Fuzzy Bounded Separation Method for Solving Fully Fuzzy Interval Integer Transportation Problems: A New Approach
DOI:
https://doi.org/10.13052/jgeu0975-1416.1423Keywords:
Fully fuzzy integer interval transportation problem, membership function, fuzzy bounded separation methodAbstract
To solve fully fuzzy interval integer transportation problems, a new approach, known as the fuzzy bounded separation method, is proposed. This approach is based on the maximum modulus zero suffix method. The given problem is split into two fuzzy transportation problems, the fuzzy upper bounded interval transportation problem (FUBITP) and fuzzy lower bounded interval transportation problem (FLBITP), and the maximum modulus zero suffix approach is used to get the best solution. Without using any ranking approaches, the suggested strategy applies to a very similar situation. Numerical examples are used to demonstrate the solution process. When treating different types of logistic problems with fully fuzzy integer interval problems, decision makers may find the fuzzy bounded separation method to be extremely useful. This method follows a methodical process and is simple to use and comprehend.
Downloads
References
Chanas, S., Delgado, M., Verdegayand, J.L. and Vila, M.A. (1993). Interval and fuzzy extensions of classical transportation problems, TranspPlann Technol., 17, pp. 203–218.
Dash, S. and Mohanty, S.P. (2013). Transportation programming under uncertain environment, International Journal of Engineering Research and Development, Vol. 7 pp. 22–28.
Fegade, M. R., Jadhav, V. A. and Mulley, A. A. (2012). Solving fuzzy transportation problem by zero suffix method and robust ranking technology, IOSR Journal of Engineering, Vol. 2(7), pp. 36–39.
Karthiyayini, G. P., Ananthalakshmi, S. and Ushaparameswari, R. (2019). An inventive method for solving fully interval transportation problem, SSRG International Journal of Mathematics Trends and Technology- special issue NCPAM, pp. 50–57.
Keerthana, G. and Ramesh, G. (2019). A New Approach for Solving Integer Interval Transportation Problem with Mixed Constraints, Journal of Physics: Conference Series 1377 012043, pp. 1–14.
Maity, G., Roy, S. K. and Verdegay, J.L. (2019). Time variant multi objective intervalvalued transportation problem in sustainable development, Sustainability, Vol. 11, pp. 0115.
Mohana, V. (2018). Optimal Solution for Integer Interval Transportation Problem using Zero Point Method, International Journal of Pure and Applied Mathematics, Vol. 118, pp. 2287–2291.
Pandian, P. and Natarajan, G. (2010). A New Method for Finding an Optimal Solution of fully interval integer transportation problem, Applied Mathematical Sciences, Vol. 4(37), pp. 1819–1830.
Pandian, P., Natarajan, G. and Akhilbasa, A. (2018). fuzzy interval integer transportation problem, International Pure and Applied Mathematics, Vol. 119(9), pp. 133–142.
Patel, J. G. and Dhodiya, J. M. (2017). Solving multi-objective interval transportation problem using grey situation decision-making theory based on grey numbers, International Journal of Pure and Applied Mathematics, Vol. 113, pp. 219–233.
Purushothkumar, M.K., Ananathanarayanan, M. and Dhanasekar, S. (2018). A diagonal optimal algorithm to solve interval integer transportation problem, International Journal of Applied Engineering Research, Vol. 13, pp. 13702–13704.
Quddoos, A., Shakeel, J. and Khalid, M. M. (2012). A New Method for Finding an Optimal Solution for Transportation Problems, International Journal on Computer Science and Engineering, Vol. 4, pp. 1271–1274.
Ramesh, G. and Ganesan, K. (2011). Interval Linear Programming with generalized interval arithmetic, International Journal of Scientific & Engineering Research, Vol. 2, pp. 1–8.
Roy, H., Pathak, G., Kumar, Rakesh and Malik, Z.A. (2024). Maximum modulus zerosuffix method for finding an optimal solution to fuzzy transportation problems. OPSEARCH 61, 897–917. https://doi.org/10.1007/s12597-023-00716-2
Safi, M. R., and Razmjoo, A. (2013). Solving Fixed Charge Transportation Problem with Interval Parameters, Applied Mathematical Modelling, Vol. 37 (18-19), pp. 83418347.
Sarfaraz, M. (2024). Interval-valued Pythagorean fuzzy aggregation operators for transportation selection, Spectrum of Engineering and Management Sciences, Vol. 2(1), pp. 1–12.
Sengupta, A., and Pal, T.K. (2003). Interval-valued transportation problem with multiple penalty factors, VU Journal of Physical Sciences, Vol. 9, pp. 71–81.
Sudhakar, V.J. and Navaneetha, V.K. (2010). A New Approach for Finding an Optimal Solution for Integer Interval Transportation Problems, Int. J. Open Problems Compt. Math., Vol. 3, pp. 131–137.
Youness, E. (2006). Characterizing solutions of rough programming problems, European Journal of Operational Research, Vol. 168, pp. 1019–1029.
Zadeh, L.A. (1965). Fuzzy sets, Inform. Control, Vol. 8, pp. 338–353.
Zimmermann, H.J. (1978). Fuzzy programming and linear programming with several objective functions. Fuzzy Sets Syst. Vol. 1, pp. 45–55.
