijns.220105.

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Groups and subgroups are rich algebraic structures, and both of them depend on binary operations in their work. The discussion of this paper is organized into two parts. In the first part, we define the notion of Qcomplex neutrosophic soft sets (Q-CNSSs) by amalgamating two previous models of Q-complex neutrosophic set (Q-CNS) and soft set (SS) to address the issues of two-dimensionality (two variables) in a universal set under a parametric environment. Subsequently, the relation between Q-CNSSs and Q- neutrosophic soft sets (Q-NSSs) is verified. A basic set theory for this hybrid model is dev

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18

Salama, Ahmad, Rasha Dalla, Malath Al Aswad, and Rozina Ali. "Some Results About 2-Cyclic Refined Neutrosophic Complex Numbers." Journal of Neutrosophic and Fuzzy Systems 4, no. 1 (2022): 41–8. http://dx.doi.org/10.54216/jnfs.040105.

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This paper is dedicated to define for the first time the concept of 2-cyclic complex refined neutrosophic numbers as a direct application of 2-cyclic refined neutrosophic sets. Also, it presents some of their elementary properties such as conjugates, absolute values, invertibility, and algebraic operations. Also, we illustrate many examples to clarify the validity of our discussion

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Fahmi, Aliya, Aziz Khan, and Thabet Abdeljawad. "A novel approach to group decision-making using generalized bipolar neutrosophic sets." PLOS One 20, no. 6 (2025): e0317746. https://doi.org/10.1371/journal.pone.0317746.

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This study introduces operational laws for Aczél-Alsina aggregation within the framework of generalized bipolar neutrosophic sets (GBNS), tailored for group decision-making scenarios. Novel aggregation operators, including the Generalized Bipolar Neutrosophic Aczél-Alsina Weighted Average (GBNAAWA), Generalized Bipolar Neutrosophic Aczél-Alsina Ordered Weighted Average (GBNAAOWA), Generalized Bipolar Neutrosophic Aczél-Alsina Hybrid Weighted Average (GBNAAHWA), Generalized Bipolar Neutrosophic Aczél-Alsina Weighted Geometric (GBNAAWG), Generalized Bipolar Neutrosophic Aczél-Alsina Ordered Weig

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20

Shi, Lilian, and Yue Yuan. "Hybrid Weighted Arithmetic and Geometric Aggregation Operator of Neutrosophic Cubic Sets for MADM." Symmetry 11, no. 2 (2019): 278. http://dx.doi.org/10.3390/sym11020278.

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Neutrosophic cubic sets (NCSs) can express complex multi-attribute decision-making (MADM) problems with its interval and single-valued neutrosophic numbers simultaneously. The weighted arithmetic average (WAA) and geometric average (WGA) operators are common aggregation operators for handling MADM problems. However, the neutrosophic cubic weighted arithmetic average (NCWAA) and neutrosophic cubic geometric weighted average (NCWGA) operators may result in some unreasonable aggregated values in some cases. In order to overcome the drawbacks of the NCWAA and NCWGA, this paper developed a new neut

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Al-Quran, Ashraf, and Shawkat Alkhazaleh. "Relations between the Complex Neutrosophic Sets with Their Applications in Decision Making." Axioms 7, no. 3 (2018): 64. http://dx.doi.org/10.3390/axioms7030064.

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The basic aim of soft computing is to trade precision for a tractableness and reduction in solution cost by pushing the limits of tolerance for imprecision and uncertainty. This paper introduces a novel soft computing technique called complex neutrosophic relation (CNR) to evaluate the degree of interaction between two complex neutrosophic sets (CNSs). CNSs are used to represent two-dimensional information that are imprecise, uncertain, incomplete and indeterminate. The Cartesian product of CNSs and subsequently the complex neutrosophic relation is formally defined. This relation is generalise

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22

Muhaya, Khulud Fahad Bin, and Kholood Mohammad Alsager. "Extending neutrosophic set theory: Cubic bipolar neutrosophic soft sets for decision making." AIMS Mathematics 9, no. 10 (2024): 27739–69. http://dx.doi.org/10.3934/math.20241347.

