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

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.

Algorithms for solving the optimization problems using fuzzy and intuitionistic fuzzy set

“…After the invention of fuzzy set theory, many authors (for example, Mohideen and Kumar 2010;Sharma et al 2015;Baykasoglu and Subulan 2017;Kumar 2016aKumar , b, 2017aKumar , 2018aSujatha et al 2018;Vidhya and Ganesan 2018;Habib 2018;Bharati 2018;Mishra et al 2018;Saini et al 2018;Ngastiti et al 2018;Maheswari and Ganesan 2018;Sam'an et al 2018;Bisht and Srivastava 2018;Ebrahimnejad and Verdegay 2018a) have solved TPs under fuzzy environment successfully. Similarly, several authors have solved fuzzy assignment problems (FAPs) successfully.…”

Intuitionistic fuzzy solid assignment problems: a software-based approach

“…The following basic definitions like fuzzy set, intuitionistic fuzzy set, intuitionistic fuzzy number, triangular intuitionistic fuzzy number and arithmetic operations on triangular intuitionistic fuzzy number which are found in, Zadeh (1965), Atanassov (1999), Burillo et al (1994), Kumar (2012c, 2013), Varghese and Kuriakose (2012), Kumar and Hussain (2014a, 2015, 2016a, Kumar (2017a, b) are used in this section.…”

The PSK Method for Solving Fully Intuitionistic Fuzzy Assignment Problems With Some Software Tools

“…Malini and Ananthanarayanan (2016) solved fuzzy APs using the ranking of generalized trapezoidal fuzzy numbers. Kumar (2016bKumar ( , 2017b developed the PSK method for solving type-1 and type-3 fuzzy transportation problems. Fuzzy systems: Concepts, methodologies, tools, and applications (Management Association, 2017) discuss the transportation problem under imprecise environments.…”