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Journal articles on the topic 'Trapezoidal function'

Author: Grafiati

Published: 3 June 2025

Last updated: 20 July 2025

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1

Han, Zhenwei, Kefei Song, and Yang Liu. "Research on Pulse Shaper Based on Trapezoidal Function." Frontiers in Computing and Intelligent Systems 3, no. 1 (2023): 182–84. http://dx.doi.org/10.54097/fcis.v3i1.6366.

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In order to improve the time resolution and spatial resolution of photon-counting imaging system, the pulse shaper based on trapezoidal function is studied. The signal with an exponential decay shape from charge sensitive amplifier is converted to digital discrete signal by ADC and then the discrete number sequence is filtered and shaped by digital signal processing technology. The amplitude linearity and time width of the trapezoidal shaper are simulated and verified using software-generated single exponential signals and double exponential signals. While the continuous pulses are applied to

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Ye, Jufeng. "Aggregation Operators of Trapezoidal Intuitionistic Fuzzy Sets to Multicriteria Decision Making." International Journal of Intelligent Information Technologies 13, no. 4 (2017): 1–22. http://dx.doi.org/10.4018/ijiit.2017100101.

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This paper presents the trapezoidal intuitionistic fuzzy weighted averaging (TIFWA) operator, trapezoidal intuitionistic fuzzy ordered weighted averaging (TIFOWA) operator, trapezoidal intuitionistic fuzzy weighted geometric (TIFWG) operator, and trapezoidal intuitionistic fuzzy ordered weighted geometric (TIFOWG) operator to aggregate the trapezoidal intuitionistic fuzzy information and investigates their properties. Furthermore, a multicriteria decision making method based on the TIFOWA and TIFOWG operators and the score function and accuracy function of a trapezoidal intuitionistic fuzzy nu

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Khairuddin, Siti Hajar, Mohd Hilmi Hasan, Manzoor Ahmed Hashmani, and Muhammad Hamza Azam. "Generating Clustering-Based Interval Fuzzy Type-2 Triangular and Trapezoidal Membership Functions: A Structured Literature Review." Symmetry 13, no. 2 (2021): 239. http://dx.doi.org/10.3390/sym13020239.

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Clustering is more popular than the expert knowledge approach in Interval Fuzzy Type-2 membership function construction because it can construct membership function automatically with less time consumption. Most research proposed a two-fuzzifier fuzzy C-Means clustering method to construct Interval Fuzzy Type-2 membership function which mainly focused on producing Gaussian membership function. The other two important membership functions, triangular and trapezoidal, are constructed using the grid partitioning method. However, the method suffers a drawback of not being able to represent actual

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Bes Hendi Rio Pardede, Bunga Diviya Kusfa, and Lauren Teresia Tamba. "Penerapan Metode Trapesium , Metode Simpson 1/3, dan Metode Simpson 3/8 Dalam Integrasi Numerik Menggunakan Software Matlab." Pentagon : Jurnal Matematika dan Ilmu Pengetahuan Alam 2, no. 4 (2024): 24–31. http://dx.doi.org/10.62383/pentagon.v2i4.268.

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Numerical integration is a method used to calculate the integral of functions that cannot be integrated analytically. Several methods that are often used in numerical integration include that Simpson 1/3 method, Simpson 3/8 method, and the Trapezoidal method. This research aims to apply and compare the accuracy and efficiency of the third method in solving various types of integral functions using computing software. With the help of software such as MATLAB and Python, the precision of the results obtained from each method is analyzed and compared with analytical solutions (if available) or ap

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Natalia, Hrudkina, Aliieva Leila, Abhari Payman, Kuznetsov Mykola, and Shevtsov Serhii. "DERIVATION OF ENGINEERING FORMULAS IN ORDER TO CALCULATE ENERGY-POWER PARAMETERS AND A SHAPE CHANGE IN A SEMI-FINISHED PRODUCT IN THE PROCESS OF COMBINED EXTRUSION." Eastern-European Journal of Enterprise Technologies 2, no. 7 (98) (2019): 49–57. https://doi.org/10.15587/1729-4061.2019.160585.

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The possibilities of using and embedding kinematic trapezoid modules with curvilinear boundaries of different shapes were explored. Based on the energy method, the generalized formulas for calculating the power of deformation forces inside the axial trapezoidal kinematic module were derived. Different types of selecting the functions that describe a curvilinear boundary of the axial trapezoidal module were identified. We have analyzed the possibilities of using known techniques for the linearization of integrand dependences in order to calculate the power of deformation forces when it is impos

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Stanojevic, Bogdana, and Milan Stanojevic. "Penalty method for fuzzy linear programming with trapezoidal numbers." Yugoslav Journal of Operations Research 19, no. 1 (2009): 149–56. http://dx.doi.org/10.2298/yjor0901149s.

