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• Open Access   Article

  Optimizing the Trapezoidal Fuzzy Travelling Salesman Problem Through Dhouib-Matrix-TSP1 Method Based on Magnitude Technique

  Sa. Dhouib, S. Dhouib

  Research Paper | Journal-Paper (IJSRMSS)

  Vol.8 , Issue.2 , pp.1-4, Apr-2021

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  In this paper, we propose to optimize the trapezoidal fuzzy Travelling Salesman Problem (TSP). First, we rank the fuzzy matrix of distance using the magnitude ranking technique. Second, the new method named Dhouib-Matrix-TSP1 is applied to easily and quickly search an optimal or a near optimal solution in polynomial computational time. A numerical example will be presented and discussed to prove the efficiency of the Dhouib-Matrix-TSP1 approach

  Key-Words / Index Term
  Fuzzy Set, Travelling Salesman Problem, Optimization, Approximation Method, Dhouib-Matrix-TSP1, Magnitude Technique

  References
  [1] L. A. Zadeh, “Fuzzy Sets,” Information and Control, Vol. 8, No.3, pp.338-353, 1965.
  [2] G. Dantzig, D. Fulkerson and S. Johnson, “Solutions of a large-scale traveling-salesman problem,” Operations Research, Vol.2 No.4, pp.393-410, 1954.
  [3] C. Changdar, S. G. Mahapatra and R. P. Kumar, “An efficient genetic algorithm for multi-objective solid travelling salesman problem under fuzziness,” Swarm and Evolutionary Computation, Vol.15, pp.27–37, 2014.
  [4] Z. Wang, J. Guo, M. Zheng and Y. Wang, “Uncertain multiobjective traveling salesman problem,” European Journal of Operational Research, Vol.241 No. 2, 2015.
  [5] W. Gu, Y. Liu Y., L. Wei and B. Dong, “A Hybrid Optimization Algorithm for Travelling Salesman Problem Based on Geographical Information System for Logistics Distribution,” International Journal of Grid Distribution Computing, Vol.8 No. 3, pp.359-370, 2015.
  [6] J. D. D. Francisco, M. Oscar and R. Sepúlveda, “Reducing the size of traveling salesman problems using vaccination by fuzzy selector,” Expert Systems with Applications, Vol.49, pp.20-30, 2016.
  [7] V. Vasilchikov,“On the Optimization and Parallelizing Little Algorithm for Solving the Traveling Salesman Problem,” Modeling and Analysis of Information Systems, Vol. 23 No.4, pp.401-411, 2016.
  [8] L. S. Smith and F. Imeson, “GLNS: an effective large neighborhood search heuristic for the generalized traveling salesman problem,” Computer Operatioanl Research, Vol.87, pp.1-19, 2017.
  [9] P. Tinarut and K. Leksakul, “Hybrid self-organizing map approach for traveling salesman problem”, Chiang Mai University Journal of Natural Sciences, Vol.18 No.1, pp.27-37, 2019.
  [10] M. Divya, “Solving Travelling Salesman Problem Using Ant Systems: A Programmer’s Approach,” International Journal of Applied and Computational Mathematics, Vol.5, pp.101, 2019.
  [11] S. Suriya and M. Rahul Kumar, "Solving Travelling Salesman Problem using an Enhanced Ant Colony Algorithm," International Journal of Computer Sciences and Engineering, Vol.7, Issue-7, July 2019.
  [12] H. Zhang, L. Xiang and X. Liu, “A SN P System for Travelling Salesman Problem,” International Conference on Human Centered Computing, pp.339-346, 2019.
  [13] M. S. Hardi, M. Zarlis, S. Effendi and S. M. Lydia, “Taxonomy Genetic Algorithm For Implementation Partially Mapped Crossover In Travelling Salesman Problem,” International Conference on Advanced Information Scientific Development (ICAISD), Vol.1641, 2020.
  [14] A. A. Mehmet, B. C. Kalayci, “A Variable Neighborhood Search Algorithm for Cost-Balanced Travelling Salesman Problem,” Metaheuristics for Combinatorial Optimization, pp. 23-36, 2021.
  [15] O. Cheikhrouhoua and I. Khoufi, “A comprehensive survey on the Multiple Traveling Salesman Problem: Applications, approaches and taxonomy,” Computer Science Review, vol.40, pp.100369, 2021.
  [16] M. Gunduza and M. Aslan, “DJAYA: A discrete Jaya algorithm for solving traveling salesman problem”, Applied Soft Computing, Vol. 105, pp.107275, 2021.
  [17] S. Dhouib, “A New Column-Row Method for Traveling Salesman Problem: The Dhouib-Matrix-TSP1,” International Journal of Recent Engineering Science, Vol. 8, No. 1, pp. 6-10, 2021.
  [18] S. Dhouib, “Stochastic Column-Row Method for Travelling Salesman Problem: the Dhouib-Matrix-TSP2,” International Journal of Engineering Research & Technology, Vol. 10, Issue 3, pp. 524-527, 2021.

