scholarly journals Two Weighted Fuzzy Goal Programming Methods to Solve Multiobjective Goal Programming Problem

2012 ◽  
Vol 2012 ◽  
pp. 1-20 ◽  
Author(s):  
Mousumi Gupta ◽  
Debasish Bhattacharjee
Keyword(s):  
Goal Programming ◽  
Real Life ◽  
Fuzzy Goal Programming ◽  
Relative Importance ◽  
Objective Functions ◽  
Weighting Method ◽  
Fuzzy Operator ◽  
New Methods ◽  
Aspiration Levels ◽  
Fuzzy Goal

We propose two new methods to find the solution of fuzzy goal programming (FGP) problem by weighting method. Here, the relative weights represent the relative importance of the objective functions. The proposed methods involve one additional goal constraint by introducing only underdeviation variables to the fuzzy operatorλ(resp., 1-λ), which is more efficient than some well-known existing methods such as those proposed by Zimmermann, Hannan, Tiwari, and Mohamed. Mohamed proposed that every fuzzy linear program has an equivalent weighted linear goal program where the weights are restricted as the reciprocals of the admissible violation constants. But the above proposition of Mohamed is not always true. Furthermore, the proposed methods are easy to apply in real-life situations which give better solution in the sense that the objective values are sufficiently closer to their aspiration levels. Finally, for illustration, two real examples are used to demonstrate the correctness and usefulness of the proposed methods.

ÇOK AMAÇLI ÜRETİM SÜREÇLERİNİN BULANIK KARAR ORTAMINDA İNCELENMESİ: BULANIK HEDEF PROGRAMLAMA VE BİR UYGULAMA

2018 ◽  
Vol 6 (2) ◽  
Author(s):  
Nurullah UMARUSMAN
Keyword(s):  
Decision Maker ◽  
Goal Programming ◽  
Programming Model ◽  
Fuzzy Goal Programming ◽  
Objective Functions ◽  
Multiobjective Linear Programming ◽  
Aspiration Levels ◽  
Ideal Solutions ◽  
Fuzzy Goals ◽  
Fuzzy Goal

If the aspiration levels of the goals are set realistically by the decision maker in Goal Programming, the deviations from the goals could occur too high as a result of the solution.  It leads the decision maker to make incorrect decisions. It is also the case for Fuzzy Goal Programming. When the fuzzy goals and their tolerance levels are not defined properly, there will be deviations from the goals. Additionally, if there are constraint functions besides the goals in the problems of either Goal Programming or Fuzzy Goal Programming, the solutions will deviate greatly from the incorrectly defined goal values as the solutions are realized based on the constraints. It is because the goals are limited by the constraints. This study firstly defines the positive and negative ideal solutions of objective functions in the problem organized in Multiobjective Linear Programming model for a business which manufactures hand crafted furniture. Afterwards, each objective is transformed into fuzzy goals using positive and negative ideal solutions.

WEIGHTED ADDITIVE MODELS FOR SOLVING FUZZY GOAL PROGRAMMING PROBLEMS

2008 ◽  
Vol 25 (05) ◽  
pp. 715-733 ◽  
Author(s):  
M. A. YAGHOOBI ◽  
D. F. JONES ◽  
M. TAMIZ
Keyword(s):  
Decision Making ◽  
Goal Programming ◽  
Real Life ◽  
Additive Model ◽  
Multiple Criteria Decision Making ◽  
Multiple Criteria ◽  
Fuzzy Goal Programming ◽  
Additive Models ◽  
New Model ◽  
Fuzzy Goal

Weighted additive models are well known for dealing with multiple criteria decision making problems. Fuzzy goal programming is a branch of multiple criteria decision making which has been applied to solve real life problems. Several weighted additive models are introduced to handle fuzzy goal programming problems. These models are based on two approaches in fuzzy goal programming namely goal programming and fuzzy programming techniques. However, some of these models are not able to solve all kinds of fuzzy goal programming problems and some of them that appear in current literature suffer from a lack of precision in their formulations. This paper focuses on weighed additive models for fuzzy goal programming. It explains the oversights within some of them and proposes the necessary corrections. A new improved weighted additive model for solving fuzzy goal programming problems is introduced. The relationships between the new model and some of the existing models are discussed and proved. A numerical example is given to demonstrate the validity and strengths of the new model.

scholarly journals Solving multi-level multiobjective fractional programming problem with rough interval parameter under neutrosophic environment

2021 ◽  
Author(s):  
FIROZ AHMAD
Keyword(s):  
Goal Programming ◽  
Fractional Programming ◽  
Optimal Solution ◽  
Fuzzy Goal Programming ◽  
Programming Algorithm ◽  
Objective Functions ◽  
Multiobjective Fractional Programming ◽  
Upper Approximation ◽  
Fuzzy Goal ◽  
Multi Level