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In this paper we shall propose an algorithm for solving fuzzy linear programming problems with trapezoidal numbers using a penalty method. We will transform the problem of maximizing a function having trapezoidal fuzzy number values under some constraints into a deterministic multi-objective programming problem by penalizing the objective function for possible constraint violation. Furthermore, the obtained deterministic problem will have only unavoidable inequalities between trapezoidal fuzzy numbers parameters as constraints.

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Syafiqoh, Ummi, Anton Yudhana, and Sunardi Sunardi. "Comparative analysis of Fuzzy Tsukamoto's membership functions for determining irrigated rice field feasibility status." ILKOM Jurnal Ilmiah 14, no. 3 (2022): 255–63. http://dx.doi.org/10.33096/ilkom.v14i3.1156.255-263.

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The representation of the fuzzy set membership curve consisting of trapezoidal, triangular, and linear shapes, has an important role in the fuzzy logic system. The selection of the curve's shapes determines the useable membership function and affects the fuzzy output value. Previous studies generally used curves that had been employed in predecessors or other studies that did not explain the reason for choosing a fuzzy member curve. This condition became problem because there was not a guide in selecting the appropriate membership function model for the parameters used in the fuzzy process so

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Mitsuishi, Takashi. "Some Properties of Membership Functions Composed of Triangle Functions and Piecewise Linear Functions." Formalized Mathematics 29, no. 2 (2021): 103–15. http://dx.doi.org/10.2478/forma-2021-0011.

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Summary. IF-THEN rules in fuzzy inference is composed of multiple fuzzy sets (membership functions). IF-THEN rules can therefore be considered as a pair of membership functions [7]. The evaluation function of fuzzy control is composite function with fuzzy approximate reasoning and is functional on the set of membership functions. We obtained continuity of the evaluation function and compactness of the set of membership functions [12]. Therefore, we proved the existence of pair of membership functions, which maximizes (minimizes) evaluation function and is considered IF-THEN rules, in the set o

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9

Mitsuishi, Takashi. "Isosceles Triangular and Isosceles Trapezoidal Membership Functions Using Centroid Method." Formalized Mathematics 31, no. 1 (2023): 59–66. http://dx.doi.org/10.2478/forma-2023-0006.

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Summary Since isosceles triangular and trapezoidal membership functions [4] are easy to manage, they were applied to various fuzzy approximate reasoning [10], [13], [14]. The centroids of isosceles triangular and trapezoidal membership functions are mentioned in this article [16], [9] and formalized in [11] and [12]. Some propositions of the composition mapping (f + · g, or f +* g using Mizar formalism, where f, g are a ne mappings), are proved following [3], [15]. Then different notations for the same isosceles triangular and trapezoidal membership function are formalized. We proved the agree

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Bilgili, Erdem, İzzet Cem Göknar, and Osman Nuri Ucan. "Cellular neural network with trapezoidal activation function." International Journal of Circuit Theory and Applications 33, no. 5 (2005): 393–417. http://dx.doi.org/10.1002/cta.328.

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11

Fan, Gui Jie. "Optimization of Trapezoidal Runner in Plastic Molding Based on MATLAB." Applied Mechanics and Materials 552 (June 2014): 66–69. http://dx.doi.org/10.4028/www.scientific.net/amm.552.66.

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The runner design is an important parts in plastic molding design. Its shape and dimensions have special effects on the molten plastic’s pressure, hot loss, injection speed, etc. At present, trapezoidal runner is used widely for better fluidity and lower assembly precision relatively compared with the circular runner. This paper uses the Fminsearch function of MATLAB and constructs an objective function based on the minimum length of the perimeter of the trapezoidal runner to optimize the trapezoidal runner section. The conclusion of this paper is that the perimeter of the trapezoidal runner i

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12

Kadak, Uğur, and Hakan Efe. "On Uniform Convergence of Sequences and Series of Fuzzy-Valued Functions." Journal of Function Spaces 2015 (2015): 1–10. http://dx.doi.org/10.1155/2015/870179.