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<p>This research introduced cubic bipolar neutrosophic sets (CBNSs), a novel framework that significantly enhanced the capabilities of bipolar neutrosophic sets (BNSs) in handling uncertainty and vagueness within data analysis. By integrating bipolarity and cubic sets, CBNSs provide a more comprehensive and accurate representation of information. We have defined key operations for CBNSs and thoroughly investigated their structural properties. Additionally, we have introduced cubic bipolar neutrosophic soft sets (CBNSSs) as a flexible parameterization tool for CBNSs. To validate the pract

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Karabašević, Darjan, Dragiša Stanujkić, Edmundas Kazimieras Zavadskas, et al. "A Novel Extension of the TOPSIS Method Adapted for the Use of Single-Valued Neutrosophic Sets and Hamming Distance for E-Commerce Development Strategies Selection." Symmetry 12, no. 8 (2020): 1263. http://dx.doi.org/10.3390/sym12081263.

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Neutrosophic sets have been recognized as an effective approach in solving complex decision-making (DM) problems, mainly when such problems are related to uncertainties, as published in numerous articles thus far. The use of the three membership functions that can be used to express accuracy, inaccuracy, and indeterminacy during the evaluation of alternatives in multiple-criteria DM can be said to be a significant advantage of these sets. By utilizing these membership functions, neutrosophic sets provide an efficient and flexible approach to the evaluation of alternatives, even if DM problems

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V.Herrera, Alex V., Lenín G. G.Flores, and José L. G. L.G.Delgado. "Treatment Alternatives to Gingival Hyperpigmentation Using Neutrosophic Correlation Coefficients." International Journal of Neutrosophic Science 18, no. 4 (2022): 108–15. http://dx.doi.org/10.54216/ijns.180409.

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Among the main techniques described in the literature for treating gingival melanosis are the use of chemical agents, free gingival grafts, abrasion with rotary or manual instruments (scalpel), cryosurgery with liquid nitrogen, gingivectomy and gingivoplasty, and the use of lasers. The present study implements a selective evaluation of therapeutic alternatives for gingival hyperpigmentation through the use of neutrosophic correlation coefficients. For this, a bibliographic review was carried out on the specialized documentary base to determine the main treatments in the matter of the object of

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Broumi, Said, Swaminathan Mohanaselvi, Tomasz Witczak, Mohamed Talea, Assia Bakali, and Florentin Smarandache. "Complex fermatean neutrosophic graph and application to decision making." Decision Making: Applications in Management and Engineering 6, no. 1 (2023): 474–501. http://dx.doi.org/10.31181/dmame24022023b.

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A new growing area of neutrosophic set (NS) theory called complex neutrosophic sets (CNS) provides useful tools for dealing with uncertainty in complex valued physical variables that are observed in the actual world. A CNS take values for the truth, indeterminacy and falsity membership functions in the complex plane's unit circle. In this research, a novel concept of complex fermatean neutrosophic graph (CFNG) is established. We proposed the order, size, degree and total degree of a vertex of CFNG. Also, we presented the primary operations such as complement, union, join, ring-sum and cartesia

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Ulucay, Vakkas, Adil Kılıç, Memet Şahin, and Harun Deniz. "A New Hybrid Distance-Based Similarity Measure for Refined Neutrosophic sets and its Application in Medical Diagnosis." MATEMATIKA 35, no. 1 (2019): 83–94. http://dx.doi.org/10.11113/matematika.v35.n1.1063.

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In recent times, refined neutrosophic sets introduced by Deli [6] has been one of the most powerful and flexible approaches for dealing with complex and uncertain situations of real world. In particular, the decision making methods between refined neutrosophic sets are important since it has applications in various areas such as image segmentation, decision making, medical diagnosis, pattern recognition and many more. The aim of this paper is to introduce a new distance-based similarity measure for refined neutrosophic sets. The properties of the proposed new distance-based similarity measure

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Dadaş, Hasanş. "Advanced Decision-Making Techniques with Generalized Close Sets in Neutrosophic Soft Bitopological Spaces." Galoitica: Journal of Mathematical Structures and Applications 10, no. 1 (2024): 08–16. http://dx.doi.org/10.54216/gjmsa.0100101.

