scholarly journals Duality theory for the matrix linear programming problem

1984 ◽  
Vol 104 (1) ◽  
pp. 47-52 ◽  
Author(s):  
H.W Corley
Keyword(s):  
Linear Programming ◽  
Programming Problem ◽  
Linear Programming Problem ◽  
Duality Theory ◽  
The Matrix

scholarly journals Calculating Fuzzy Inverse Matrix Using Linear Programming Problem: An Improved Approach

2021 ◽  
pp. 983-996
Author(s):  
Fatemeh Babakordi ◽  
Nemat Allah Taghi-Nezhad
Keyword(s):  
Linear Programming ◽  
Programming Problem ◽  
Linear Programming Problem ◽  
Fuzzy Numbers ◽  
Equation System ◽  
Matrix Inverse ◽  
Fuzzy Matrix ◽  
Linear Equation System ◽  
The Matrix ◽  
Left And Right

Calculating the matrix inverse is a key point in solving linear equation system, which involves complex calculations, particularly  when the matrix elements are  (Left and Right) fuzzy numbers. In this paper, first, the method of Kaur and Kumar for calculating the matrix inverse is reviewed, and its disadvantages are discussed. Then, a new method is proposed to determine the inverse of  fuzzy matrix based on linear programming problem. It is demonstrated that the proposed method is capable of overcoming the shortcomings of the previous matrix inverse. Numerical examples are utilized to verify the performance and applicability of the proposed method.

scholarly journals A comparative study on interval arithmetic operations with intuitionistic fuzzy numbers for solving an intuitionistic fuzzy multi–objective linear programming problem

2017 ◽  
Vol 27 (3) ◽  
pp. 563-573 ◽  
Author(s):  
Rajendran Vidhya ◽  
Rajkumar Irene Hepzibah
Keyword(s):  
Linear Programming ◽  
Programming Problem ◽  
Linear Programming Problem ◽  
Fuzzy Numbers ◽  
Optimization Method ◽  
Arithmetic Operations ◽  
Intuitionistic Fuzzy Numbers ◽  
Multi Objective ◽  
Intuitionistic Fuzzy ◽  
Interval Valued

AbstractIn a real world situation, whenever ambiguity exists in the modeling of intuitionistic fuzzy numbers (IFNs), interval valued intuitionistic fuzzy numbers (IVIFNs) are often used in order to represent a range of IFNs unstable from the most pessimistic evaluation to the most optimistic one. IVIFNs are a construction which helps us to avoid such a prohibitive complexity. This paper is focused on two types of arithmetic operations on interval valued intuitionistic fuzzy numbers (IVIFNs) to solve the interval valued intuitionistic fuzzy multi-objective linear programming problem with pentagonal intuitionistic fuzzy numbers (PIFNs) by assuming differentαandβcut values in a comparative manner. The objective functions involved in the problem are ranked by the ratio ranking method and the problem is solved by the preemptive optimization method. An illustrative example with MATLAB outputs is presented in order to clarify the potential approach.

A Fast Approach to Solve Matrix Games with Payoffs of Trapezoidal Fuzzy Numbers

2016 ◽  
Vol 33 (06) ◽  
pp. 1650047 ◽  
Author(s):  
Sanjiv Kumar ◽  
Ritika Chopra ◽  
Ratnesh R. Saxena
Keyword(s):  
Linear Programming ◽  
Linear Programming Problem ◽  
Fuzzy Numbers ◽  
Optimization Problems ◽  
Fuzzy Linear Programming ◽  
Matrix Game ◽  
Matrix Games ◽  
Trapezoidal Fuzzy Numbers ◽  
Fast Approach ◽  
The Matrix

The aim of this paper is to develop an effective method for solving matrix game with payoffs of trapezoidal fuzzy numbers (TrFNs). The method always assures that players’ gain-floor and loss-ceiling have a common TrFN-type fuzzy value and hereby any matrix game with payoffs of TrFNs has a TrFN-type fuzzy value. The matrix game is first converted to a fuzzy linear programming problem, which is converted to three different optimization problems, which are then solved to get the optimum value of the game. The proposed method has an edge over other method as this focuses only on matrix games with payoff element as symmetric trapezoidal fuzzy number, which might not always be the case. A numerical example is given to illustrate the method.

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