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The class of membership functions is restricted to trapezoidal one, as it is general enough and widely used. In the present paper since the utilization of Zadeh’s extension principle is quite difficult in practice, we prefer the idea of level sets in order to construct for a fuzzy-valued function via related trapezoidal membership function. We derive uniform convergence of fuzzy-valued function sequences and series with some illustrated examples. Also we study Hukuhara differentiation and Henstock integration of a fuzzy-valued function with some necessary inclusions. Furthermore, we introduce

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Journal, Baghdad Science. "Solving Fuzzy Games Problems by Using Ranking Functions." Baghdad Science Journal 15, no. 1 (2018): 98–101. http://dx.doi.org/10.21123/bsj.15.1.98-101.

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In this paper, we deal with games of fuzzy payoffs problem while there is uncertainty in data. We use the trapezoidal membership function to transform the data into fuzzy numbers and utilize the three different ranking function algorithms. Then we compare between these three ranking algorithms by using trapezoidal fuzzy numbers for the decision maker to get the best gains

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Afzal, Waqar, Najla Aloraini, Mujahid Abbas, Jong-Suk Ro, and Abdullah A. Zaagan. "Hermite-Hadamard, Fejér and trapezoid type inequalities using Godunova-Levin Preinvex functions via Bhunia's order and with applications to quadrature formula and random variable." Mathematical Biosciences and Engineering 21, no. 2 (2024): 3422–47. http://dx.doi.org/10.3934/mbe.2024151.

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<abstract><p>Convex and preinvex functions are two different concepts. Specifically, preinvex functions are generalizations of convex functions. We created some intriguing examples to demonstrate how these classes differ from one another. We showed that Godunova-Levin invex sets are always convex but the converse is not always true. In this note, we present a new class of preinvex functions called $ (\mathtt{h_1}, \mathtt{h_2}) $-Godunova-Levin preinvex functions, which is extensions of $ \mathtt{h} $-Godunova-Levin preinvex functions defined by Adem Kilicman. By using these notion

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15

Qin, Yusheng, Xiangxian Li, Xin Han, Jingjing Tong, and Minguang Gao. "Research on Spectral Restoration and Gas Concentration Inversion Accuracy Based on Quasi-Trapezoidal Window." Photonics 9, no. 11 (2022): 885. http://dx.doi.org/10.3390/photonics9110885.

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The Fourier transform is a popular method for analyzing and processing interference data in which spectrum leakage occurs. Generally, window function (also called apodization function) weighting is employed to limit spectrum leakage. A rectangular window with optimal main-lobe performance and the Rife-Vincent (R-V) window were introduced to improve the window function performance, resulting in the establishment of a quasi-trapezoidal window function. Based on the experimental interference data, the quasi-trapezoidal window function was used in the spectral restoration process. The experimental

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Et. al., Indira Singuluri. "An unknown Transit technique for Solving Generalized Trapezoidal Intuitionistic Fuzzy Transportation Problems using Centroid of Centroids." Turkish Journal of Computer and Mathematics Education (TURCOMAT) 12, no. 3 (2021): 5121–28. http://dx.doi.org/10.17762/turcomat.v12i3.2053.

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In the present day by day life circumstances TP we habitually face the circumstance of unreliability in addition to unwillingness due to various unmanageable segments. To deal with unreliability and unwillingness multiple researchers have recommended the intuitionistic fuzzy (IF) delineation for material. This paper proposes the approach used by generalized trapezoidal intuitionistic fuzzy number to solve these transport problem, i.e. capacity and demand are considered as real numbers and charge of transport from origin to destination is considered as generalized trapezoidal intuitionistic fuz

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Mamman, John Ojima. "Computational Algorithm for Approximating Fractional Derivatives of Functions." Journal of Modeling and Simulation of Materials 5, no. 1 (2022): 31–38. http://dx.doi.org/10.21467/jmsm.5.1.31-38.

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This paper presents an algorithmic approach for numerically solving Caputo fractional diﬀerentiation. The trapezoidal rule was modiﬁed, the new modiﬁcation was used to derive an algorithm to approximate fractional derivatives of order α > 0, the fractional derivative used was based on Caputo deﬁnition for a given function by a weighted sum of function and its ordinary derivatives values at speciﬁed points. The trapezoidal rule was used in conjunction with the finite difference scheme which is the forward, backward and central difference to derive the computational algorithm for the numerica

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18

Li, Xihua, Fuqiang Wang, and Xiaohong Chen. "Trapezoidal Intuitionistic Fuzzy Multiattribute Decision Making Method Based on Cumulative Prospect Theory and Dempster-Shafer Theory." Journal of Applied Mathematics 2014 (2014): 1–8. http://dx.doi.org/10.1155/2014/279138.