In this study, a novel algorithm is developed to solve the multi-level multiobjective fractional programming problems, using the idea of a neutrosophic fuzzy set. The co-efficients in each objective functions is assumed to be rough intervals. Furthermore, the objective functions are transformed into two sub-problems based on lower and upper approximation intervals. The marginal evaluation of pre-determined neutrosophic fuzzy goals for all objective functions at each level is achieved by different membership functions, such as truth, indeterminacy/neutral, and falsity degrees in neutrosophic uncertainty. In addition, the neutrosophic fuzzy goal programming algorithm is proposed to attain the highest degrees of each marginal evaluation goals by reducing their deviational variables and consequently obtain the optimal solution for all the decision-makers at all levels. To verify and validate the proposed neutrosophic fuzzy goal programming techniques, a numerical example is adressed in a hierarchical decision-making environment along with the conclusions.

scholarly journals An Interactive Dynamic Fuzzy Goal Programming for Bi-level Multiobjective Linear Fractional Programming Problems.

2017 ◽  
Vol 12 (12) ◽  
pp. 6991-7007
Author(s):  
MAHMOUD A ABO-SINNA ◽  
Azza H Amer
Keyword(s):  
Membership Function ◽  
Goal Programming ◽  
Fractional Programming ◽  
Fuzzy Goal Programming ◽  
Linear Fractional Programming ◽  
Aspiration Levels ◽  
Fuzzy Goals ◽  
Fuzzy Goal ◽  
Interactive Dynamic ◽  
The Membership Function

This paper presents an interactive dynamic fuzzy goal programming (DFGP) approach for solving bi-level multiobjective linear fractional programming (BL MOLFP) problems with the characteristics of dynamic programming (DP). In the proposed approach, the membership function of the objective goals of a problem with fuzzy aspiration levels are defined first as the membership function for vector of fuzzy goals of the decision variables controlled by first–level decision maker are developed first in the model formulation of the problem. The method of variable change, on the under and over deviational variables of the membership goals associated with the fuzzy goals of the model, is introduced to solve the problem efficiently by using linear goal programming (LGP) methodology. Then, under the framework of preemptive priority based GP, a multi  stage DP model of the problem is used for achievement of the highest degree (unity) of each of the membership functions. In the decision process, the goal satisficing philosophy of GP is used recursively to arrive at the most satisfactory solution and the suggested algorithm to simplify the solution procedure by DP at each stage is proposed. This paper is considered as an extension work of Mahmoud A. Abo-Sinna and Ibrahim A. Baky (2010) by using dynamic approach. Finally, this approach is illustrated by a given numerical example.

Disaster Risk Planning With Fuzzy Goal Programming

Risk Analysis ◽  
2021 ◽  
Author(s):  
Terry R. Rakes ◽  
Jason K. Deane ◽  
Loren P. Rees ◽  
David M. Goldberg
Keyword(s):  
Goal Programming ◽  
Disaster Risk ◽  
Fuzzy Goal Programming ◽  
Fuzzy Goal ◽  
Risk Planning

On Solving Multiobjective Transportation Problems with Fuzzy Random Supply and Demand Using Fuzzy Goal Programming

2017 ◽  
Vol 8 (3) ◽  
pp. 54-81 ◽  
Author(s):  
Animesh Biswas ◽  
Nilkanta Modak
Keyword(s):  
Goal Programming ◽  
Fuzzy Numbers ◽  
Optimal Allocation ◽  
Programming Model ◽  
Fuzzy Goal Programming ◽  
Chance Constrained Programming ◽  
Transportation Problems ◽  
Goal Programming Model ◽  
Fuzzy Goal ◽  
Fuzzy Random

In this article a fuzzy goal programming model is developed to solve multiobjective unbalanced transportation problems with fuzzy random parameters. In model formulation process the cost coefficients of the objectives are considered as fuzzy numbers and the supplies and demands are considered as fuzzy random variables with known fuzzy probability distribution from the view point of probabilistic as well as possibilistic uncertainties involved with the model. A fuzzy programming model is first constructed by applying chance constrained programming methodology in fuzzy environment. Then, the model is decomposed on the basis of the tolerance ranges of the fuzzy numbers associated with it. The individual optimal solution of each decomposed objectives is found in isolation to construct the membership goals of the objectives. Finally, priority based fuzzy goal programming technique is used to achieve the highest degree of each of the defined membership goals to the extent possible by minimizing the under deviational variables and thereby obtaining optimal allocation of products by using distance function in a cost minimizing decision making environment. An illustrative example is solved and compared with existing technique to explore the potentiality of the proposed methodology.

Sign in / Sign up

Export Citation Format

Share Document