Abstract
In this paper, a new approach is introduced to solve transportation problem with type-2-fuzzy variables. In most of the real-life situations, the available data do not happen to be crisp in nature. It gives rise to the fuzzy transportation problem (FTP). This proposed approach concentrates on the problem when the vertical slices of type-2-fuzzy sets (T2FSs) are trapezoidal fuzzy numbers (TFNs). The original problem reduces to three different linear programming problems (LPPs) which are solved using the simplex algorithm. Then the effectiveness of this paper is discussed with numerical example. In conclusion, the significance of the paper and the scope of future study are discussed.
Highlights
The transportation problem (TP) is one of the important linear programming problem which arises in many real-life situations
In contrast to classical transportation problem, we have considered all the constraints and variables to be type-2-fuzzy variables which has given rise to fuzzy transportation problem
In most of the existing methods, in order to solve the problems, the original problem is transformed into a single crisp problem and which comes up with crisp solution
Summary
The transportation problem (TP) is one of the important linear programming problem which arises in many real-life situations. 3. Basic Operations of Fuzzy Sets Here we define some binary operations of fuzzy set in the universe of real numbers using extension principle. Addition: Let A and B be two fuzzy sets in the universe of real numbers. Supxy=zmin{μA(x), μB(y)} = 0 i.e., the membership function of μA⊗ B is given by, μA⊗B(x). Some order relations in the set of trapezoidal fuzzy numbers belonging to F[0,1] are needed to be introduced for formulating the proposed model. In real-life situation, the decision maker may not be provided with crisp data In this model, all the given data and variables are considered to be type2-fuzzy variables. If we split the above fuzzy problem in coordinate wise, we get three mutually different crisp LPPs. Considering the first coordinate xij we obtain the LPP, is defined in Model 2 as follows: Model 2 Minimize mn. The required solution would be (Z1∗, T(Z2∗,Z3∗))
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callMore From: International Journal of Mathematical, Engineering and Management Sciences
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