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In recent years, neutrosophic soft bitopological spaces have emerged as a promising framework for handling uncertainty and imprecision in various domains, particularly in the context of decision-making problems. This paper presents a comprehensive study of advanced decision-making techniques using generalized close sets in neutrosophic soft bitopological spaces. The primary objective of this research is to develop a better understanding of the theoretical underpinnings of generalized close sets and their practical applications in decision-making under uncertain conditions. We begin by providin

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Kamran, Muhammad, Shahzaib Ashraf, Shahid Khan, Aamir Khan, Hedia Zardi, and Saba Mehmood. "Integrated decision-making framework for hospital development: A single-valued neutrosophic probabilistic hesitant fuzzy approach with innovative aggregation operators." Yugoslav Journal of Operations Research, no. 00 (2023): 34. http://dx.doi.org/10.2298/yjor230915034k.

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This research article proposes an innovative algorithm for analyzing parallelism in the evolution of hospital building features, with the goal of advancing decisionmaking processes in both urban and rural hospitals. As an additional generalization of the concepts of fuzzy sets, intuitionistic fuzzy sets, single-valued neutrosophic sets, hesitant fuzzy sets, and probabilistic fuzzy sets this paper proposes a single-valued neutrosophic probabilistic hesitant fuzzy set (SV-NPHFS). It is derived from the combination of single-valued neutrosophic sets, probabilistic fuzzy sets, and hesitant fuzzy s

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Aiyared, Aiyared, Murugan Palanikumar, and T. T. Raman. "Algebraic structures such as distributive, associativity and boundedness properties via tangent neutrosophic set acting generalized weighted averaging and geometric." International Journal of Neutrosophic Science 25, no. 4 (2025): 203–17. https://doi.org/10.54216/ijns.250417.

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A novel technique to produce complicated tangent trigonometric (ζ,∂,e) neutrosophic sets is presented in this study. Complex tangent trigonometric (ζ,∂,e) neutrosophic weighted averaging, geometric, generalized weighted averaging, and generalized weighted geometric will all be discussed in this article. We calculated the weighted average and geometric using an aggregating model. The following algebraic methods will be used to further study several sets having significant properties.

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W. B., Vasantha, Ilanthenral Kandasamy, Florentin Smarandache, Vinayak Devvrat, and Shivam Ghildiyal. "Study of Imaginative Play in Children Using Single-Valued Refined Neutrosophic Sets." Symmetry 12, no. 3 (2020): 402. http://dx.doi.org/10.3390/sym12030402.

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This paper introduces Single Valued Refined Neutrosophic Set (SVRNS) which is a generalized version of the neutrosophic set. It consists of six membership functions based on imaginary and indeterminate aspect and hence, is more sensitive to real-world problems. Membership functions defined as complex (imaginary), a falsity tending towards complex and truth tending towards complex are used to handle the imaginary concept in addition to existing memberships in the Single Valued Neutrosophic Set (SVNS). Several properties of this set were also discussed. The study of imaginative pretend play of c

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Rehman, Ateeq Ur, Muhammad Gulistan, Nasreen Kausar, Sajida Kousar, Mohammed M. Al-Shamiri, and Rashad Ismail. "Novel Development to the Theory of Dombi Exponential Aggregation Operators in Neutrosophic Cubic Hesitant Fuzzy Sets: Applications to Solid Waste Disposal Site Selection." Complexity 2022 (September 26, 2022): 1–16. http://dx.doi.org/10.1155/2022/3828370.

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The neutrosophic cubic hesitant fuzzy set can efficiently handle the complex information in a decision-making problem because it combines the advantages of the neutrosophic cubic set and the hesitant fuzzy set. The algebraic operations based on Dombi norms and co-norms are more flexible than the usual algebraic operations as they involve an operational parameter. First, this paper establishes Dombi algebraic operational laws, score functions, and similarity measures in neutrosophic cubic hesitant fuzzy sets. Then, we proposed Dombi exponential operational laws in which the exponents are neutro

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Ebru, Ebru, Nasreen Kausar, Emre Ozbilge, and Ebru Ozbilge. "Extending the concepts of complex interval valued neutrosophic subbisemiring of bisemiring." International Journal of Neutrosophic Science 23, no. 4 (2024): 117–35. http://dx.doi.org/10.54216/ijns.230409.