  Citation
  Sa. Dhouib, S. Dhouib, "Optimizing the Trapezoidal Fuzzy Travelling Salesman Problem Through Dhouib-Matrix-TSP1 Method Based on Magnitude Technique," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.8, Issue.2, pp.1-4, 2021

• Open Access   Article

  Improved Product type Estimator for Estimation of Population Mean

  Rizwan Yousuf, Khalid Ul Islam Rather

  Research Paper | Journal-Paper (IJSRMSS)

  Vol.8 , Issue.2 , pp.5-7, Apr-2021

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  Abstract
  In this manuscript, when the linear combination of median and correlation coefficient of the auxiliary variable is defined, we propose an adapted product estimator of population mean. When the correlation between the study variable and the auxiliary variable is negative, product estimators are used, as seen in this article. Our proposed estimators` Bias and Mean Squared Error (MSE) have been calculated. Our proposed estimator performs better in contrast, according to a theoretical review. The determined mean square error stamps the performance in addition to the numerical analysis.

  Key-Words / Index Term
  Auxiliary variable, bias, MSE, product estimator, simple random sampling.

  References
  [1] Subramani, J. A new median based ratio estimator for estimation of the finite population mean. Statistics in Transition. New Series, 17(4), pp.591-604 (2016).
  [2] Subramani, J. A new modified ratio estimator for estimation of population mean when median of the auxiliary variable is known. Pakistan Journal of Statistics and Operation Research, 9(2), pp.137-145 (2013).
  [3] Subramani, J., and Kumarapandiyan, G. Estimation of population mean using known correlation coefficient and median. Journal of Statistical Theory and Applications, 13(4), pp.333-343 (2014).
  [4] Subramani, J., and Kumarap, G. Modified ratio estimators for population mean using function of quartiles of auxiliary variable. Bonfring International Journal of Industrial Engineering and Management Science, 2(2), pp.19-23 (2012).
  [5] Shittu, O. I., and Adepoju, K. A. On the efficiency of modified ratio estimator based on linear combination of kurtosis, median and quartile deviation. International Journal of Modern Mathematical Sciences, 11(2), pp.103-107 (2014).
  [6] Subramani, J., and Prabavathy, G. Median based modified ratio estimators with known quartiles of an auxiliary variable. Journal of Modern Applied Statistical Methods, 13(1), pp.15-22 ( 2014).
  [7] Subramani, J., and Kumarapandiyan, G. Estimation of population mean using known median and co-efficient of skewness. American Journal of Mathematics and Statistics, 2(5), pp.101-107 (2012).
  [8] Subramani, J., and Prabavathy, G. Median based modified ratio estimators with known skewness and correlation coefficient for the estimation of finite population mean. Journal of Reliability and Statistical Studies, 8(1),( 2015 ) 23-30
  [9] Kumar, S. An estimator of the mean estimation of study variable using median of auxiliary variable. Sri Lankan Journal of Applied Statistics, 16(2), 2015
  [10] Subramani, J., and Kumarapandiyan, G. Estimation of population mean using co-efficient of variation and median of an auxiliary variable. International Journal of Probability and Statistics, 1(4), pp.111-118 (2012).
  [11] Sharma, P., and Singh, R. Generalized class of estimators for population median using auxiliary information. Hacettepe Journal of Mathematics and Statistics, 44(2), pp.443-453, (2015).
  [12] Singh, S. Advanced Sampling Theory With Applications: How Michael"" Selected"" Amy. Springer Science & Business Media, Vol. 2 (2003)
  [13] Yadav, S. K., Gupta, S., Mishra, S. S., and Shukla, A. K. Modified Ratio and Product Estimators for Estimating Population Mean in Two-Phase Sampling. American Journal of Operational Research, 6(3), pp.61-68 (2016),
  [14] Sukhatme, P. V. Sampling theory of surveys with applications. The Indian Society Of Agricultural Statistics; New Delhi, (1957)
  [15] W. Cohran, Sampling Techniques, Newyork: John Wiley, (1977).
  [16] M.N Murthy. Sampling Theory and Methods, (1967)
  [17] Md. ZahidHasan, Ali Hasan, A New Regression Type Estimator and its Industrial Application, Conference paper, 1st national Conference on Application of Statistics on Sustainable Development Goals, Tangail, Bangladesh, (2018 )
  [18] Rather, K.U.I and Yousuf, R. Improved Estimator for Estimating the Population Mean In Simple Random Sampling.International Journal of Scientific Research in Mathematical and Statistical Sciences, 7(5) pp.16-18, (2020).

