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Journal articles on the topic 'Trapezoidal fuzzy neutrosophic number'

Author: Grafiati

Published: 2 June 2025

Last updated: 31 July 2025

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1

Fahmi, Aliya, Muhammad Aslam, and Saleem Abdullah. "Analysis of migraine in mutlicellular organism based on trapezoidal neutrosophic cubic hesitant fuzzy TOPSIS method." International Journal of Biomathematics 12, no. 08 (2019): 1950084. http://dx.doi.org/10.1142/s1793524519500840.

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In this paper, we define a new idea of trapezoidal neutrosophic cubic hesitant fuzzy number based on migraine diseases. We define and the migraine diseases on trapezoidal neutrosophic cubic hesitant fuzzy number and operational laws of trapezoidal neutrosophic cubic hesitant fuzzy number and hamming distance of TrNCHFNs. The new concept of trapezoidal neutrosophic cubic hesitant fuzzy TOPSIS method is introduced. Furthermore, we extend MCDM method based on the trapezoidal neutrosophic cubic hesitant fuzzy TOPSIS method. Finally, an illustrative example is given to verify and demonstrate the pr

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Mathew, Ligin P., Lovelymol Sebastian, and Baiju Thankachan. "Some Operations on Trapezoidal Single Valued Neutrosophic Fuzzy Numbers." International Journal of Neutrosophic Science 23, no. 3 (2024): 29–43. http://dx.doi.org/10.54216/ijns.230303.

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Almost all situations that arise in applied mathematics involve uncertainty, inconsistency, and indeterminacy. This can be simultaneously handled by the use of single valued neutrosophic fuzzy sets and single valued neutrosophic fuzzy numbers. In this paper, we propose the operations of addition, subtraction, and scalar multiplication on trapezoidal single valued neutrosophic fuzzy numbers. We introduce some component-wise interval operations on the union of closed bounded intervals. Then we show how this can be used to perform the proposed operations on trapezoidal single valued neutrosophic

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3

S, Santhi. "Flow Shop Scheduling Problem in Neutrosophic Environment Using Trapezoidal Fuzzy Numbers." International Journal of Psychosocial Rehabilitation 24, no. 4 (2020): 4921–26. http://dx.doi.org/10.37200/ijpr/v24i4/pr201593.

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Uma, Uma, Uma .., and Ganesan K. "A New Approach to Solve Transportation Problems Under Neutrosophic Environment." International Journal of Neutrosophic Science 23, no. 4 (2024): 224–37. http://dx.doi.org/10.54216/ijns.230417.

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The transportation problem has received a lot of attention in the field of operations research. In many circumstances, transportation planners may lack clear information on supply, demand, and transportation costs. Fuzzy sets can accept incomplete information by allowing for degrees of membership, which describe the level of certainty or uncertainty associated with each parameter. Three components—truth-membership, indeterminacy-membership, and falsity-membership degrees—are added to fuzzy numbers to create neutrosophic fuzzy numbers, which enables a more complex depiction of uncertainty. In t

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K., K., M. Santoshi Kumari, K. Kalaiarasi, Manjula G. J., and Shrivalli H. Y. "Energizing Inventory Management to Optimize Energy Consumption of Handling Shortages by Neutrosophic Fuzzy Trapezoidal Number." International Journal of Neutrosophic Science 24, no. 1 (2024): 219–36. http://dx.doi.org/10.54216/ijns.240120.

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Embarking on the exploration of integrating environmental sustainability principles and neutrosophic fuzzy theory in inventory management, this study aims to effectively tackle shortages. It underscores the vital balance between economic efficiency and ecological responsibility in contemporary inventory management practices. Neutrosophic fuzzy theory emerges as a robust tool for navigating the inherent uncertainties in inventory optimization, offering a versatile framework for modelling intricate problems. Strategies for optimizing resource consumption and minimizing waste generation within in

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K., Kalaivani, and Palanivel Kaliyaperumal. "A neutrosophic approach to the transportation problem using single-valued trapezoidal neutrosophic numbers." Proyecciones (Antofagasta) 42, no. 2 (2023): 533–47. http://dx.doi.org/10.22199/issn.0717-6279-5374.

