BOUNDED LINEAR PROGRAMS WITH TRAPEZOIDAL FUZZY NUMBERS

2010 ◽  
Vol 18 (03) ◽  
pp. 269-286 ◽  
Author(s):  
ALI EBRAHIMNEJAD ◽  
SEYED HADI NASSERI ◽  
FARHAD HOSSEINZADEH LOTFI
Keyword(s):  
Linear Programming ◽  
Fuzzy Numbers ◽  
Natural Extension ◽  
Upper Bounds ◽  
Linear Programs ◽  
Bounded Linear ◽  
New Approach ◽  
Trapezoidal Fuzzy Numbers ◽  
Linear Programming Problems ◽  
Crisp Linear Programming

Recently Ganesan and Veeramani introduced a new approach for solving a kind of linear programming problems involving symmetric trapezoidal fuzzy numbers without converting them to the crisp linear programming problems. But their approach is not efficient for situations in which some or all variables are restricted to lie within fuzzy lower and fuzzy upper bounds. In this paper, by a natural extension of their approach we obtain some new results leading to a new method to overcome this shortcoming.

scholarly journals A Mathematical Model for Solving the Linear Programming Problems Involving Trapezoidal Fuzzy Numbers via Interval Linear Programming Problems

2021 ◽  
Vol 2021 ◽  
pp. 1-17
Author(s):  
Ladji Kané ◽  
Daouda Diawara ◽  
Lassina Diabaté ◽  
Moussa Konaté ◽  
Souleymane Kané ◽  
...  
Keyword(s):  
Linear Programming ◽  
Fuzzy Numbers ◽  
Strong Duality ◽  
Optimal Solutions ◽  
Interval Numbers ◽  
Complementary Slackness ◽  
Trapezoidal Fuzzy Numbers ◽  
Linear Programming Problems ◽  
Primal And Dual Problems ◽  
Primal And Dual

We define linear programming problems involving trapezoidal fuzzy numbers (LPTra) as the way of linear programming problems involving interval numbers (LPIn). We will discuss the solution concepts of primal and dual linear programming problems involving trapezoidal fuzzy numbers (LPTra) by converting them into two linear programming problems involving interval numbers (LPIn). By introducing new arithmetic operations between interval numbers and fuzzy numbers, we will check that both primal and dual problems have optimal solutions and the two optimal values are equal. Also, both optimal solutions obey the strong duality theorem and complementary slackness theorem. Furthermore, for illustration, some numerical examples are used to demonstrate the correctness and usefulness of the proposed method. The proposed algorithm is flexible, easy, and reasonable.

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.

scholarly journals Linear Programming Problem with Interval Type 2 Fuzzy Coefficients and an Interpretation for Its Constraints

2016 ◽  
Vol 2016 ◽  
pp. 1-11 ◽  
Author(s):  
A. Srinivasan ◽  
G. Geetharamani
Keyword(s):  
Linear Programming ◽  
Fuzzy Numbers ◽  
Optimal Solution ◽  
Fuzzy Linear Programming ◽  
Trapezoidal Fuzzy Numbers ◽  
Degree Of Satisfaction ◽  
Linear Programming Problems ◽  
Interval Type ◽  
Perfectly Normal

Interval type 2 fuzzy numbers are a special kind of type 2 fuzzy numbers. These numbers can be described by triangular and trapezoidal shapes. In this paper, first, perfectly normal interval type 2 trapezoidal fuzzy numbers with their left-hand and right-hand spreads and their core have been introduced, which are normal and convex; then a new type of fuzzy arithmetic operations for perfectly normal interval type 2 trapezoidal fuzzy numbers has been proposed based on the extension principle of normal type 1 trapezoidal fuzzy numbers. Moreover, in this proposal, linear programming problems with resources and technology coefficients are perfectly normal interval type 2 fuzzy numbers. To solve this kind of fuzzy linear programming problems, a method based on the degree of satisfaction (or possibility degree) of the constraints has been introduced. In this method the fulfillment of the constraints can be measured with the help of ranking method of fuzzy numbers. Optimal solution is obtained at different degree of satisfaction by using Barnes algorithm with the help of MATLAB. Finally, the optimal solution procedure is illustrated with numerical example.

Bounded Primal Simplex Algorithm for Bounded Linear Programming with Fuzzy Cost Coefficients

2013 ◽  
pp. 40-63
Author(s):  
Ali Ebrahimnejad ◽  
Seyed Hadi Nasseri ◽  
Sayyed Mehdi Mansourzadeh
Keyword(s):  
Linear Programming ◽  
Auxiliary Problem ◽  
Simplex Algorithm ◽  
Upper Bounds ◽  
Bounded Linear ◽  
Fuzzy Variables ◽  
Decision Variables ◽  
Bounded Variables ◽  
Linear Programming Problems ◽  
Fuzzy Cost

In most practical problems of linear programming problems with fuzzy cost coefficients, some or all variables are restricted to lie within lower and upper bounds. In this paper, the authors propose a new method for solving such problems called the bounded fuzzy primal simplex algorithm. Some researchers used the linear programming problem with fuzzy cost coefficients as an auxiliary problem for solving linear programming with fuzzy variables, but their method is not efficient when the decision variables are bounded variables in the auxiliary problem. In this paper the authors introduce an efficient approach to overcome this shortcoming. The bounded fuzzy primal simplex algorithm starts with a primal feasible basis and moves towards attaining primal optimality while maintaining primal feasibility throughout. This algorithm will be useful for sensitivity analysis using primal simplex tableaus.

scholarly journals Optimization of LR -Type Fully Bipolar Fuzzy Linear Programming Problems

2021 ◽  
Vol 2021 ◽  
pp. 1-36
Author(s):  
Muhammad Athar Mehmood ◽  
Muhammad Akram ◽  
Majed G. Alharbi ◽  
Shahida Bashir
Keyword(s):  
Linear Programming ◽  
Programming Problem ◽  
Linear Programming Problem ◽  
Fuzzy Numbers ◽  
Equality Constraints ◽  
Fuzzy Linear Programming ◽  
Numerical Examples ◽  
Linear Programming Problems ◽  
Formula Type ◽  
Crisp Linear Programming

In this study, we present a technique to solve LR -type fully bipolar fuzzy linear programming problems (FBFLPPs) with equality constraints. We define LR -type bipolar fuzzy numbers and their arithmetic operations. We discuss multiplication of LR -type bipolar fuzzy numbers. Furthermore, we develop a method to solve LR -type FBFLPPs with equality constraints involving LR -type bipolar fuzzy numbers as parameters and variables. Moreover, we define ranking for LR -type bipolar fuzzy numbers which transform the LR -type FBFLPP into a crisp linear programming problem. Finally, we consider numerical examples to illustrate the proposed method.

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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