A Maximin Approach for the Bi-criteria 0–1 Random Fuzzy Programming Problem Based on the Necessity Measure

2009 ◽  
Author(s):  
Takashi Hasuike ◽  
Hideki Katagiri ◽  
Hiroaki Ishii ◽  
Sio-Iong Ao ◽  
Alan Hoi-Shou Chan ◽  
...  
Keyword(s):  
Programming Problem ◽  
Fuzzy Programming ◽  
Necessity Measure

Possibilistic Linear Programming Problems involving Normal Random Variables

2016 ◽  
Vol 5 (3) ◽  
pp. 1-13 ◽  
Author(s):  
Suresh Kumar Barik ◽  
M. P. Biswal
Keyword(s):  
Linear Programming ◽  
Programming Problem ◽  
Random Variables ◽  
Fuzzy Programming ◽  
Solution Procedure ◽  
Mathematical Programming Problem ◽  
Possibility Distribution ◽  
Linear Programming Problems ◽  
The Right ◽  
Possibilistic Linear Programming

A new solution procedure of possibilistic linear programming problem is developed involving the right hand side parameters of the constraints as normal random variables with known means and variances and the objective function coefficients are considered as triangular possibility distribution. In order to solve the proposed problem, convert the problem into a crisp equivalent deterministic multi-objective mathematical programming problem and then solved by using fuzzy programming method. A numerical example is presented to illustrate the solution procedure and developed methodology.

Multiobjective Random Fuzzy Linear Programming Problems Based on the Possibility Maximization Model

2009 ◽  
Vol 13 (4) ◽  
pp. 373-379 ◽  
Author(s):  
Takashi Hasuike ◽  
◽  
Hideki Katagiri ◽  
Hiroaki Ishii ◽  
Keyword(s):  
Linear Programming ◽  
Programming Problem ◽  
Fuzzy Programming ◽  
Fuzzy Linear Programming ◽  
Maximization Problem ◽  
Deterministic Equivalent ◽  
Linear Programming Problems ◽  
Previous Solution ◽  
Fuzzy Goal ◽  
Equivalent Problems

Two multiobjective random fuzzy programming problems considered based on the possibility maximization model using possibilistic and stochastic programming are not initially well defined due to the random variables and fuzzy numbers included. To solve them analytically, probability criteria are set for objective functions and chance constraints are introduced. Taking into account the decision maker’s subjectivity and the original plan’s flexibility, a fuzzy goal is introduced for each objective function. The original problems are then changed into deterministic equivalent problems to make the possibility fractile optimization problem equivalent to a linear programming problem. The possibility maximization problem for probability is changed into a nonlinear programming problem, and an analytical solution is constructed extending previous solution approaches.

scholarly journals Modelling and Allocation of Crops: Mathematical Programming Approach

2019 ◽  
pp. 1-5
Author(s):  
M. A. Lone ◽  
S. A. Mir ◽  
Tabasum Mushtaq
Keyword(s):  
Mathematical Programming ◽  
Programming Problem ◽  
Fuzzy Programming ◽  
Programming Approach ◽  
Cropping Pattern ◽  
Vegetable Crops ◽  
Mathematical Programming Approach ◽  
Programming Techniques ◽  
Total Profit ◽  
Optimal Cropping

Mathematical programming techniques are commonly used by decision makers for achieving efficiency in agricultural production planning. Due to increasing demands of growing population of world, one needs to utilize the limited available resources in the most efficient and economic way. In this paper, the fractional programming problem is formulated and is used to determine the optimal cropping pattern of vegetable crops in such a way that the total profit is maximized. The solution of the formulated Fuzzy programming problem is obtained using LINGO.

FUZZY GOAL PROGRAMMING VS ORDINARY FUZZY PROGRAMMING APPROACH FOR MULTI OBJECTIVE PROGRAMMING PROBLEM

2013 ◽  
Vol 22 ◽  
pp. 757-761 ◽  
Author(s):  
KAILASH LACHHWANI
Keyword(s):  
Programming Problem ◽  
Membership Function ◽  
Goal Programming ◽  
Fuzzy Programming ◽  
Fuzzy Goal Programming ◽  
Programming Approach ◽  
Perpendicular Distance ◽  
Multi Objective Programming ◽  
Fuzzy Goals ◽  
Fuzzy Goal

This paper presents the comparison between two solution methodologies Fuzzy Goal Programming (FGP) and ordinary Fuzzy Programming (FP) for multiobjective programming problem. Ordinary fuzzy programming approach is used to develop the solution algorithm for multiobjective functions which works for the minimization of the perpendicular distances between the parallel hyper planes at the optimum points of the objective functions. Suitable membership function is defined as the supremum perpendicular distance and a compromise optimum solution is obtained as a result of minimization of supremum perpendicular distance. Whereas, In the FGP model formulation, firstly the objectives are transformed into fuzzy goals (membership functions) by means of assigning an aspiration level to each of them and suitable membership function is defined for each objectives. Then achievement of the highest membership value of each of fuzzy goals is formulated by minimizing the negative deviational variables.

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