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In general, a fuzzy set can’t handle situations of inconsistencies and inexact data, however, the Neutrosophic Set (NS) has been used to address such types of issues in all real world problems. The neutrosophic set is an extension of the fuzzy set and the intuitionistic fuzzy set, that can deal with imperfect, inconsistent, and indeterminate data in all the related problems. This article proposed a conventional neutrosophic approach using a ranking function for the transportation problem. This approach has considered a single-valued neutrosophic set for the entire transportation problem with t

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Sinika, S., and G. Ramesh. "An interval arithmetic approach in solving interval-valued trapezoidal neutrosophic fuzzy multi-objective multi-item solid transportation problem." Yugoslav Journal of Operations Research, no. 00 (2025): 18. https://doi.org/10.2298/yjor240818018s.

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Unpredictability and uncertainty occur worldwide in various aspects of real life. We cannot predict some specific outcomes or events precisely due to multiple factors, randomness, complexity and limited information. These situations can be handled efficiently in a systematic way by using neutrosophic sets. In real-world applications, transportation is essential in all sorts of movement of goods, services and people to meet various needs and demands efficiently. This study concentrated on the multiple objectives, multiple choice transportation problem in interval-valued trapezoidal neutrosophic

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Tan, Ruipu, and Wende Zhang. "Multiple attribute decision making method based on DEMATEL and fuzzy distance of trapezoidal fuzzy neutrosophic numbers and its application in typhoon disaster evaluation." Journal of Intelligent & Fuzzy Systems 39, no. 3 (2020): 3413–39. http://dx.doi.org/10.3233/jifs-191758.

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Trapezoidal fuzzy neutrosophic decision making plays an important role in decision-making processes with uncertain, indeterminate, and inconsistent information. In this paper, we propose a new multi-attribute decision-making method based on decision-making trial and evaluation laboratory (DEMATEL), fuzzy distance, and linear assignment method (LAM), and we express evaluation values as the trapezoidal fuzzy neutrosophic numbers (TrFNNs). First, attribute weights are obtained using the DEMATEL method and the new fuzzy distance of TrFNNs based on graded mean integration representation is defined.

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Yasodai, P., and W. Ritha. "Scrutinization of a Neutrosophic Fuzzy Erlangian Queuing Model Using a Parametric Programming Technique." International Journal of Neutrosophic Science 21, no. 3 (2023): 115–25. http://dx.doi.org/10.54216/ijns.210311.

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This article examines an Erlangian queuing model in a neutrosophic fuzzy environment. The inter-arrival rates and service rates are trapezoidal neutrosophic fuzzy numbers integrated into the Erlangian queuing model. The membership functions of the performance metrics of the corresponding queuing model have been outlined using parametric programming techniques in accordance with the (σ, β, γ)- cuts and Zadeh's extension principle. The neutrosophic fuzzy queues are converted into a family of crisp queues using this principle. The applicability of the provided approach for various cutting possibi

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Yang, Lehua, Dongmei Li, and Ruipu Tan. "Shortest Path Solution of Trapezoidal Fuzzy Neutrosophic Graph Based on Circle-Breaking Algorithm." Symmetry 12, no. 8 (2020): 1360. http://dx.doi.org/10.3390/sym12081360.

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The shortest path problem is a topic of increasing interest in various scientific fields. The damage to roads and bridges caused by disasters makes traffic routes that can be accurately expressed become indeterminate. A neutrosophic set is a collection of the truth membership, indeterminacy membership, and falsity membership of the constituent elements. It has a symmetric form and indeterminacy membership is their axis of symmetry. In uncertain environments, the neutrosophic number can more effectively express the edge distance. The objectives in this study are to solve the shortest path probl

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K. Kalaiarasi and R. Divya. "SHORTEST PATH ON INTERVAL-VALUED INTUITIONISTIC TRAPEZOIDAL NEUTROSOPHIC FUZZY GRAPHS WITH APPLICATION." jnanabha 53, no. 01 (2023): 243–52. http://dx.doi.org/10.58250/jnanabha.2023.53129.

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In this article, stretch esteemed Interval Valued Intuitionistic Trapezoidal Neutrosophic Fuzzy Graph (IVITrNFG) of SPP, which is drew on trapezoidal numbers and IVITrNFG. Hear a genuine application is given an illustrative model for IVITrNFG. Additionally Shortest way is determined for this model. This present Dijkstra’s Algorithm briefest way was checked.