  Citation
  Rizwan Yousuf, Khalid Ul Islam Rather, "Improved Product type Estimator for Estimation of Population Mean," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.8, Issue.2, pp.5-7, 2021

• Open Access   Article

  Robust Model for the Quadratic Production Function in Presence of High Leverage Points

  Rizwan Yousuf, Manish Sharma, M. Iqbal Jeelani Bhat , S.E.H. Rizvi

  Research Paper | Journal-Paper (IJSRMSS)

  Vol.8 , Issue.2 , pp.8-13, Apr-2021

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  Abstract
  As in the presence of High leverage points (HLP) i.e. outliers, the ordinary least square (OLS) method does not provide the precise and true estimates of production function. In this study, we have used the simulation data to study the behaviour of estimates of quadratic production function in presence of HLP. The HLP were identified through different techniques like Mahanablios distance, Robust minimum covariance determinant (MCD)Distance, Standard robust residuals, Cook’s distance, studentized residual, WSSDI, Hat Diagonals and deleted residuals. The data set is influenced by the influential observations. The Robust techniques viz M estimation, MM estimation, S estimation, LTS estimation and OLS after resolving the issue of HLP have been used. The estimates of the quadratic function have been compared and observed that the influential observations have affected the size, sign and significance of the parameter(s).The LTS estimation found to be the best as compared to the others on the basis of AIC, SBIC and R2.

  Key-Words / Index Term
  Outliers, Residuals, , Cook’s distance , OLS, Robust M estimation and LTS estimation

