JMD method for transforming an unbalanced fully intuitionistic fuzzy transportation problem into a balanced fully intuit
- PDF / 361,113 Bytes
- 16 Pages / 595.276 x 790.866 pts Page_size
- 82 Downloads / 197 Views
(0123456789().,-volV)(0123456789(). ,- volV)
METHODOLOGIES AND APPLICATION
JMD method for transforming an unbalanced fully intuitionistic fuzzy transportation problem into a balanced fully intuitionistic fuzzy transportation problem Akansha Mishra1 • Amit Kumar1
Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract Mahmoodirad et al. (Soft Comput, 2018. https://doi.org/10.1007/s00500-018-3115-z) proposed an approach for solving fully intuitionistic fuzzy transportation problems (FIFTPs) (transportation problems in which each parameter is represented as a triangular intuitionistic fuzzy number). In this approach, firstly, an unbalanced fully intuitionistic fuzzy transportation problem (FIFTP) is transformed into a balanced FIFTP, and then the intuitionistic fuzzy (IF) optimal solution of the transformed balanced FIFTP is obtained. In this paper, it is shown that Mahmoodirad et al.’s approach fails to transform an unbalanced FIFTP and hence, Mahmoodirad et al.’s approach fails to find the IF optimal solution of unbalanced FIFTPs. It is obvious that to overcome this limitation of Mahmoodirad et al.’s approach, there is need to propose a method to transform an unbalanced FIFTP into a balanced FIFTP. Therefore, in this paper, a new method (named as JMD method) is proposed to transform an unbalanced FIFTP into a balanced FIFTP. Keywords Transportation problem TIFN Intuitionistic fuzzy transportation problem Optimal solution
1 Introduction The cost of each product depends upon several factors. One of these factors is transportation cost. Although several methods have been proposed in the literature to find the optimal quantity of the product that should be supplied from a source to a destination, the total transportation cost is minimum. But, all these methods can be used only if all the required parameters are precisely known. However, it is not a realistic assumption as the transportation cost between two fixed places may vary due to several reasons, like weather condition, traffic jam, route diversion, etc.; the availability of the product may vary due to insufficient availability of the raw material, strike of workers, etc.; the
Communicated by V. Loia. & Akansha Mishra [email protected] Amit Kumar [email protected] 1
School of Mathematics, Thapar Institute of Engineering and Technology, Patiala, Punjab, India
demand of the product may vary due to unexpected change in weather, unexpected arrivals of tourists, etc. One way, adopted by several researchers to handle such uncertain data, is to represent the data as fuzzy set (Zadeh 1965) and intuitionistic fuzzy set (Atanassov 1986). Due to the same reason, several researchers have used fuzzy set and intuitionistic fuzzy set to represent the parameters of the transportation problems (Aggarwal and Gupta 2017; Basirzadeh 2011; Das et al. 2018; Dinager and Palanivel 2009; Ganesan and Veeramani 2006; Kaur and Kumar 2012; Kumar and Hussain 2016; Liu 2016; Mahmoodirad et al. 2014, 2018; Mohideen and Kumar 2010; Nagoorgani and Razak 2006;
Data Loading...