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Khalifa, Hamiden Abd El Wahed, Ashraf Al Al-Quran, Faisal Al Al-Sharqi, et al. "Utilization of neutrosophic Kuhn-Tucker’s optimality conditions for Solving Pythagorean fuzzy Two-Level Linear Programming Problems." International Journal of Neutrosophic Science 23, no. 3 (2024): 87–96. http://dx.doi.org/10.54216/ijns.230308.

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This article considers a bi-level linear programming with single valued trapezoidal fuzzy neutrosophic cost coefficient matrix and Pythagorean fuzzy parameters in the set of constraints both in the right and left sides. Based on the score functions of the neutrosophic numbers and Pythagorean fuzzy numbers, the model is changed to the corresponding crisp bi-level linear programming (BLP) problem. This problem is designated as a Pythagorean fuzzy bi-level linear programming (PFBLP) problem under neutrosophic environment. Kuhn-Tucker's conditions for optimality are necessary and sufficient for th

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Khalifa, Hamiden Abd El-Wahed, and Pavan Kumar. "Solving fully neutrosophic linear programming problem with application to stock portfolio selection." Croatian Operational Research Review 11, no. 2 (2020): 165–76. http://dx.doi.org/10.17535/crorr.2020.0014.

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Neutrosophic set is considered as a generalized of crisp set, fuzzy set, and intuitionistic fuzzy set for representing the uncertainty, inconsistency, and incomplete knowledge about the real world problems. In this paper, a neutrosophic linear programming (NLP) problem with single-valued trapezoidal neutrosophic numbers is formulated and solved. A new method based on the so-called score function to find the neutrosophic optimal solution of fully neutrosophic linear programming (FNLP) problem is proposed. This method is more flexible than the linear programming (LP) problem, where it allows the

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Khalifa, Hamiden Abd El Wahed, Faisal Al Al-Sharqi, Ashraf Al Al-Quran, et al. "Neutrosophic parametric study of piecewise quadratic fuzzy multi-objective dynamic programming problems." International Journal of Neutrosophic Science 23, no. 1 (2024): 299–310. http://dx.doi.org/10.54216/ijns.230125.

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The goal of this research is to investigate fuzzy multiobjective dynamic programming issues with fuzzy parameters in the objective functions and single valued trapezoidal neutrosophic numbers in the left hand side of the constraints. Piecewise quadratic fuzzy numbers characterize these fuzzy parameters. In addition, applying the score function of the neutrosophic numbers to convert the constraints parameters into its crisp . Some basic notions in the problem under the pareto optimal solution concept is redefined and analyzed to study the stability of the problem. Furthermore, a technique is pr

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Subasri, S., and K. Selvakumari. "Neutrosophic Travelling Salesman Problem in Trapezoidal Fuzzy number using Branch and Bound Technique." Journal of Physics: Conference Series 1362 (November 2019): 012098. http://dx.doi.org/10.1088/1742-6596/1362/1/012098.

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Prasad, Rajan, and Praveen Kumar Shukla. "Indeterminacy Handling of Adaptive Neuro-fuzzy Inference System Using Neutrosophic Set Theory: A Case Study for the Classification of Diabetes Mellitus." International Journal of Intelligent Systems and Applications 15, no. 3 (2023): 1–15. http://dx.doi.org/10.5815/ijisa.2023.03.01.

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Early diabetes diagnosis allows patients to begin treatment on time, reducing or eliminating the risk of serious consequences. In this paper, we propose the Neutrosophic-Adaptive Neuro-Fuzzy Inference System (N-ANFIS) for the classification of diabetes. It is an extension of the generic ANFIS model. Neutrosophic logic is capable of handling the uncertain and imprecise information of the traditional fuzzy set. The suggested method begins with the conversion of crisp values to neutrosophic sets using a trapezoidal and triangular neutrosophic membership function. These values are fed into an infe

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R., R., and W. Ritha. "A Legitimate Productive Repertoire Replica Betwixt Envirotech Outlay Towards Fragile Commodities Using Trapezoidal Neutrosophic Fuzzy Number." International Journal of Neutrosophic Science 24, no. 1 (2024): 104–18. http://dx.doi.org/10.54216/ijns.240110.