  References
  [1] C. Ackello-Ogutu, Q. Paris, W.A. Williams, “Testing a von Liebig Crop Response Function against Polynomial Specifications”. American Journal of Agricultural Economics, Vol.67, pp.873–880, 1985.
  [2] R. L. Anderson, L. A. Nelson, “A Family of Models Involving Intersecting Straight Lines and Concomitant Experimental Designs Useful in Evaluating Response to Fertilizer Nutrients”. Biometrics, Vol.31, pp.303–318, 1975.
  [3] G.Bélanger, J. R.Walsh, J. E. Richards, P. H. Milburn, N. Ziadi, “Comparison of Three Statistical Models Describing Potato Yield Response to Nitrogen Fertilizer”. Agronomy Journal, Vol.92, pp.902–908,2000
  [4] P. Berck, G.Helfand, “Reconciling the von Liebig and Differentiable Crop Production Functions”. American Journal of Agricultural Economics, Vol.72, pp.985–996,1990.
  [5] C. Chen (2002), Robust Regression and Outlier Detection with the ROBUSTREG Procedure. Statistics and Data Analysis. Conference paper.
  [6] P.J.Huber, “Robust Regression: Asymptotics, Conjectures and Monte Carlo”. The Annals of Statistics, Vol,1,pp.799–821,1973.
  [7] P.J.Huber, “Robust Statistical Procedures”.Philadelphia: Society for Industrial and Applied Mathematics.Vol.3,pp.231-241,1996.
  [8] Rousseeuw, “Least median of squares Regression”, Journal of the American Statistical Association, Vol.79,871-880,1984
  [9] J.E.Sturm, J.De Haan, “How Robust is the Relationship between Economic Freedom and Economic Growth” .In Applied Economics .Vol.33,pp.834-44. 2001.
  [10] V J. Yohai, “High breakdown-point and high efficiency robust estimates for regression”. The Annals of Statistics. Vol.pp.15:642-656. 1987.

  Citation
  Rizwan Yousuf, Manish Sharma, M. Iqbal Jeelani Bhat , S.E.H. Rizvi, "Robust Model for the Quadratic Production Function in Presence of High Leverage Points," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.8, Issue.2, pp.8-13, 2021

• Open Access   Article

  Construction of Incubation Building Facilities and Laboratory for Integration of Remote Sensing Data and Information Services in Economic View

  N. Romsari, Misran, H.W. Indratmo

  Research Paper | Journal-Paper (IJSRMSS)

  Vol.8 , Issue.2 , pp.14-19, Apr-2021

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  In general, number of studies that explain the space technology is still considered a high cost technology that is not grounded and cannot be utilized, has been refuted, especially with remote sensing technology. This technology has been proven to bring economic benefits to users such as fishing potential zone information analyzed from satellite data has been proven to help fishermen determine potential fishing areas, proven to increase fishermen`s catch. Prove taxpayer reports on plantation, mining and forestry management so that taxes paid are not lower, assist insurance companies to prove claims and assist in monitoring crop growth, assist in identifying potential natural resources, and streamline disaster management are tangible benefits of remote sensing technology. Increasing the use of research and development (R & D) results and information that has been produced still needs to be done because of the development of science and technology. The development of science and technology has an influence on the development of data types with higher resolution, both spectral and spatial resolution. Likewise with the development of information technology that allows people to obtain fast and accurate information. Therefore, this study is needed to examine a more significant impact if Indonesia can facilitate the construction of an incubation building facility and an integrated laboratory for remote sensing data and information services.

  Key-Words / Index Term
  Remote Sensing Technology, Economics, Incubation Building, Integration Laboratory