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The objective of this paper is to investigate the innovative concept of complex neutrosophic subbisemiring. The novelty of the complex neutrosophic subbisemiring lies in its wide range of truth, indeterminacy, and false function values. It goes beyond the range of [0,1] in the complex plane in contrast to the traditional range [0,1]. Therefore, these three functions can be described mathematically using a complex number in the complex neutrosophic subbisemiring. We develop and analyze the concept of complex interval-valued neutrosophic subbisemiring (CIVNSBS). Moreover, we study homomorphic ch

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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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Quek, Shio Gai, Said Broumi, Ganeshsree Selvachandran, Assia Bakali, Mohamed Talea, and Florentin Smarandache. "Some Results on the Graph Theory for Complex Neutrosophic Sets." Symmetry 10, no. 6 (2018): 190. http://dx.doi.org/10.3390/sym10060190.

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Dat, Luu Quoc, Nguyen Tho Thong, Le Hoang Son, et al. "Linguistic Approaches to Interval Complex Neutrosophic Sets in Decision Making." IEEE Access 7 (2019): 38902–17. http://dx.doi.org/10.1109/access.2019.2902841.

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Romdhini, Mamika Ujianita, Ashraf Al Al-Quran, Faisal Al Al-Sharqi, Hazwani Hashim, and Abdalwali Lutfi. "Unveiling an Innovative Approach to Q-Complex Neutrosophic Soft Rings." International Journal of Neutrosophic Science 22, no. 4 (2023): 29–35. http://dx.doi.org/10.54216/ijns.220402.

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In this paper, our aim is to investigate the algebraic structures within the Q-complex neutrosophic soft model. We introduce two fundamental concepts: the Q-complex neutrosophic soft ring (Q-CNSR) and the Q-complex neutrosophic soft ideal (Q-CNSI). Q-CNSRs combine the properties of Q-complex neutrosophic soft sets (Q-CNSSs) with ring theory, effectively capturing uncertainty and indeterminacy present in ring operations through the incorporation of Q-complex neutrosophic membership values. Additionally, we define Q-CNSIs as subsets of Q-CNSRs that possess distinctive properties and hold signifi

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Arindam, Arindam, Said Broumi, Ranjan Kumar, and Jayanta Pratihar. "Fermatean Shortest Route Problem with Interval Fermatean Neutrosophic Fuzzy Arc Length: Formulation and a Modified Dijkstra’s Algorithm." International Journal of Neutrosophic Science 23, no. 3 (2024): 288–95. http://dx.doi.org/10.54216/ijns.230323.

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Dijkstra’s algorithm (DA) is a very popular approach for finding the shortest route (SR) in the shortest route problem (SRP). The SRP becomes a challenging and complex problem in real life scenarios. The Fermatean neutrosophic set is a mathematical model that combines Fermatean sets with neutrosophic sets. It can handle the unclear, ambiguous, inconsistent, confusing, and uncertain information that comes from real-world problems. Decision-makers face difficulty accurately determining the precise membership (MG) and non membership levels due to the lack of appropriate data available. The FNS ca

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Jamil, Muhammad, Farkhanda Afzal, Deeba Afzal, Dhana Kumari Thapa, and Ayesha Maqbool. "Multicriteria Decision-Making Methods Using Bipolar Neutrosophic Hamacher Geometric Aggregation Operators." Journal of Function Spaces 2022 (January 27, 2022): 1–13. http://dx.doi.org/10.1155/2022/5052867.

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The study presents a novel conception of aggregation operators (AOs) based on bipolar neutrosophic sets by using Hamacher operations and their application in modeling real-life multicriteria decision-making problems. The neutrosophic set represents incomplete, inconsistent, and indeterminate information effectively. For better understanding in this paper, we have explained all essential definitions and their respective derived neutrosophic sets (NSs) and generalization bipolar neutrosophic sets (BNSs). The primary focus of our work is Hamacher aggregation operators like BN Hamacher weighted ge

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Şahin, Memet, and Arif Sarıoğlan. "Neutrosophic Quadruple Metric Spaces." Symmetry 17, no. 7 (2025): 1096. https://doi.org/10.3390/sym17071096.