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This present contemplate confers a productive repertoire replica in which ultimatum is appraised as a basis of medical utilization of fragile commodities by the juvenile diabetes. Abundant embalming mechanisms are drawn on to preserve the Confectionary from putrefaction over time. It is consequential to ascertain that greenhouse gas emissions by virtue of transportation, production and storage of Confectionary is susceptible to putrefaction that has to be steered up. This contemplate recommends an optimal productive repertoire replica considering the production and inventory components for com

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C.Jayabharathi, C. Jayabharathi, and R. Sophia Porchelvi. "An Analysis of Trapezoidal Neutrosphic Fuzzy Traveling Salesman Problem for Medical Equipment Distribution to Hospitals." International Journal of Advances in Engineering and Management 6, no. 11 (2024): 599–604. https://doi.org/10.35629/5252-0611599604.

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The Traveling Salesman problem (TSP) is one optimization problem that has received a lot of interest in research. Trapezoidal Neutrosophic numbers (NNs) are used in the present work to examine the Neutrosophic Fuzzy Travelling Salesman Problem (NFTSP). The main objective of this TSP is to optimize the routes for medical items, like equipment or vaccines, to be transported to hospitals and clinics in order to guarantee quick and effective distribution. Here , we use the diagonal completion approach to solve the given TSP.

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Yasodai, P., and W. Ritha. "Analytical Study of Neutrosophic Fuzzy Unobservable On-Off Fluid Queues in Equipoise Strategies." International Journal of Neutrosophic Science 21, no. 2 (2023): 196–203. http://dx.doi.org/10.54216/ijns.210216.

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An unobservable fluid queuing model with alternately occurring on and off states is being examined in this study. The sojourn times differ from one another and are dispersed in a distribution that is exponential. Flow of fluid into the buffer's system accompanied by a few waiting procedures according to the first service is given to those who come first. In a neutrosophic fuzzy environment, the information acquired when the fluid enters the system can be split into fully and partially observable cases. The arrival and outflow rates are both neutrosophic trapezoidal fuzzy numbers. We calculate

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Gaber, Mohamed, Majed G. Alharbi, Abd Alwahed Dagestani, and El-Saeed Ammar. "Optimal Solutions for Constrained Bimatrix Games with Payoffs Represented by Single-Valued Trapezoidal Neutrosophic Numbers." Journal of Mathematics 2021 (June 18, 2021): 1–13. http://dx.doi.org/10.1155/2021/5594623.

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Single-valued neutrosophic set (SVNS) is considered as generalization and extension of fuzzy set, intuitionistic fuzzy set (IFS), and crisp set for expressing the imprecise, incomplete, and indeterminate information about real-life decision-oriented models. The theme of this research is to develop a solution approach to solve constrained bimatrix games with payoffs of single-valued trapezoidal neutrosophic numbers (SVTNNs). In this approach, the concepts and suitable ranking function of SVTNNs are defined. Hereby, the equilibrium optimal strategies and equilibrium values for both players can b

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Touqeer, Muhammad, and Ehtisham Rasool. "Multiple Attribute Decision Making Based on Interval-Valued Neutrosophic Trapezoidal Fuzzy Numbers and its Application in the Diagnosis of Viral Flu." International Journal of Emerging Multidisciplinaries: Mathematics 1, no. 2 (2022): 124–44. http://dx.doi.org/10.54938/ijemdm.2022.01.2.74.

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Decision-making technique (DMT) is mostly used in artificial intelligence and cognitive sciences to elaborate individual and social perception. So, one of the most important strategies in DMT evolved in medical diagnosis scrutiny regarding the connection of symptoms and diagnosis of diseases due to uncertainty and fuzziness in the relevant information. The focus of this article is to develop a diagnostic decision making strategy for the diagnosis of Viral diseases with close related symptoms using the Interval-valued trapezoidal neutrosophic fuzzy Numbers (IVTrNFN) w.r.t multiple attribute dec

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Tan, Ruipu, and Wende Zhang. "Multiple attribute group decision making methods based on trapezoidal fuzzy neutrosophic numbers." Journal of Intelligent & Fuzzy Systems 33, no. 4 (2017): 2547–64. http://dx.doi.org/10.3233/jifs-161984.

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.., S. A., Hamiden Abd El Wahed Khalifa, Ashraf Al Al-Quran, Faisal Al Al-Sharqi, Zahari Rodzi, and Abdalwali Lutfi. "Enhancing neutrosophic fuzzy goal programming approach for solving multi-objective probabilistic linear programming problems." International Journal of Neutrosophic Science 23, no. 1 (2024): 312–22. http://dx.doi.org/10.54216/ijns.230126.