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With respect to decision making problems under uncertainty, a trapezoidal intuitionistic fuzzy multiattribute decision making method based on cumulative prospect theory and Dempster-Shafer theory is developed. The proposed method reflects behavioral characteristics of decision makers, information fuzziness under uncertainty, and uncertain attribute weight information. Firstly, distance measurement and comparison rule of trapezoidal intuitionistic fuzzy numbers are used to derive value function under trapezoidal intuitionistic fuzzy environment. Secondly, the value function and decision weight

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Kumar, Tarun, Reema Singh, Pradeep Chaudhary, and M. K. Sharma. "Cost Analysis of Fuzzy Transportation Models with Ranking Function in Two Stages." INTERNATIONAL JOURNAL OF AGRICULTURAL AND STATISTICAL SCIENCES 20, no. 01 (2024): 161. http://dx.doi.org/10.59467/ijass.2024.20.161.

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According to the research conducted so far, a crisp value is obtained by defuzzifying the fuzzy value using any defuzzification approach and this value is then used to analyze the entire problem. It is possible, however, that the crisp value generated using existing approaches may not exactly be matched with the fuzzy values. It is probable that any figure slightly early or slightly later than the obtained crisp value will produce the better outcome. So, the purpose of this research work is to provide a technique that can defuzzify fuzzy parameter values so that there are more than one possibl

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20

Kashuri, Artion, and Rozana Liko. "Fractional trapezium type inequalities for twice differentiable preinvex functions and their applications." An International Journal of Optimization and Control: Theories & Applications (IJOCTA) 10, no. 2 (2020): 226–36. http://dx.doi.org/10.11121/ijocta.01.2020.00795.

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Trapezoidal inequalities for functions of divers natures are useful in numerical computations. The authors have proved an identity for a generalized integral operator via twice differentiable preinvex function. By applying the established identity, the generalized trapezoidal type integral inequalities have been discovered. It is pointed out that the results of this research provide integral inequalities for almost all fractional integrals discovered in recent past decades. Various special cases have been identified. Some applications of presented results to special means have been analyzed. T

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SCHWARTZ, CHARLES. "MORE SPECIAL FUNCTIONS TRAPPED." International Journal of Modern Physics C 24, no. 02 (2013): 1350004. http://dx.doi.org/10.1142/s0129183113500046.

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We extend the technique of using the trapezoidal rule for efficient evaluation of the special functions of mathematical physics given by integral representations. This technique was recently used for Bessel functions, and here we treat incomplete gamma functions and the general confluent hypergeometric function.

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Lira, I. "The generalized maximum entropy trapezoidal probability density function." Metrologia 45, no. 4 (2008): L17—L20. http://dx.doi.org/10.1088/0026-1394/45/4/n01.

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Holze, Rudolf. "A trapezoidal function voltage generator for electrochemical applications." Review of Scientific Instruments 60, no. 10 (1989): 3348–50. http://dx.doi.org/10.1063/1.1140530.

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Archana, D. "Fuzzy Linear Fractional Programming Problem Using Trapezoidal Fuzzy Numbers." International Journal for Research in Applied Science and Engineering Technology 13, no. 3 (2025): 3483–88. https://doi.org/10.22214/ijraset.2025.67956.

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Abstract: In order to solve Fully Fuzzy Linear Fractional Programming Problems (FFLFPP) with trapezoidal fuzzy integers as the objective function and constraints, this study aims to develop a novel trapezoidal fuzzy number ranking function. The simplex method and crisp linear fractional programming serve as the foundation for the suggested approach. With the aid of a recently proposed ranking function, we first converted FFLFPP into a Crisp Linear Programming Problem. The resulting problem was then transformed into LPP. The suggested method is demonstrated using a numerical example.

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Al-Douri, Eman M. Farhan. "Optimum Design of Trapezoidal Combined Footings." Tikrit Journal of Engineering Sciences 14, no. 1 (2007): 85–115. http://dx.doi.org/10.25130/tjes.14.1.05.