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Instead of measuring the distance between two points with a positive real number, determining the degree to which the distance between these two points is close, not close, or uncertain allows for more detailed measurement. Recently, researchers have overcome this grading problem by using probability distribution functions, along with fuzzy, intuitionistic fuzzy, and neutrosophic sets. This study pioneers neutrosophic quadruple metric spaces as a powerful new tool for quantifying distances under complex, multi-dimensional uncertainty. It provides a comprehensive mathematical structure, includi

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Liu, Jia-Bao, Rashad Ismail, Muhammad Kamran, Esmail Hassan Abdullatif Al-Sabri, Shahzaib Ashraf, and Ismail Naci Cangul. "An optimization strategy with SV-neutrosophic quaternion information and probabilistic hesitant fuzzy rough Einstein aggregation operator." AIMS Mathematics 8, no. 9 (2023): 20612–53. http://dx.doi.org/10.3934/math.20231051.

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<abstract><p>The single valued neutrosophic probabilistic hesitant fuzzy rough Einstein aggregation operator (SV-NPHFRE-AO) is an extension of the neutrosophic probabilistic hesitant fuzzy rough set theory. It is a powerful decision-making tool that combines the concepts of neutrosophic logic, probability theory, hesitant fuzzy sets, rough sets, and Einstein aggregation operators. SV-NPHFRE-AO can be applied in many fields, including livestock decision making. Making judgments about a wide range of issues, including feed formulation, breeding program design, disease diagnostics, an

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Muhammad, Gulistan, Smarandache Florentin, and Abdullah Amir. "An application of complex neutrosophic sets to the theory of groups." May 18, 2019. https://doi.org/10.5281/zenodo.2837860.

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In this article we introduce the concept of complex neutrosophıc subgroups (normal subgroups). We define the notion of alpha-cut of complex neutrosophıc set, give examples and study some of its related results. We also define the Cartesian product of complex neutrosophic subgroups. Furthermore, we introduce the concept of image and preimage of complex neutrosophic set and prove some of its properties.

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Said, Broumi, Bakali Assia, Smarandache Florentin, Talea Mohamed, Ali Mumtaz, and Selvachandran Ganeshsree. "Complex Neutrosophic Soft Set." July 10, 2017. https://doi.org/10.5281/zenodo.888849.

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In this paper, we propose the complex neutrosophic soft set model, which is a hybrid of complex fuzzy sets, neutrosophic sets and soft sets. The basic set theoretic operations and some concepts related to the structure of this model are introduced, and illustrated. An example related to a decision making problem involving uncertain and subjective information is presented, to demonstrate the utility of this model.

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Ashraf, Al-Quran, and Hassan Nasruddin. "Mapping on complex neutrosophic soft expert sets." August 26, 2018. https://doi.org/10.5281/zenodo.1413097.

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We introduce the mapping on complex neutrosophic soft expert sets. Further, we investigated the basic operations and other related properties of complex neutrosophic soft expert image and complex neutrosophic soft expert inverse image of complex neutrosophic soft expert sets.

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Said, Broumi, Bakali Assia, Talea Mohamed, Smarandache Florentin, Uluçay Vakkas, and Sahin Mehmet. "Neutrosophic Sets: An Overview." April 30, 2018. https://doi.org/10.5281/zenodo.1237940.

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In this study, we give some concepts concerning the neutrosophic sets, single valued neutrosophic sets, interval-valued neutrosophic sets, bipolar neutrosophic sets, neutrosophic hesitant fuzzy sets, inter-valued neutrosophic hesitant fuzzy sets, refined neutrosophic sets, bipolar neutrosophic refined sets, multi-valued neutrosophic sets, simplified neutrosophic linguistic sets, neutrosophic over/off/under sets, rough neutrosophic sets, rough bipolar neutrosophic sets, rough neutrosophic hyper-complex set, and their basic operations. Then we introduce triangular neutrosophic numbers, trapezoid

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Mumtaz, Ali, and Smarandache Florentin. "Complex neutrosophic set." December 21, 2015. https://doi.org/10.5281/zenodo.49143.