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This article considers a stochastic multi-objective linear programming problem in a neutrosophic framework. The right-hand sides of the constraints are random variables associated with their means and variances, and the single-valued trapezoidal neutrosophic numbers are included in the coefficients of the objective functions to investigate the problem. The problem is successfully converted into the related deterministic programming model based on the formulation of the scoring function and several distributions, such as the Uniform, Exponential, and Gama distributions. Applying fuzzy goal prog

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Yong, Rui, Jun Ye, and Shigui Du. "Multicriteria Decision-Making Method and Application in the Setting of Trapezoidal Neutrosophic Z-Numbers." Journal of Mathematics 2021 (March 5, 2021): 1–13. http://dx.doi.org/10.1155/2021/6664330.

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The information expression and modeling of decision-making are critical problems in the fuzzy decision theory and method. However, existing trapezoidal neutrosophic numbers (TrNNs) and neutrosophic Z-numbers (NZNs) and their multicriteria decision-making (MDM) methods reveal their insufficiencies, such as without considering the reliability measures in TrNN and continuous Z-numbers in NZN. To overcome the insufficiencies, it is necessary that one needs to propose trapezoidal neutrosophic Z-numbers (TrNZNs), their aggregation operations, and an MDM method for solving MDM problems with TrNZN inf

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E. Chandrasekaran. "Revealing Advanced Inventory Management Approaches through Python-Based Visualization and Modelling of Neutrosophic and Fuzzy Mathematical Models for Enhanced Decision-Making and Optimization." Advances in Nonlinear Variational Inequalities 28, no. 5s (2025): 649–64. https://doi.org/10.52783/anvi.v28.4026.

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This paper explores the application of the Neutrosophic Fuzzy Set hypothesis to optimize inventory management in the vicinity of instability, indeterminacy, and conflicting information. We present a few hypotheses and scientific models to illustrate how neutrosophic fluffy sets can handle the complexity of inventory control by consolidating participation, non-membership, and indeterminacy. Through the definition of key inventory management equations, we point to downplay the addition of costs by considering the costs of inventory, requests, and shortages, while welcoming instabilities, such as

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Nivetha, Martin, Lilly Merline W., and Pandiammal P. "AN ANALYSIS OF THE SHORTCOMINGS OF WEATHER FORECAST BY IMD OVER DEVELOPED COUNTRIES USING NEUTROSOPHIC FUZZY WEIGHTED MULTI EXPERT ARTIFICIAL NEURAL NETWORK SYSTEM." International Journal of Current Research and Modern Education, Special Issue (August 13, 2017): 43–46. https://doi.org/10.5281/zenodo.842204.

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The Indian Meteorological Department (IMD) plays a vital role in forecasting weather. Since India, basically an agricultural nation which purely depends on monsoons, the prediction of future happenings such as rainfall, extreme coolness, hotness, disasters such as flood, storm, strong wind blow and so on are very much important in long term planning. But the prediction of weather fails many a times in India which makes us to compare with the developed countries such as USA, Japan and other western nations where the accuracy of weather prediction is very high. The factors contributing to the sh

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Tan, Ruipu, Wende Zhang, and Shengqun Chen. "Decision-Making Method Based on Grey Relation Analysis and Trapezoidal Fuzzy Neutrosophic Numbers Under Double Incomplete Information and its Application in Typhoon Disaster Assessment." IEEE Access 8 (2020): 3606–28. http://dx.doi.org/10.1109/access.2019.2962330.

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Begum, S. Ghousia, N. Jose Parvin .., A. .., D. Nagarajan, and Broumi Said. "Analyses the least cost using Travelling Salesman problem through Neutrosophic Fuzzy system." International Journal of Neutrosophic Science 20, no. 1 (2023): 68–76. http://dx.doi.org/10.54216/ijns.200106.

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The following paper introduces a methodology to calculate the least cost for a directed network through Travelling salesman problem. Dynamic programming method is used to find the minimum Cost. The recursion formula is used. The edge weights of the networks are being taken in terms of Triangular, Trapezoidal and Pentagonal Neutrosophic set. Score function for the Triangular, Trapezoidal and Pentagonal Neutrosophic sets are being defined for deneutrosophication. The least cost is estimated using all the above said Neutrosophic sets and the result is compared

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Dayana, Kesavankutty, Boopathi Vennila, and Thirumalaiswami Poongodi. "PERCEPTIONIZATION OF M/D/1 QUEUING MODEL UNDER TRAPEZOIDAL NEUTROSOPHIC NUMBERS." Suranaree Journal of Science and Technology 31, no. 3 (2024): 030190(1–10). http://dx.doi.org/10.55766/sujst-2024-03-e05910.