  References
  [1]. Prayudha, B., et al. “Pemanfaatan Citra Satelit Penginderaan Jauh dan Sistem Informasi Geografi Untuk Analisis Nilai Ekonomi Ekosistem Pesisir Studi kasus: Desa Teluk Limau, Kecamatan Jebus, Kabupaten Bangka Barat, Provinsi Bangka Belitung”. Oseanologi dan Limnologi di Indonesia, 5(1), pp.33-46, 2020.
  [2]. Shalihati, S. F. “Pemanfaatan Penginderaan Jauh dan Sistem Informasi Geografi Dalam Pembangunan Sektor Kelautan Serta Pengembangan Sistem Pertahanan Negara Maritim”. Geoedukasi, Vol. III No. 2, pp.115 – 126, 2014.
  [3]. Indrianingrum, R.D. “Analisis Nilai Lahan Di Kecamatan Ngawi Dengan Aplikasi Penginderaan Jauh dan Sistem Informasi Geografis”. Skripsi S1 Fakultas Geografi Universitas Muhammadiyah Surakarta, 2015.
  [4]. Diana, S.R., et al. “Nilai Ekonomi Data dan Informasi Penginderaan Jauh Sebagai Wujud Pelaksanaan Visi Keantariksaan di Indonesia. Seminar Nasional Kebijakan Penerbangan dan Antariksa III” (SINAS KPA-III), Indonesia, 2018.
  [5]. Ariyora, Yuan Karisma Sang, Yanto Budisusanto, dan Indah Prasasti. “Pemanfaatan Data Penginderaan Jauh dan Sig Untuk Analisa Banjir (Studi Kasus : Banjir Provinsi DKI Jakarta)”. GEOID, 10 (2), pp.137-146, 2015.
  [6]. Gusmawati, Niken Financia, Ariani Andayani, dan Umi Mu’awanah. “Pemanfaatan Data Penginderaan Jauh Resolusi Tinggi Untuk Pemetaan Tambak Di Kecamatan Ujung Pangkah, Gresik”. Jurnal Kelautan Nasional, 11 (1), pp.35-51, 2016.
  [7]. Lubis, Muhammad Zainuddin, et al.. “Penerapan Teknologi Penginderaan Jauh di Bidang Pesisir dan Lautan”. Oseana, XLII (3), pp.56-64, 2017
  [8]. Khomarudin, M.Rokhis, dkk. “Pengkajian Pemanfaatan Data Penginderaan Jauh Multi Skala/Resolusi Untuk Kegiatan Mitigasi Bencana”. Seminar Nasional Penginderaan Jauh, Indonesia, 2014.
  [9]. Mailendra. “Pemanfaatan Data Penginderaan Jauh dan Teknologi Sig Untuk Mengidentifikasi Built Up Area dan Kaitannya Dengan RTRW Di Kabupaten Kendal”. Seminar Nasional Geomatika 2018: Penggunaan dan Pengembangan Produk Informasi Geospasial Mendukung Daya Saing Nasional, Indonesia, 2018.
  [10]. Raharjo, Puguh Dwi. “Teknik Penginderaan Jauh Dan Sistem Informasi Geografis Untuk Identifikasi Potensi Kekeringan”. Makara Teknologi, Indonesia, 14 (2), pp.97-105, 2010.

  Citation
  N. Romsari, Misran, H.W. Indratmo, "Construction of Incubation Building Facilities and Laboratory for Integration of Remote Sensing Data and Information Services in Economic View," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.8, Issue.2, pp.14-19, 2021

• Open Access   Article

  Two-Dimensional Solute Transport in a Semi-Infinite Porous Medium with Variable Dispersion and Groundwater Velocity

  Joy Roy, Lav Kush Kumar, Vijayshree Yadav, R.R. Yadav

  Research Paper | Journal-Paper (IJSRMSS)

  Vol.8 , Issue.2 , pp.20-28, Apr-2021

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  Abstract
  In this paper, a theoretical model is developed for solving a two-dimensional advection-dispersion problem for semi-infinite porous medium. Dispersion coefficient and groundwater velocity are functions of space as well as time. Due to heterogeneity of the medium retardation factor is also considered space dependent. Initial concentration distribution is uniform throughout the domain. The time-dependent pulse type point source is being injected from the origin along the flow. Input concentration is provided in tabulated data form for certain points of time (i.e., discrete data). The concentration gradient at other end of the boundary is supposed to be zero. The advection-dispersion equation (ADE) with variable coefficients is transformed into constant coefficients using appropriate transformations. The transport scenario has been analytically solved through the Laplace Integral Transformation Technique (LITT). A time-space concentration curves are drawn for various parameters responsible for transport scenario.