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p>Complex fuzzy sets and complex intuitionistic fuzzy sets cannot handle imprecise, indeterminate, inconsistent, and incomplete information of periodic nature. To overcome this difﬁculty, we introduce complex neutrosophic set. A complex neutrosophic set is a neutrosophic set whose complex-valued truth membership function, complex-valued indeterminacy membership function, and complex-valued falsehood membership functions are the combination of real-valued truth amplitude term in association with phase term, real-valued indeterminate amplitude term with phase term, and real-valued false ampli

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Muhammad, Akram, Shabir Maria, and Ashraf Ather. "Complex neutrosophic N-soft sets: A new model with applications." April 22, 2021. https://doi.org/10.5281/zenodo.4711562.

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In this paper we establish the notion of complex single-valued neutrosophic N-soft set. It improves the traits of three general models, namely, single-valued neutrosophic sets, single-valued neutrosophic soft sets and single-valued neutrosophic Nsoft sets, in such way that it makes two dimensional ambiguous information and parameterized grading evaluation compatible. We explain the modeling abilities of complex single-valued neutrosophic N-soft sets and investigate some of their fundamental properties. Moreover, the intended approach hinges on rational attributes to support the choice of the m

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Madad, Khan, Anis Saima, Iqbal Sohail, Shams Fatima, and Song Seok-Zun. "Norms and Delta-Equalities of Complex Neutrosophic Sets." February 11, 2022. https://doi.org/10.5281/zenodo.6041601.

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The purpose of this paper is to put forward the basics results of complex fuzzy sets (CFSs) such as union, intersection, complement, product into complex neutrosophic sets because as the CFSs and complex intuitionistics sets does give the erroneous and inconvenient information about uncertainty and periodicity and also there are results related to different norms. Moreover we give some results about the distance measures of complex neutrosophic sets and define some notions.

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Rahoumah, Fatimah, Kai Siong Yow, Nik Mohd Asri Nik Long, and Menshawi Gasim. "On properties and operations of complex neutrosophic soft groups." Journal of Inequalities and Applications 2024, no. 1 (2024). http://dx.doi.org/10.1186/s13660-024-03173-7.

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AbstractComplex neutrosophic soft groups represent a significant advancement in handling uncertainty by integrating the concepts of fuzzy logic, soft sets, and neutrosophic logic. These groups generalize complex fuzzy soft groups and introduce an additional dimension through neutrosophic membership functions, namely truth, indeterminacy, and falsity. This creates a richer framework for dealing with uncertainty and ambiguity, making it well-suited for managing complex data structures in real-world applications. We explore some important definitions and theoretical frameworks surrounding complex

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LUU, QUOC DAT, THO THONG NGUYEN, HOANG SON LE, et al. "Linguistic Approaches to Interval Complex Neutrosophic Sets in Decision Making." May 16, 2019. https://doi.org/10.5281/zenodo.2861558.

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One of the most efcient tools for modeling uncertainty in decision-making problems is the neutrosophic set (NS) and its extensions, such as complex NS (CNS), interval NS (INS), and interval complex NS (ICNS). Linguistic variables have been long recognized as a useful tool in decision-making problems for solving the problem of crisp neutrosophic membership degree. In this paper, we aim to introduce new concepts: single-valued linguistic complex neutrosophic set (SVLCNS-2) and interval linguistic complex neutrosophic set (ILCNS-2) that are more applicable and adjustable to real-world implementat

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Memet, Şahin, and Kargın Abdullah. "Neutrosophic Triplet Group Based on Set Valued Neutrosophic Quadruple Numbers." December 10, 2019. https://doi.org/10.5281/zenodo.3569671.

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Smarandache introduced neutrosophic quadruple sets and neutrosophic quadruple numbers [45] in 2015. These sets and numbers are real or complex number valued. In this study, we firstly introduce set valued neutrosophic quadruple sets and numbers. We give some known and special operations for set valued neutrosophic quadruple numbers. Furthermore, Smarandache and Ali obtained neutrosophic triplet groups [30] in 2016. In this study, we firstly give neutrosophic triplet groups based on set valued neutrosophic quadruple number thanks to operations for set valued neutrosophic quadruple numbers. In t

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