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In this paper, we provide an NM/ND/1 queuing model with an infinite limit based on the neutrosophic environment. Both the entry and utility rates are represented in terms of single valued neutrosophic trapezoidal numbers (SVTNN). The performance measures of the proposed model are evaluated using the DSW approach and (α, β, γ)-cut approach. A numerical example pertaining to a single valued trapezoidal neutrosophic number is obtained for different values of α, β, γ.

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Pathinathan, T., and E. Anita Dolorosa. "Fuzzy Fourier Series Using Trapezoidal, Reverse Order Trapezoidal and Intuitionistic Trapezoidal Fuzzy Number." Journal of Computer and Mathematical Sciences 9, no. 12 (2018): 2004–13. http://dx.doi.org/10.29055/jcms/948.

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Jun, Ye. "Some weighted aggregation operators of trapezoidal neutrosophic numbers and their multiple attribute decision making method." January 17, 2015. https://doi.org/10.5281/zenodo.32278.

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Based on the combination of single valued neutrosophic sets (SVNSs) and fuzzy numbers, this paper proposes the concepts of a neutrosophic number and a trapezoidal neutrosophic number (TNN) as the extension of an intuitionistic fuzzy number and an intuitionistic trapezoidal fuzzy number (ITFN), the basic operational relations of TNNs and the score function of TNN.

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Jun, Ye. "Some weighted aggregation operators of trapezoidal neutrosophic numbers and their multiple attribute decision making method." February 6, 2015. https://doi.org/10.5281/zenodo.23073.

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Based on the combination of single valued neutrosophic sets (SVNSs) and fuzzy numbers, this paper proposes the concepts of a neutrosophic number and a trapezoidal neutrosophic number (TNN) as the extension of an intuitionistic fuzzy number and an intuitionistic trapezoidal fuzzy number (ITFN), the basic operational relations of TNNs and the score function of TNN. Then, we develop a trapezoidal neutrosophic weighted arithmetic averaging (TNWAA) operator and a trapezoidal neutrosophic weighted geometric averaging (TNWGA) operator to aggregate TNN information and investigate their properties

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Pranab, Biswas, Pramanik Surapati, and C. Giri Bibhas. "Cosine Similarity Measure Based Multi-attribute Decision-making with Trapezoidal Fuzzy Neutrosophic Numbers." July 1, 2015. https://doi.org/10.5281/zenodo.22446.

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The objective of the study is to present cosine similarity measure based multi-attribute decision making under neutrosophic environment. The assesments of alternatives over the attributes are expressed with trapezoidal fuzzy neutrosophic numbers in which the three independent components namely, truth-membership degree (T), indeterminacy-membership degree (I) and falsity-membership degree (F) are expressed by trapezoidal fuzzy numbers. Cosine similarity measure between two trapezoidal fuzzy neutrosophic numbers and its properties are introduced. Expe

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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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Biswas, Pranab, Surapati Pramanik, and Bibhas Giri. "Cosine Similarity Measure Based Multi-attribute Decision-making with Trapezoidal Fuzzy Neutrosophic Numbers." Neutrosophic Sets and Systems 8, 2014 (May 4, 2014). https://doi.org/10.5281/zenodo.571274.

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The objective of the study is to present cosine similarity measure based multi-attribute decision making under neutrosophic environment. The assesments of alternatives over the attributes are expressed with trapezoidal fuzzy neutrosophic numbers in which the three independent components namely, truth-membership degree (T), indeterminacy-membership degree (I) and falsity-membership degree (F) are expressed by trapezoidal fuzzy numbers. Cosine similarity measure between two trapezoidal fuzzy neutrosophic numbers and its properties are introduced.

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Ye, Jun. "Trapezoidal neutrosophic set and its application to multiple attribute decision-making." May 8, 2015. https://doi.org/10.5281/zenodo.233984.

