New Method to Posynomial Geometric Programming of Trapezoidal Fuzzy Numbers

2013 ◽  
Vol 5 (3) ◽  
pp. 373-380
Author(s):  
Zeinab Kheiri ◽  
Faezeh Zahmatkesh ◽  
Bing-Yuan Cao
Keyword(s):  
Geometric Programming ◽  
Fuzzy Numbers ◽  
New Method ◽  
Trapezoidal Fuzzy Numbers

Trapezoidal fuzzy model to optimize transportation problem

2016 ◽  
Vol 07 (03) ◽  
pp. 1650028 ◽  
Author(s):  
Nirbhay Mathur ◽  
Pankaj Kumar Srivastava ◽  
Ajit Paul
Keyword(s):  
Transportation Problem ◽  
Fuzzy Numbers ◽  
Fuzzy Model ◽  
Optimal Solution ◽  
Transportation Cost ◽  
New Method ◽  
Trapezoidal Fuzzy Numbers ◽  
North West ◽  
Fuzzy Environment ◽  
Practical Usefulness

The main aim of this paper is to develop an approach based on trapezoidal fuzzy numbers to optimize transportation problem in fuzzy environment. The present algorithm has representation of availability, demand and transportation cost as trapezoidal fuzzy numbers. This algorithm is found quicker in terms of runtime as comparison to fuzzy VAM discussed in [Kaur A., Kumar A., A new method for solving fuzzy transportation problem using ranking function, Appl. Math. Model. 35:5652–5661, 2011; Ismail Mohideen S., Senthil Kumar P., A comparative study on transportation problem in fuzzy environment, Int. J. Math. Res. 2:151–158, 2010]. On the other hand this technique gives much better results than some classical methods like north-west corner and least cost method. Another benefit of this algorithm is that for certain transportation problems it directly gives optimal solution. It is one of the simplest methods to apply and perceive. Practical usefulness of the new method over other existing methods is demonstrated with two numerical examples.

scholarly journals A New Method to Optimize the Satisfaction Level of the Decision Maker in Fuzzy Geometric Programming Problems

Mathematics ◽  
2019 ◽  
Vol 7 (5) ◽  
pp. 464
Author(s):  
Armita Khorsandi ◽  
Bing-Yuan Cao ◽  
Hadi Nasseri
Keyword(s):  
Mathematical Modeling ◽  
Objective Function ◽  
Programming Problem ◽  
Decision Maker ◽  
Geometric Programming ◽  
Fuzzy Numbers ◽  
Optimal Solution ◽  
New Method ◽  
Satisfaction Level ◽  
Simple Parameter

Geometric programming problems are well-known in mathematical modeling. They are broadly used in diverse practical fields that are contemplated through an appropriate methodology. In this paper, a multi-parametric vector α is proposed for approaching the highest decision maker satisfaction. Hitherto, the simple parameter α , which has a scalar role, has been considered in the problem. The parameter α is a vector whose range is within the region of the satisfaction area. Conventionally, it is assumed that the decision maker is sure about the parameters, but, in reality, it is mostly hesitant about them, so the parameters are presented in fuzzy numbers. In this method, the decision maker can attain different satisfaction levels in each constraint, and even full satisfaction can be reached in some constraints. The goal is to find the highest satisfaction degree to maintain an optimal solution. Moreover, the objective function is turned into a constraint, i.e., one more dimension is added to n-dimensional multi-parametric α . Thus, the fuzzy geometric programming problem under this multi-parametric vector α ∈ ( 0 , 1 ] n + 1 gives a maximum satisfaction level to the decision maker. A numerical example is presented to illustrate the proposed method and the superiority of this multi-parametric α over the simple one.

scholarly journals Sensitivity Analysis for Interval-valued Fully Fuzzy Linear Programming Problems

2012 ◽  
Vol 10 (6) ◽  
Author(s):  
Neha Bhatia ◽  
Amit Kumar
Keyword(s):  
Sensitivity Analysis ◽  
Linear Programming ◽  
Fuzzy Numbers ◽  
Fuzzy Linear Programming ◽  
New Method ◽  
Trapezoidal Fuzzy Numbers ◽  
Linear Programming Problems ◽  
Interval Valued

In previous studies, it is pointed out that in several situations it is better to use interval-valued fuzzy numbers insteadof triangular or trapezoidal fuzzy numbers. But till now, there is no method that deals with the sensitivity analysis ofsuch linear programming problems in which all the parameters are represented by interval-valued fuzzy numbers. Inthis paper, a new method is proposed for the sensitivity analysis. Finally, the proposed method is illustrated using anumerical example.

A new method for trapezoidal fuzzy numbers ranking based on the Shadow length and its application to manager's risk taking

2014 ◽  
Vol 26 (1) ◽  
pp. 77-89 ◽  
Author(s):  
Nasser Shahsavari-Pour ◽  
Reza Tavakkoli-Moghaddam ◽  
Mohammad-Ali Basiri
Keyword(s):  
Risk Taking ◽  
Fuzzy Numbers ◽  
New Method ◽  
Trapezoidal Fuzzy Numbers

scholarly journals Mehar Methods for Fuzzy Optimal Solution and Sensitivity Analysis of Fuzzy Linear Programming with Symmetric Trapezoidal Fuzzy Numbers

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Sukhpreet Kaur Sidhu ◽  
Amit Kumar ◽  
S. S. Appadoo
Keyword(s):  
Sensitivity Analysis ◽  
Linear Programming ◽  
Fuzzy Numbers ◽  
Optimal Solution ◽  
Fuzzy Linear Programming ◽  
New Method ◽  
Real Numbers ◽  
Trapezoidal Fuzzy Numbers ◽  
Fuzzy Optimal Solution ◽  
Linear Programming Problems

The drawbacks of the existing methods to obtain the fuzzy optimal solution of such linear programming problems, in which coefficients of the constraints are represented by real numbers and all the other parameters as well as variables are represented by symmetric trapezoidal fuzzy numbers, are pointed out, and to resolve these drawbacks, a new method (named as Mehar method) is proposed for the same linear programming problems. Also, with the help of proposed Mehar method, a new method, much easy as compared to the existing methods, is proposed to deal with the sensitivity analysis of the same type of linear programming problems.

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