scholarly journals Algorithmic Approach for Solving Intuitionistic Fuzzy Transportation Problem

2017 ◽  
Author(s):  
R. Jahir Hussain ◽  
P. Senthil Kumar
Keyword(s):  
Transportation Problem ◽  
Fuzzy Numbers ◽  
Optimal Solution ◽  
Zero Point ◽  
Point Method ◽  
Algorithmic Approach ◽  
Intuitionistic Fuzzy Numbers ◽  
Numerical Example ◽  
Intuitionistic Fuzzy ◽  
Fuzzy Transportation Problem

In this paper, we investigate transportation problem in which supplies and demands are intuitionistic fuzzy numbers. Intuitionistic fuzzy zero point method is proposed to find the optimal solution in terms of triangular intuitionistic fuzzy numbers. A new relevant numerical example is also included.

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 A new Approach for Obtaining Optimal Solution of Unbalanced Fuzzy Transportation Problem

2016 ◽  
Vol 15 (6) ◽  
pp. 6824-6832
Author(s):  
Nidhi Joshi ◽  
Surjeet Singh Chauhan
Keyword(s):  
Transportation Problem ◽  
Fuzzy Numbers ◽  
Optimal Solution ◽  
New Approach ◽  
Trapezoidal Fuzzy Numbers ◽  
Numerical Example ◽  
Fuzzy Optimal Solution ◽  
Fuzzy Transportation Problem ◽  
Ranking Technique

The present paper attempts to study the unbalanced fuzzy transportation problem so as to minimize the transportationcost of products when supply, demand and cost of the products are represented by fuzzy numbers. In this paper, authorsuse Roubast ranking technique to transform trapezoidal fuzzy numbers to crisp numbers and propose a new algorithm tofind the fuzzy optimal solution of unbalanced fuzzy transportation problem. The proposed algorithm is more efficient thanother existing algorithms like simple VAM and is illustrated via numerical example. Also, a comparison between the resultsof the new algorithm and the result of algorithm using simple VAM is provided.

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.

scholarly journals Solving unbalanced intuitionistic fuzzy transportation problem

10.26524/cm61 ◽  
2020 ◽  
Vol 4 (1) ◽  
Author(s):  
Soundararajan S ◽  
Suresh Kumar M
Keyword(s):  
Approximation Method ◽  
Fuzzy Number ◽  
Transportation Problem ◽  
Optimal Solution ◽  
Intuitionistic Fuzzy Number ◽  
Numerical Example ◽  
Intuitionistic Fuzzy ◽  
Triangular Intuitionistic Fuzzy Number ◽  
Fuzzy Transportation Problem ◽  
Number Of Iterations

In this paper, we find the optimal solution for an unbalanced intuitionistic fuzzy transportation problem by using monalisha’s approximation method. The main aim of this method is to avoid large number of iterations. To illustrate this method a numerical example Triangular intuitionistic fuzzy number, unbalanced intuitionistic fuzzy transportation problem, accuracy function.is given.

scholarly journals A note on 'a new approach for solving intuitionistic fuzzy transportation problem of type-2'

2018 ◽  
Author(s):  
P. Senthil Kumar
Keyword(s):  
Transportation Problem ◽  
Real Life ◽  
Optimal Solution ◽  
Simple Method ◽  
Distribution Method ◽  
Intuitionistic Fuzzy Numbers ◽  
Intuitionistic Fuzzy ◽  
Study Results ◽  
Fuzzy Transportation Problem

In real-life decisions, usually we happen to suffer through different states of uncertainties. In order to counter these uncertainties, in this paper, the author formulated a transportation problem in which costs are triangular intuitionistic fuzzy numbers, supplies and demands are crisp numbers. In this paper, a simple method for solving type-2 intuitionistic fuzzy transportation problem (type-2 IFTP) is proposed and optimal solution is obtained without using intuitionistic fuzzy modified distribution method and intuitionistic fuzzy zero point method. So, the proposed method gives the optimal solution directly. The solution procedure is illustrated with the help of three real life numerical examples. Defect of existing results proposed by Singh and Yadav (2016a) is discussed. Validity of Pandian's (2014) method is reviewed. Finally, the comparative study, results and discussion are given.

Methods for Solving Fully Fuzzy Transportation Problems Based on Classical Transportation Methods

2013 ◽  
pp. 328-347 ◽  
Author(s):  
Amit Kumar ◽  
Amarpreet Kaur
Keyword(s):  
Transportation Problem ◽  
Fuzzy Numbers ◽  
Real Life ◽  
Optimal Solution ◽  
Fuzzy Linear Programming ◽  
Programming Formulation ◽  
Transportation Problems ◽  
Fuzzy Optimal Solution ◽  
Linear Programming Formulation ◽  
Fuzzy Transportation Problem

There are several methods, in literature, for finding the fuzzy optimal solution of fully fuzzy transportation problems (transportation problems in which all the parameters are represented by fuzzy numbers). In this paper, the shortcomings of some existing methods are pointed out and to overcome these shortcomings, two new methods (based on fuzzy linear programming formulation and classical transportation methods) are proposed to find the fuzzy optimal solution of unbalanced fuzzy transportation problems by representing all the parameters as trapezoidal fuzzy numbers. The advantages of the proposed methods over existing methods are also discussed. To illustrate the proposed methods a fuzzy transportation problem (FTP) is solved by using the proposed methods and the obtained results are discussed. The proposed methods are easy to understand and to apply for finding the fuzzy optimal solution of fuzzy transportation problems occurring in real life situations.

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