scholarly journals Two-Stage Intuitionistic Fuzzy Transportation Problem through the Prism of Index Matrices

2021 ◽  
Author(s):  
Velichka Traneva ◽  
Stoyan Tranev
Keyword(s):  
Transportation Problem ◽  
Two Stage ◽  
Intuitionistic Fuzzy ◽  
Fuzzy Transportation Problem

A Novel Ranking Approach to Solving Fully LR-Intuitionistic Fuzzy Transportation Problems

2018 ◽  
Vol 15 (01) ◽  
pp. 95-112 ◽  
Author(s):  
Abhishekh ◽  
A. K. Nishad
Keyword(s):  
Transportation Problem ◽  
Fuzzy Numbers ◽  
Optimal Solution ◽  
Solution Procedure ◽  
Ranking Functions ◽  
Transportation Problems ◽  
Intuitionistic Fuzzy Numbers ◽  
Intuitionistic Fuzzy ◽  
Fuzzy Environment ◽  
Fuzzy Transportation Problem

To the extent of our knowledge, there is no method in fuzzy environment to solving the fully LR-intuitionistic fuzzy transportation problems (LR-IFTPs) in which all the parameters are represented by LR-intuitionistic fuzzy numbers (LR-IFNs). In this paper, a novel ranking function is proposed to finding an optimal solution of fully LR-intuitionistic fuzzy transportation problem by using the distance minimizer of two LR-IFNs. It is shown that the proposed ranking method for LR-intuitionistic fuzzy numbers satisfies the general axioms of ranking functions. Further, we have applied ranking approach to solve an LR-intuitionistic fuzzy transportation problem in which all the parameters (supply, cost and demand) are transformed into LR-intuitionistic fuzzy numbers. The proposed method is illustrated with a numerical example to show the solution procedure and to demonstrate the efficiency of the proposed method by comparison with some existing ranking methods available in the literature.

scholarly journals Value- and Ambiguity-Based Approach for Solving Intuitionistic Fuzzy Transportation Problem with Total Quantity Discounts and Incremental Quantity Discounts

2020 ◽  
Vol 2020 ◽  
pp. 1-21
Author(s):  
C. Veeramani ◽  
M. Joseph Robinson ◽  
S. Vasanthi
Keyword(s):  
Linear Programming ◽  
Transportation Problem ◽  
Fuzzy Numbers ◽  
Quantity Discounts ◽  
Intuitionistic Fuzzy Numbers ◽  
Intuitionistic Fuzzy ◽  
Fuzzy Transportation Problem ◽  
The Cost ◽  
Incremental Quantity Discounts ◽  
Trapezoidal Intuitionistic Fuzzy Numbers

The cost of goods per unit transported from the source to the destination is considered to be fixed regardless of the number of units transported. But, in reality, the cost is often not fixed. Quantity discount is often allowed for large shipments. Furthermore, the transportation cost and the price break quantities are not deterministic. In this study, we introduce the concept of Value- and Ambiguity-based approach for solving the intuitionistic fuzzy transportation problem with total quantity discounts and incremental quantity discounts. Here, the cost and quantity price breakpoints are represented by trapezoidal intuitionistic fuzzy numbers. The Values and Ambiguities are defined as the degree of acceptance and rejection for trapezoidal intuitionistic fuzzy numbers. The trapezoidal intuitionistic fuzzy transportation problem is converted to a parametric transportation problem based on their Value indices and Ambiguity indices. Then, for different Values of the parameter, the transformed problem is reduced to the linear programming problem. Then, the linear programming problem is solved by using the classical methods. The proposed method is demonstrated with a numerical example. In conclusion, the intuitionistic fuzzy transportation problem with total quantity discounts is compared with the intuitionistic fuzzy transportation problem with incremental quantity discounts.

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