Abstract
A transportation model is an appropriate case for the linear programming problem. This paper focuses on solving fuzzy transportation problems by assuming that a decision maker is only uncertain about the precise values of the transportation cost and not about the supply and demand of the product. In this method transportation, costs are represented by generalized quadratic fuzzy numbers. It deals with transporting the bearings of alien article from sources to destinations in which both the capacity (tons) absolute and requirements (tons) are accepted as generalized quadratic fuzzy numbers. In this paper, an appropriate type of optimal solution of Band-Aid for application was produced from GQFVAM and GQFMODI method.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Dantzig, G.B., Thapa, M.N.: Springer: Linear Programming: 2: Theory and Extensions. Princeton University Press, New Jersey (1963)
Gass SI (1990) On solving the transportation problem. J. Oper. Res. Soc. 41(4), 291–297
Zadeh, L.A.: Fuzzy sets. Inform. Control 8, 338–353 (1965)
Dubois, D., Prade, H.: Fuzzy set and systems theory and application. Academic Press, New York (1980)
Abbasbandy, S., Hajjari, T.: A new approach for the ranking of trapezoidal fuzzy numbers. Comput. Math. Appl. 57, 413–419 (2009)
Venkatachalapathy, M., Edward Samuel, A.: An alternative method for solving Fuzzy transportation problems using ranking functions. Int. J. Appl. Math. Sci. 9(1), 61–68 (2016)
Kaur, A., Kumar, A.: A new approach for solving fuzzy transportation problems using generalized trapezoidal fuzzy numbers. Appl. Soft Comput. 1–34 (2011)
Vimala, S., Thiagarajan, K., Amaravathy, A.: OFSTF method—an optimal solution for transportation problem. Indian J. Sci. Technol. 9(48), 1–3 (2016)
Zimmermann, H.J.: Fuzzy programming and linear programming with several objective functions. Fuzzy Sets Syst. 1, 45–55 (1978)
Stephan Dinagar, D., Christoper Raj, B.: A method for solving fully Fuzzy transportation problem with generalized quadrilateral Fuzzy numbers. Malaya J. Matematik S(1), 24–27 (2019)
Muthuperumal, S., Titus, P., Venkatachalapathy, M.: An algorithmic approach to solve unbalanced triangular Fuzzy transportation problems. In: Soft Computing, Springer-Verlag GmbH Germany, part of Springer Nature (2020)
Amaravathy, A., Seerengasamy, V., Vimala, S.: Comparative study on MDMA Method with OFSTF method in transportation problem. Int. J. Comput. Organ. Trends (IJCOT) 6(6), 50–55 (2016)
Venkatachalapathy, M., Jayaraja, A., Samuel, A.E.: A study on solving octagonal Fuzzy numbers using the modified Vogel’s approximation method. Int. J. Pure Appl. Math. 118(6), 201–207 (2018)
Venkatachalapathy, M., Pandiarajan, R., Ganeshkumar, S.: A special type of solving transportation problems using generalized quadratic fuzzy number. Int. J. Sci. Technol. Res. 9(2), 6344–6348 (2020)
Amaliah, B., Fatichah, C., Suryani, E.: Total opportunity cost matrix—minimal total: a new approach to determine initial basic feasible solution of a transportation problem. Egypt. Inform. J. 20, 131–141 (2019)
Öztürk, S., Karakuzu, C., Kuncan, M., Erdil, A.: Fuzzy neural network controller as a real time controller using PSO. Akademik Platform Mühendislik ve Fen Bilimleri Dergisi 5(1), 15–22 (2017)
Kuncan, M., Kaplan, K., Acar, F., Kundakçi, I.M., Ertunç, H.M.: Fuzzy logic based ball on plate balancing system real time control by image processing. Int. J. Nat. Eng. Sci. 10(3), 28–32 (2016)
Karakoç, H., Erin, K., Çağıran, R., Kuncan, M., Kaplan, K., Ertunç, H.M.: The Performance Comparison of PD Controller and Fuzzy Logic Controller for the Aircraft Height Control Otomatik Kontrol Ulusal Toplantısı, TOK’2015, pp. 10–12 (2015)
Ramesh Babu, A., Rama Bhupal Reddy, B.: Feasibility of fuzzy new method in finding initial basic feasible solution for a fuzzy transportation problem. J. Comput. Math. Sci. 10(1), 43–54 (2019)
Mathur, N., Srivastava, P.K.: An inventive approach to optimize fuzzy transportation problem. Int. J. Math. Eng. Manage. Sci. 5(5), 985–994 (2020)
Doğan, H., Kaplan, K., Kuncan, M., Ertunç, H.M.: PID and fuzzy logic approach to vehicle suspension system control. Otomatik Kontrol Ulusal Toplantısı 10–12 (2015)
Kaplan, K., Kuncan, M., Ertunc, H.M.: Prediction of bearing fault size by using model of adaptive neuro-fuzzy inference system. In: 2015 23nd Signal Processing and Communications Applications Conference (SIU) IEEE, pp. 1925–1928 (2015)
Edward Samuel A, Venkatachalapathy M (2012) A new procedure for solving the generalized trapezoidal Fuzzy transportation problem. Adv Fuzzy Sets Syst 12(2), 111–125
Acknowledgments
The authors would like to thank to the editor-in-chief and the anonymous reviewers for their suggestions that have led to an improvement in both the quality and clarity of the paper
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2022 The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd.
About this chapter
Cite this chapter
Venkatachalapathy, M., Muthuperumal, S., Rajasekar, R. (2022). An Innovative Method for Finding Optimal Solution Fully Solved by Using Generalized Quadratic Fuzzy Transportation Problems. In: Kannan, S.R., Last, M., Hong, TP., Chen, CH. (eds) Fuzzy Mathematical Analysis and Advances in Computational Mathematics. Studies in Fuzziness and Soft Computing, vol 419. Springer, Singapore. https://doi.org/10.1007/978-981-19-0471-4_3
Download citation
DOI: https://doi.org/10.1007/978-981-19-0471-4_3
Published:
Publisher Name: Springer, Singapore
Print ISBN: 978-981-19-0470-7
Online ISBN: 978-981-19-0471-4
eBook Packages: Intelligent Technologies and RoboticsIntelligent Technologies and Robotics (R0)