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PSK Method for Solving Type-1 and Type-3 Fuzzy Transportation Problems

PSK Method for Solving Type-1 and Type-3 Fuzzy Transportation Problems

P. Senthil Kumar
Copyright: © 2017 |Pages: 26
ISBN13: 9781522519089|ISBN10: 1522519084|EISBN13: 9781522519096
DOI: 10.4018/978-1-5225-1908-9.ch017
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MLA

Kumar, P. Senthil. "PSK Method for Solving Type-1 and Type-3 Fuzzy Transportation Problems." Fuzzy Systems: Concepts, Methodologies, Tools, and Applications, edited by Information Resources Management Association, IGI Global, 2017, pp. 367-392. https://doi.org/10.4018/978-1-5225-1908-9.ch017

APA

Kumar, P. S. (2017). PSK Method for Solving Type-1 and Type-3 Fuzzy Transportation Problems. In I. Management Association (Ed.), Fuzzy Systems: Concepts, Methodologies, Tools, and Applications (pp. 367-392). IGI Global Scientific Publishing. https://doi.org/10.4018/978-1-5225-1908-9.ch017

Chicago

Kumar, P. Senthil. "PSK Method for Solving Type-1 and Type-3 Fuzzy Transportation Problems." In Fuzzy Systems: Concepts, Methodologies, Tools, and Applications, edited by Information Resources Management Association, 367-392. Hershey, PA: IGI Global, 2017. https://doi.org/10.4018/978-1-5225-1908-9.ch017

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Abstract

In conventional transportation problem (TP), supplies, demands and costs are always certain. In this paper, the author tried to categories the TP under the mixture of certain and uncertain environment and formulates the problem and utilizes the crisp numbers, triangular fuzzy numbers (TFNs) and trapezoidal fuzzy numbers (TrFNs) to solve the TP. The existing ranking procedure of Liou and Wang is used to transform the type-1 and type-3 fuzzy transportation problem (FTP) into a crisp one so that the conventional method may be applied to solve the TP. The solution procedure differs from TP to type-1 and type-3 FTP in allocation step only. Therefore, the new method called PSK method and new multiplication operation on TrFN is proposed to find the mixed optimal solution in terms of crisp numbers, TFNs and TrFNs. The main advantage of this method is computationally very simple, easy to understand and also the optimum objective value obtained by our method is physically meaningful. The effectiveness of the proposed method is illustrated by means of a numerical example.

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