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Based on the combination of trapezoidal fuzzy numbers and a single-valued neutrosophic set, this paper proposes a trapezoidal neutrosophic set, some operational rules, score and accuracy functions for trapezoidal neutrosophic numbers.

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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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Jun, Ye. "Trapezoidal neutrosophic set and its application to multiple attribute decision making." October 8, 2015. https://doi.org/10.5281/zenodo.34916.

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Based on the combination of trapezoidal fuzzy numbers and a single valued neutrosophic set, this paper proposes a trapezoidal neutrosophic set, some operational rules, score and accuracy functions for trapezoidal neutrosophic numbers

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Jun, Ye. "Trapezoidal neutrosophic set and its application to multiple attribute decision-making." September 28, 2015. https://doi.org/10.5281/zenodo.1041717.

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Based on the combination of trapezoidal fuzzy numbers and a single-valued neutrosophic set, this paper proposes a trapezoidal neutrosophic set, some operational rules, score and accuracy functions for trapezoidal neutrosophic numbers.

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S., Santhi, and Selvakumari K. "Flow Shop Scheduling Problem in Neutrosophic Environment Using Trapezoidal Fuzzy Numbers." May 20, 2019. https://doi.org/10.5281/zenodo.3051447.

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In this paper, we propose to solve the flow shop scheduling problem using Branch and Bound method. This paper presents an algorithm with the help of branch and bound approach for a flow shop scheduling problems consisting of 4 jobs and 4 machines in which the processing time as Neutrosophic trapezoidal fuzzy numbers which are further converted in to crisp value using graded mean ranking method. Numerical example is given to illustrate the study of solving flow shop scheduling under Neutrosophic trapezoidal fuzzy number using branch and bound technique.

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Pranab, Biswas, Pramanik Surapati, and C. Giri Bibhas. "Multi-attribute Group decision Making Based on Expected Value of Neutrosophic Trapezoidal Numbers." April 30, 2018. https://doi.org/10.5281/zenodo.1237907.

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We present an expected value based method for multiple attribute group decision making (MAGDM), where the preference values of alternatives and the importance of attributes are expressed in terms of neutrosophic trapezoidal numbers (NTrNs).

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Rajesh, Kumar Saini, Sangal Atul, and Ahirwar Ashik. "A Novel Approach by using Interval-Valued Trapezoidal Neutrosophic Numbers in Transportation Problem." October 2, 2022. https://doi.org/10.5281/zenodo.7135283.

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In today's scenario transportation problem [TP] is the prominent area of optimization. In the present paper, a TP in a neutrosophic environment, known as a neutrosophic transportation problem [NTP] is introduced with interval-valued trapezoidal neutrosophic numbers [IVTrNeNs]. To maintain physical distance among the industrialists and researchers during the covid-19 pandemic, the intervalvalued fuzzy numbers [IVFNs] in place of crisp numbers are very much essential to address the hesitation and uncertainty in real-life situations. IVTrNeN is the generalization of single-valued neutrosophic

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Broumi, said, Lathamaheswari Malayalan, Tan Ruipu, et al. "A new distance measure for trapezoidal fuzzy neutrosophic numbers based on the centroids." July 19, 2020. https://doi.org/10.5281/zenodo.3951706.

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Distance measure is a numerical measurement of the distance between any two objects. The aim of this paper is to propose a new distance measure for trapezoidal fuzzy neutrosophic numbers based on the centroids with graphical representation. In addition, the metric properties of the proposed measure are examined in detail. A decision making problem also has been solved using the proposed distance measure for a software selection process. comparative analysis has been done with the existing methods to show the potential of the proposed distance measure and various forms of trapezoidal fuzzy neut

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Sinika, S., and G. Ramesh. "Trapezoidal neutrosophic assignment problem with new interval arithmetic costs." Journal of Intelligent & Fuzzy Systems, June 1, 2023, 1–13. http://dx.doi.org/10.3233/jifs-222796.

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Due to present condition, the expenses of allocating a job to a specific person or scheduling transport with a precise value may result in ambiguity. To deal with this, neutrosophic sets which is an extended form of fuzzy sets, appear alongside membership, non-membership and indeterminacy. The assignment problem in a trapezoidal neutrosophic environment with cost as the trapezoidal neutrosophic numbers is discussed in this work. The paper’s motive is to convert the trapezoidal neutrosophic numbers into new interval arithmetic form and the efficiency of the same is shown by comparing the existi

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Fatina, Masri, Bisher Zeina Mohamed, and Zeitouny Omar. "Some Single Valued Neutrosophic Queueing Systems with Maple Code." January 14, 2023. https://doi.org/10.5281/zenodo.7536023.