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This study is an application of one of the non-linear programming methods ; Hooke & Jeeves method to the structural design of the trapezoidal combined footings , considering the total cost of the footing as an objective function . The cost function was formulated in terms of the following design variables : Smaller and larger footing width, footing width, thickness, depth of embedment and left and right projections A computer program was developed to solve this design problem using the conventional structural design approach in conjunction with Hooke & Jeeves method. A simple study was

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Prasetya, Fabrian Ivan, and Chairisni Lubis. "APLIKASI SISTEM INFERENSI FUZZY UNTUK MENDIAGNOSIS PENYAKIT MATA BERBASIS WEBSITE." Jurnal Ilmu Komputer dan Sistem Informasi 8, no. 1 (2020): 48. http://dx.doi.org/10.24912/jiksi.v8i1.11467.

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On this research a fuzzy inference system application program will be designed to diagnose web-based diseases. In addition to diagnosing the disease, this research was conducted to increase the severity of the disease. Data collection in this study uses the literature method, documentation method, and interview method. The inference engine used is the forward chaining method and the calculation of the severity using the Sugeno’s fuzzy method with triangular and trapezoidal membership functions. Fuzzy Inference System Application Program created can be used to diagnose diseases in general that

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Almutairi, Ohud Bulayhan, and Muhammad Amer Latif. "Two-variable Trapezoidal Types Inequalites in Banach Spaces." European Journal of Pure and Applied Mathematics 18, no. 1 (2025): 5613. https://doi.org/10.29020/nybg.ejpam.v18i1.5613.

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This study presents weighted trapezoidal-type inequalities for the product of two functions. While one function takes its values in the Banach spaces, the other takes values in the complex plane. We employed the technique of integration by parts for Bochner integrals for functions of two variables, along with principles of analysis for functions taking values in the productof Banach spaces, to report our findings. In addition to the extension of previous studies on functions of a single variable, our work generalizes results reported in Dragomir for two functions whose product of their variabl

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Awan, Muhammad, Muhammad Noor, Marcela Mihai, and Khalida Noor. "Two point trapezoidal like inequalities involving hypergeometric functions." Filomat 31, no. 8 (2017): 2281–92. http://dx.doi.org/10.2298/fil1708281a.

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In this paper, we derive a new integral identity for differentiable function. Using this new integral identity as an auxiliary result, we derive some new two point trapezoidal like inequalities for differentiable harmonic h-convex functions. These inequalities can also be viewed as Hermite-Hadamard type inequalities. We also discuss some new special cases which can be deduced from our main results.

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Parthiban, Selvam, and P. Gajivaradhan. "Statistical Hypothesis Test in Three Factor ANOVA Model under Fuzzy Environments Using Trapezoidal Fuzzy Numbers." Bulletin of Mathematical Sciences and Applications 14 (February 2016): 23–42. http://dx.doi.org/10.18052/www.scipress.com/bmsa.14.23.

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This paper deals with the problem of three factor ANOVA model (Latin Square Design-LSD) test using Trapezoidal Fuzzy Numbers (tfns.). The proposed test is analysed under various types of trapezoidal fuzzy models such as Alpha Cut Interval, Membership Function, Ranking Function, Total Integral Value and Graded Mean Integration Representation. Finally a comparative view of the conclusions obtained from various test is given. Moreover, two numerical examples having different conclusions have been given for a concrete comparative study.

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Robinson, John P. "Contrasting Correlation Coefficient with Distance Measure in Interval Valued Intuitionistic Trapezoidal Fuzzy MAGDM Problems." International Journal of Fuzzy System Applications 5, no. 4 (2016): 16–51. http://dx.doi.org/10.4018/ijfsa.2016100102.

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In this paper, Multiple Attribute Group Decision Making (MAGDM) problems in which the data is of the form of Interval Valued Intuitionistic Trapezoidal Fuzzy Numbers (IVITzFNs) is presented. Some operational laws of IVITzFNs are introduced. Then some new aggregation operators including interval valued Intuitionistic Trapezoidal Fuzzy Weighted Averaging (IVITzFWA) operator, interval valued Intuitionistic Trapezoidal Fuzzy Ordered Weighted Averaging (IVITzFOWA) operator and Interval Intuitionistic Trapezoidal Fuzzy Hybrid Averaging (IVITzFHA) operator, are proposed and some desirable properties

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P.Thangamani. "A Novel Ranking Technique to Resolve Unbalanced Fuzzy Transportation Problems Using Trapezoidal Fuzzy Numbers." Panamerican Mathematical Journal 35, no. 4s (2025): 247–57. https://doi.org/10.52783/pmj.v35.i4s.4674.

