A Mathematical Approach to Eliminate the Deficiency of Minerals in Soils using Fuzzy Linear Programming

International Journal of Mathematics Trends and Technology (IJMTT)
© 2018 by IJMTT Journal
Volume-55 Number-5
Year of Publication : 2018
Authors : Rama S, Anna Rose K.B and Palliyil Stefy Solomon


Rama S, Anna Rose K.B and Palliyil Stefy Solomon "A Mathematical Approach to Eliminate the Deficiency of Minerals in Soils using Fuzzy Linear Programming", International Journal of Mathematics Trends and Technology (IJMTT). V55(5):380-387 March 2018. ISSN:2231-5373. www.ijmttjournal.org. Published by Seventh Sense Research Group.

Project planning is the important task in many areas like construction, resource allocation and many. A sequence of activities has to be performed to complete one task. Each activity has its unique processing time and all together to identify the critical activities which affect the completion of the project. In this project the fertility of the soil is to be improved for a better crop production by removing the deficiency of the minerals from the soils by adding appropriate manures according to the requirements. This paper discuss about the fuzzy linear programming problem. In this paper a fuzzy optimization problem has been modelled, which work as pure fuzzy linear programming problem using trapezoidal fuzzy numbers and solved it with the help of fuzzy version of Big M method. By applying the fuzzy concepts, the infeasibility of the optimal solution has been eliminated and an optimal solution has been obtained. The results are tabulated. For numerical study the data for the soils in the northern and southern part of India has been taken.

1) Ali Ebrahimnejad (2011), “A primal dual simplex algorithm for solving linear programming problems with symmetric trapezoidal fuzzy numbers”, Applied Mathematics, 2, 676-684.
2) Amit Kumar, PushpinderSingh and Jagadeep Kaur (2010), “Generalized simplex algorithm to solve fuzzy linear programming problems with ranking of generalized fuzzy numbers”, Turkish Journal of Fuzzy System, 1(2), 80-103.
3) H M I U Hareth and Samarathanga (2015), “Multi objective fuzzy linear programming in agriculture production planning”, International Journal of Scientific and Technology Research,4(10), 242-250.
4) S. K. Jain and D. M. Mehta, “Operation Research (Theory and Application)”, Galgotia Publications Private Limited, 2nd edition.
5) S. Kalavathy, “Operations Research”, Vikas Publishing House Private Limited, 4thedition.
6) Mansur Hassan (2015), “Proposed simplex method for fuzzy linear programming with fuzziness at the right hand side”, IOSR Journal of Mathematics,11(3), 58-65.
7) S. A. Mohaddes and MohdGhazaliMohayidean (2008), “Application of the Fuzzy Approach for Agricultural Production Planning in a Watershed, a Case Study of the Atrak Watershed, Iran”, American-Eurasian Journal of Agriculture& Environment Science, 3 (4):636-648.
8) S. H. Nasseri and E. Ardil (2009), “Simplex Method for Fuzzy Variable Linear Programming Problems”, World Academy of Science, Engineering and Technology International Journal of Mathematical and Computational Sciences,3(10), 884-888.
9) Neela Patel, Manish Thaker and Chandrika Chaudhary(2016), “Study of Some Agricultural Crop Production Planning Condition through Fuzzy Multi-Objective Linear Programming Mathematical Model”, International Journal of Science and Research,5(4), 1329-1332.
10) R.Parvathi and L.Malathi (2012), “Intuitionistic fuzzy simplex method”, International Journal of Computer Application, 48(6),39-48.
11) M Pattnaik (2013), “Fuzzy multi objective linear programming problem sensitive analysis”, Journal of Mathematics and Computer Science, 7, 131-137.
12) Poonam Gupta(2017), “Applications of Fuzzy Logic in Daily life”, International Journal of Advanced Research in Computer Science, 8(5),1795-1800.
13) P Rajarajeswari and A.SahayaSudha (2013), “Ranking of Hexagonal Fuzzy Numbers for Solving Multi Objective Fuzzy Linear Programming Problem”, International Journal of Computer Applications, 84(8), 14-19.
14) P. Rajarajeswari, A.SahayaSudha and R.Karthika (2013), “A new operation on Hexagonal Fuzzy Number”, International Journal of Fuzzy Logic Systems, 3(3),15-26.
15) N. Ravi Shankar, G. Ananda Rao, J MadhuLatha and V. Sireesha (2010), “Solving a fuzzy non- linear optimization problem by genetic algorithm”,International Journalof Contemporary Mathematical Sciences,5(16),791-803.
16) Samir Dey and Tapan Kumar Roy (2006), “Solving Multi-Objective Structural Design Problem using Fuzzy Optimization Method: A Comparative Study”,International Journal of Innovative Research in Science & Engineering, 3(4),161-170.
17) B. SatheeshKumar and R Nandhini (2017), “An Optimum Solution for the Fuzzy Linear Programming Problem”, International Journal of Pure and Applied Mathematics, 117(13), 91-98.
18) Shapla Shirin and Kamrunnahar(2014), “Application of Fuzzy Optimization Problem in Fuzzy Environment”, Dhaka University Journal of Science, 62(2), 119-125.
19) S. R. Singh and S. K. Bharathi, “Intuitionistic fuzzy optimization technique in agriculture production planning: A small farm holder perspective”, International Journal of Computer Application, 89(6),17-23.
20) Stefan Chanas and Pawel Zielinski (2000), “The equivalence of two optimization method for fuzzy linear programming problem”, European Journal of Operation Research,121,56-63.
21) Dr. P. R. Vittal and V. Malini , “ Operations Research”, Margham publications.
22) A Yazdani, R. Zaefarian, S. H. Nasseri and E. Ardil(2005), “Simplex Method for Solving Linear Programming Problems with Fuzzy Numbers”, World Academy of Science, Engineering and Technology, 10,284-288.

Fuzzy linear programming, deficiency, trapezoidal fuzzy numbers.