  Key-Words / Index Term
  Advection, Aquifer, Contaminant, Dispersion, Heterogeneous, Interpolation, Retardation

  References
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  [3] G.S. Kumar, M. Sekhar, D. Misra, “Time-Dependent Dispersivity of Linearly Sorbing Solutes in a Single Fracture with Matrix Diffusion,” J. Hydrol., Eng. Vol. 13, pp. 250–257, 2008. doi.org/10.1061/(asce)10840699(2008)13:4(250).
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  [5] J.D. Logan, “Solute Transport in Porous Media with Scale Dependent Dispersion and Periodic Boundary Conditions,” Journal of Hydrology, Vol. 184, No. 3-4, pp. 261-276, 1996.
  [6] A.A. Jayawardena, P.H. Lui, “Numerical Solution of the Dispersion Equation Using a Variable Dispersion Coefficient: Method And Applications,” Hydrol. Sci. J., Vol. 29, Issue 3, pp. 293–309, 1984. doi.org/10.1080/02626668409490947
  [7] P.A. Domenico, “An Analytical Model for Multidimensional Transport of a Decaying Contaminant Species,” Journal of Hydrology, Vol. 91, Issue 1–2, pp. 49–58, 1987.
  [8] V. Batu, M.Th.Van Genuchten, “First and Third-Type Boundary Conditions in 2d Solute Transport Modelling,” Water Resour. Res., Vol. 26, No.2, pp. 339-350, 1990.
  [9] C. Zoppou, J.H. Knight, “Analytical solution of a spatially variable coefficient advection-diffusion equation in up to three dimensions,” Appl Math Model , Vol. 23, pp. 667–685, 1999.
  [10] P.B. Bedient, H.S. Rifai, C.J. Newell, “Ground Water Contamination: Transport and Remediation,” 2nd Ed., Prentice-Hall PTR, Upper Saddle River, N.J., 1999.
  [11] L. Pang, B. Hunt, “Solutions and Verification of a Scale-Dependent Dispersion Model,” Journal of Contaminant Hydrology, Vol. 53, pp. 21-39, 2001.
  [12] F.D. Smedt, “Analytical Solutions for Transport of Decaying Solutes in Rivers with Transient Storage,” J. Hydrol., Vol. 330, pp. 672–680, 2006.
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  [17] R.R. Yadav, L.K. Kumar, “Two-Dimensional Conservative Solute Transport with Temporal and Scale-Dependent Dispersion: Analytical Solution,” International Journal of Advances in Mathematics , Vol. 2, pp. 90-111 , 2018.
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  Citation
  Joy Roy, Lav Kush Kumar, Vijayshree Yadav, R.R. Yadav, "Two-Dimensional Solute Transport in a Semi-Infinite Porous Medium with Variable Dispersion and Groundwater Velocity," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.8, Issue.2, pp.20-28, 2021

• Open Access   Article

  Mathematical Comparison of Defuzzification of Fuzzy Logic Controller for Intelligence Air Conditioning System

  M.A. Islam, M.S. Hossain, I.S.M. Haque

  Research Paper | Journal-Paper (IJSRMSS)

  Vol.8 , Issue.2 , pp.29-37, Apr-2021

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  Abstract
  The objective of this paper is to compare several defuzzification techniques for the application of an air cooler control design in order to predict the error difference between different methods. The four input parameters are considered to be user temperature (UT), temperature difference (Tdf), dew point (Td), and number of peoples (NP). However, Compressor Speed (CS), Fan Speed (FS) and Fin Direction (FD) are used as outputs. The simulation of this paper is carried out by using MATLAB.

  Key-Words / Index Term
  Fuzzy logic controller, defuzzification techniques, fuzzy rule base, MATLAB simulation

  References
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  [8] R. Roshmi, M.S. Hossain, “Regularity and Normality in Bitopological Spaces”, Int. J. Sci. Res. In Mathematical and Statistical Sciences, Vol.7, Issue.1, pp.21-25, 2020.
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  Citation
  M.A. Islam, M.S. Hossain, I.S.M. Haque, "Mathematical Comparison of Defuzzification of Fuzzy Logic Controller for Intelligence Air Conditioning System," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.8, Issue.2, pp.29-37, 2021