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This research uses trapezoidal fuzzy numbers to solve a fuzzy transportation problem in a fuzzy environment. Applied mathematics has extensively researched the transportation problem, which involves solving a set of linear equations with various scientific applications. Simultaneous mathematical models play a crucial role in operational research. This research paper's primary goal is to determine the lowest possible transportation cost for certain supplies via a capacitated network, where the demand and availability notes are previously represented by fuzzy trapezoidal values. The membership f

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R., Sophia Porchelvi, Uma S., and Irene Hepzibah R. "ON SOLVING FULLY FUZZY MULTI-OBJECTIVE LINEAR PROGRAMMING PROBLEM BY USING SYMMETRIC TRAPEZOIDAL FUZZY NUMBERS." International Journal of Current Research and Modern Education, Special Issue (August 14, 2017): 65–69. https://doi.org/10.5281/zenodo.842838.

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In this paper, a new approach for solving fully fuzzy multi-objective linear programming problem (FFMLPP) by using symmetric trapezoidal fuzzy numbers. Fuzzy arithmetic operations and simplex algorithm is proposed for solving fully fuzzy multi-objective linear programming problem with parameters represented by symmetric trapezoidal fuzzy numbers without converting it to crisp numbers. Using the proposed method the fuzzy optimal solution of fully fuzzy multi-objective linear programming problem can be easily obtained. Finally a numerical example is provided to check the efficiency of the propos

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Xu, Yonggui, Yuxin Hao, Wei Zhang, and Yuhan Zhang. "Free Vibration Analysis of Trapezoidal Bi-Stable Laminates Supported at the Elastic Midpoint of the Median Line." Mathematics 11, no. 15 (2023): 3326. http://dx.doi.org/10.3390/math11153326.

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This study investigates the natural vibration of trapezoidal bi-stable laminates (TBL) with elastic supports at the midpoints of the median lines. Configuration of the midplane of the TBL is expressed by a polynomial with 17 parameters. Then, the first order shear deformation theory, curing temperature, and nonlinear strain displacement relations combining energy principles are applied to obtain the bi-stable shapes numerically. Three translational springs and two rotational springs are added at the midpoint of the median line in the trapezoidal bi-stable laminate to acquire elastic point supp

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Wang, Fan, Rongli Guo, Jinping Ni, and Tao Dong. "Modulation transfer function of a trapezoidal pixel array detector." Optical Engineering 55, no. 1 (2016): 013106. http://dx.doi.org/10.1117/1.oe.55.1.013106.

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Fan, Quanping, Yuwei Liu, Chuanke Wang, et al. "Single-order diffraction grating designed by trapezoidal transmission function." Optics Letters 40, no. 11 (2015): 2657. http://dx.doi.org/10.1364/ol.40.002657.

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Wang, Zhiqiang, Chao Wu, Jianqiao Luo, Wenyu Lv, Lei Shi, and Peng Wang. "Research on Stress Analysis and Control of Surrounding Rock of Trapezoidal Roadways Based on Complex Variable Theory." Shock and Vibration 2021 (August 3, 2021): 1–14. http://dx.doi.org/10.1155/2021/6381785.

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Aiming at the problem of the serious deformation of the mining roadways in the trapezoidal section of the coal mine, the method of combining theoretical analysis and field application is used to study the surrounding rock control method of the trapezoidal roadways. The conformal mapping function of the trapezoidal roadways is calculated by the theory of complex change, and then from the analytical solution of the tangential stress distributed in the surrounding rock of trapezoidal roadways which is under the influence of the bidirectional unequal pressure, homogeneous, isotropic, and elastic r

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Noor, Muhammad, Khalida Noor, and Sabah Iftikhar. "Integral inequalities for differentiable p-harmonic convex functions." Filomat 31, no. 20 (2017): 6575–84. http://dx.doi.org/10.2298/fil1720575n.

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In this paper, we consider a new class of harmonic convex functions, which is called p-harmonic convex function. Several new Hermite-Hadamard, midpoint, Trapezoidal and Simpson type inequalities for functions whose derivatives in absolute value are p-harmonic convex are obtained. Some special cases are discussed. The ideas and techniques of this paper may stimulate further research.

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Topal, Umut. "Thermal buckling load optimization of laminated general quadrilateral and trapezoidal thin plates." Science and Engineering of Composite Materials 20, no. 1 (2013): 87–94. http://dx.doi.org/10.1515/secm-2012-0103.