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In this paper we introduce for the first time the concept of single valued neutrosophic queueing systems (SVNQSs) as an extension of crisp and fuzzy queueing systems which are very applicable and important in controlling systems. SVNQSs have been defined assuming that arrival rates and departure rates are single valued neutrosophic trapezoidal numbers, and depending on this assumption probabilities and performance measures were also single valued neutrosophic trapezoidal numbers. Numerical examples were presented and solved successfully, and because of hard computations, a maple code is presen

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Karaaslan, Faruk. "Gaussian single-valued neutrosophic numbers and its application in multi-attribute decision making." Neutrosophic Sets and Systems 22 (December 10, 2018). https://doi.org/10.5281/zenodo.2159763.

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The fuzzy set and intuitionistic fuzzy set are two useful mathematical tool for dealing with impression and uncertainty. However sometimes these theories may not suffice to model indeterminate and inconsistent information encountered in real world. To overcome this insufficiency, neutrosophic set theory and single-valued neutrosophic set (SVNS) theory which is useful in practical applications, were proposed. Many researchers have studied on single-valued triangular neutrosophic numbers and single-valued trapezoidal neutrosophic numbers. In this paper, concepts of Gaussian single-valued neutros

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Elsayed, Badr, Nada Shokry, Ali Saeed, and Elrokh Ashraf. "Solving Neutrosophic Linear Programming Problems Using Exterior Point Simplex Algorithm." September 7, 2021. https://doi.org/10.5281/zenodo.5486426.

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In this manuscript, three contributions are proposed. First contribution is proposing a good evaluation between the fuzzy and neutrosophic approaches using a novel fuzzy-neutrosophic transfer. Second contribution is introducing a general framework for solving the neutrosphic linear programming problems using the advantages of the method of Abdel-Basset et al. and the advantages of Singh et al.'s method. Third contribution is proposing a new neutrosophic exterior point simplex algorithm NEPSA and its fuzzy version FEPSA. NEPSA has two paths to get optimal solutions. One path consists of bas

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Said, Broumi, Bakali Assia, Talea Mohamed, and Smarandache Florentin. "Shortest Path Problem under Trapezoidal Neutrosophic Information." July 20, 2017. https://doi.org/10.5281/zenodo.888901.

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In this research paper, a new approach is proposed for computing the shortest path length from source node to destination node in a neutrosophic environment. The edges of the network are assigned by trapezoidal fuzzy neutrosophic numbers. A numerical example is provided to show the performance of the proposed approach.

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Bera, Tuhin, and Nirmal Kumar Mahapatra. "An Approach to Solve the Linear Programming Problem Using Single Valued Trapezoidal Neutrosophic Number." International Journal of Neutrosophic Science, 2020, 54–66. http://dx.doi.org/10.54216/ijns.030202.

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While making a decision, the neutrosophic set theory includes the uncertainty part beside certainty part (i.e., Yes or No). In the present uncertain socio-economic fashion, this pattern is highly acceptable and hence, the limitations of fuzzy set and intuitionistic fuzzy set are overcome with neutrosophic set theory. The present study provides a modified structure of linear programming problem (LP-problem) and its solution approach in neutrosophic sense. A special type of neutrosophic set defined over the set of real number, viz., single valued trapezoidal neutrosophic number (SVTN-number) is

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Pai, Sunay P., and Rajesh S. Prabhu Gaonkar. "Safety modelling of marine systems using neutrosophic logic." Proceedings of the Institution of Mechanical Engineers, Part M: Journal of Engineering for the Maritime Environment, June 16, 2020, 147509022092573. http://dx.doi.org/10.1177/1475090220925733.

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Precisely assessing risk associated with critical and complex engineering systems operating in an environment with high amount of uncertainty is extremely difficult. Taking proper decisions to reduce risk level depends on how accurately the risks associated with the system are assessed. Risk assessment and safety modelling of complex systems were studied using various tools such as crisp sets, Bayesian belief network, fuzzy sets, classical logic and fuzzy logic. Neutrosophic set which is an extension of fuzzy set represents the real world better than fuzzy set due to the inclusion of the hesit

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