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Psk Method For Solving Type-1 And Type-3 Fuzzy Transportation Problems

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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  Cite this Chapter as follows:   MLA Kumar, P. Senthil. PSK Method for Solving Type-1 and Type-3 Fuzzy Transportation Problems.  Fuzzy Systems: Concepts, Methodologies, Tools, and Applications.  IGI Global, 2017. 367-392. Web. 2 Mar. 2017. doi: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  Fuzzy Systems: Concepts, Methodologies, Tools, and Applications  (pp. 367-392). Hershey, PA: IGI Global. doi: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,  367-392 (2017), accessed March 02, 2017. doi:10.4018/978-1-5225-1908-9.ch017  Fuzzy Systems: Concepts, Methodologies, Tools, and Applications Information Resources Management Association USA    Editor-in-Chief  Mehdi Khosrow-Pour, DBA  Information Resources Management Association, USA   Associate Editors Steve Clarke, University of Hull, UK  Murray E. Jennex, San Diego State University, USA Annie Becker, Florida Institute of Technology, USA Ari-Veikko Anttiroiko, University of Tampere, Finland  Editorial Advisory Board Sherif Kamel,  American University in Cairo, Egypt  In Lee, Western Illinois University, USA  Jerzy Kisielnicki, Warsaw University, Poland  Amar Gupta,  Arizona University, USA Craig van Slyke, University of Central Florida, USA  John Wang,  Montclair State University, USA Vishanth Weerakkody,  Brunel University, UK