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AbstractThis paper deals with thermal buckling load optimization of symmetrically laminated angle-ply general quadrilateral and trapezoidal thin plates. The objective function is to maximize the critical temperature capacity of the quadrilateral and trapezoidal laminated plates and the fiber orientation is considered as a design variable. The mathematical formulation is based on the classical laminated plate theory for the frequency analysis. The modified feasible direction method is used as the optimization routine. Therefore, a program based on FORTRAN is used. Finally, the significant effec

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Niazkar, Majid. "Assessment of artificial intelligence models for calculating optimum properties of lined channels." Journal of Hydroinformatics 22, no. 5 (2020): 1410–23. http://dx.doi.org/10.2166/hydro.2020.050.

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Abstract Lined channels with trapezoidal, rectangular and triangular sections are the most common manmade canals in practice. Since the construction cost plays a key role in water conveyance projects, it has been considered as the prominent factor in optimum channel designs. In this study, artificial neural networks (ANN) and genetic programming (GP) are used to determine optimum channel geometries for trapezoidal-family cross sections. For this purpose, the problem statement is treated as an optimization problem whose objective function and constraint are earthwork and lining costs and Mannin

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Dhouib, Souhail. "Solving the Single-Valued Trapezoidal Neutrosophic Transportation Problems through the Novel Dhouib-Matrix-TP1 Heuristic." Mathematical Problems in Engineering 2021 (November 2, 2021): 1–11. http://dx.doi.org/10.1155/2021/3945808.

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The transportation problem has been widely studied in the field of supply chain management where circulation of products with a minimal transportation cost is an important issue. This paper presents the first adaptation of the Dhouib-Matrix-TP1 heuristic to solve the transportation problem in single-valued trapezoidal neutrosophic environment. Hence, the recently developed Dhouib-Matrix-TP1 heuristic is enriched with two functions to solve the neutrosophic transportation problem. On the one hand, a defuzzification function is exploited in order to convert the single-valued trapezoidal neutroso

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Belov, Aleksandr A., and Valentin S. Khokhlachev. "Asymptotically accurate error estimates of exponential convergence for the trapezoidal rule." Discrete and Continuous Models and Applied Computational Science 29, no. 3 (2021): 251–59. http://dx.doi.org/10.22363/2658-4670-2021-29-3-251-259.

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In many applied problems, efficient calculation of quadratures with high accuracy is required. The examples are: calculation of special functions of mathematical physics, calculation of Fourier coefficients of a given function, Fourier and Laplace transformations, numerical solution of integral equations, solution of boundary value problems for partial differential equations in integral form, etc. For grid calculation of quadratures, the trapezoidal, the mean and the Simpson methods are usually used. Commonly, the error of these methods depends quadratically on the grid step, and a large numbe

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Latif, Muhammad Amer. "General Trapezoidal-Type Inequalities in Fuzzy Settings." Mathematics 12, no. 19 (2024): 3112. http://dx.doi.org/10.3390/math12193112.

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In this study, trapezoidal-type inequalities in fuzzy settings have been investigated. The theory of fuzzy analysis has been discussed in detail. The integration by parts formula of analysis of fuzzy mathematics has been employed to establish an equality. Trapezoidal-type inequality for functions with values in the fuzzy number-valued space is proven by applying the proven equality together with the properties of a metric defined on the set of fuzzy number-valued space and Höler’s inequality. The results proved in this research provide generalizations of the results from earlier existing resul

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Arya, Varun, Sundeep Sharma, Keerat Preet Koour, Aasimah Hameed, Jingade Krishnojirao Dayashankara Rao, and Ayushi Gupta. "Stability of single 3-D trapezoidal plate in condylar fracture in comparison to 2 Miniplates." International journal of health sciences 6, S1 (2022): 425–38. http://dx.doi.org/10.53730/ijhs.v6ns1.4783.

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Background: Condylar fractures account for one third of all mandibular fractures being in the range of 17.5–52%1, 2 of all mandibular fractures. The main goal in the treatment of condylar fractures is to predictably restore pre-injury anatomical form, with associated aesthetics and function. Aim: The aim of this study is to assess the efficacy and stability of single 3-D trapezoidal condylar plate and compare it with 2.0mm conventional miniplates in the Open Reduction and Internal Fixation of mandibular sub-condylar fractures. Methods: This study was conducted on 20 patients with subcondylar f

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Gupta, Arun Kumar, and Shanu Sharma. "Free Transverse Vibration of Orthotropic Thin Trapezoidal Plate of Parabolically Varying Thickness Subjected to Linear Temperature Distribution." Shock and Vibration 2014 (2014): 1–6. http://dx.doi.org/10.1155/2014/392325.

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The present paper deals with the free transverse vibration of orthotropic thin trapezoidal plate of parabolically varying thickness inx-direction subjected to linear temperature distribution inx-direction through a numerical method. The deflection function is defined by the product of the equations of the prescribed continuous piecewise boundary shape. Rayleigh-Ritz method is used to evaluate the fundamental frequencies. The equations of motion, governing the free transverse vibrations of orthotropic thin trapezoidal plates, are derived with boundary condition CSCS. Frequency corresponding to

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Singh, Narayan, Bindu Vaish, and S. R. Singh. "Manufacturer-supplier cooperative inventory model for deteriorating item with trapezoidal type demand." Yugoslav Journal of Operations Research 26, no. 1 (2016): 103–20. http://dx.doi.org/10.2298/yjor140101021s.

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This paper investigates a Supply Chain System for deteriorating items in which a supplier supplies a manufacturer with raw material, and the manufacturer produces the finished goods. Demand rate is assumed to be time-sensitive in nature (Trapezoidal type), which allows three-phase variation in demand, and production rate is demand dependent. Our adoption of trapezoidal type demand reflects a real market demand for newly launched product. We show that the total cost function is convex. With the convexity, a simple solution algorithm is presented to determine the optimal order quantity and optim

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Nonlaopon, Kamsing, Muhammad Uzair Awan, Muhammad Zakria Javed, Hüseyin Budak, and Muhammad Aslam Noor. "Some q-Fractional Estimates of Trapezoid like Inequalities Involving Raina’s Function." Fractal and Fractional 6, no. 4 (2022): 185. http://dx.doi.org/10.3390/fractalfract6040185.

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In this paper, we derive two new identities involving q-Riemann-Liouville fractional integrals. Using these identities, as auxiliary results, we derive some new q-fractional estimates of trapezoidal-like inequalities, essentially using the class of generalized exponential convex functions.

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Barnett, N. S., P. Cerone, and S. S. Dragomir. "A sharp bound for the error in the corrected trapezoid rule and application." Tamkang Journal of Mathematics 33, no. 3 (2002): 253–58. http://dx.doi.org/10.5556/j.tkjm.33.2002.253-258.

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Karnan, Gopalakrishnan, and Chien-Chang Yen. "Refinable Trapezoidal Method on Riemann–Stieltjes Integral and Caputo Fractional Derivatives for Non-Smooth Functions." Fractal and Fractional 7, no. 3 (2023): 263. http://dx.doi.org/10.3390/fractalfract7030263.

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The Caputo fractional α-derivative, 0<α<1, for non-smooth functions with 1+α regularity is calculated by numerical computation. Let I be an interval and Dα(I) be the set of all functions f(x) which satisfy f(x)=f(c)+f′(c)(x−a)+gc(x)(x−c)|(x−c)|α, where x,c∈I and gc(x) is a continuous function for each c. We first extend the trapezoidal method on the set Dα(I) and rewrite the integrand of the Caputo fractional integral as a product of two differentiable functions. In this approach, the non-smooth function and the singular kernel could have the same impact. The trapezoidal method using the

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Pourbakhshian, Somayyeh, and Majid Pouraminian. "Analytical Models for Optimal Design of a Trapezoidal Composite Channel Cross-Section." Civil and Environmental Engineering Reports 31, no. 1 (2021): 118–38. http://dx.doi.org/10.2478/ceer-2021-0009.

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Abstract In this paper, several analytical models are presented for the optimal design of a trapezoidal composite channel cross-section. The objective function is the cost function per unit length of the channel, which includes the excavation and lining costs. To define the system, design variables including channel depth, channel width, side slopes, freeboard, and roughness coefficients were used. The constraints include Manning’s equation, flow velocity, Froude number, and water surface width. The Simultaneous Perturbation Stochastic Approximation (SPSA) algorithm was used to solve the optim

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Jyoti, Arora, and Sharma Surbhi. "Solving Triangular Fuzzy Linear Fractional Programming Problem." Journal of Applied Mathematics and Statistical Analysis 4, no. 1 (2023): 8–14. https://doi.org/10.5281/zenodo.7808513.

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<em>In this paper we propose to solve linear fractional programming problem, where all the decision parameters are trapezoidal fuzzy numbers. Our approach and computational procedures may be efficient and simple to implement for calculation in a trapezoidal fuzzy environment for all fields of engineering and science where impreciseness occur. Here we are formulating the given objective function into three objective bounds with constraints which can be solved further by Simplex method. A numerical example is presented to illustrate the proposed approach.</em>

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