scholarly journals ALGORITMA FUZZY GOAL PROGRAMMING UNTUK MASALAH PEMROGRAMAN BILEVEL MULTIOBJEKTIF

2018 ◽  
Vol 10 (1) ◽  
pp. 1
Author(s):  
Syarifah Inayati
Keyword(s):  
Membership Function ◽  
Goal Programming ◽  
Fuzzy Goal Programming ◽  
Hierarchical Organization ◽  
Decision Makers ◽  
Decision Variables ◽  
Fuzzy Goals ◽  
Fuzzy Goal ◽  
Upper Level ◽  
The Membership Function

Bilevel multiobjective programming problems are mathematical programming that solves the problem of planning with two decision makers (DM) in two level or hierarchical organization with the objective function of each organization can be more than one. In this paper, we discussed the special case of this problem with single decision maker at the upper level and multiple decision makers at the lower level. This problem can be solved using fuzzy goal programming (FGP) approach. In this approach, the membership function for the defined fuzzy goals of all objective functions of DMs at the two levels was developed first in the model formulation of the problem. Thus the membership function for vector of fuzzy goals of the decision variables controlled by the leader. Then FGP approach requires the leader to set goals for each objective that he/she wishes to attain. A preferred solution is then defined for minimizes the deviations from the set of goals. Numerical example is provided to illustrate the approach.

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.

scholarly journals Fuzzy Goal Programming Procedure to Bilevel Multiobjective Linear Fractional Programming Problems

2010 ◽  
Vol 2010 ◽  
pp. 1-15 ◽  
Author(s):  
Mahmoud A. Abo-Sinna ◽  
Ibrahim A. Baky
Keyword(s):  
Goal Programming ◽  
Fractional Programming ◽  
Programming Model ◽  
Fuzzy Goal Programming ◽  
Decision Makers ◽  
Membership Functions ◽  
Linear Fractional Programming ◽  
Goal Programming Model ◽  
Fuzzy Goals ◽  
Fuzzy Goal

This paper presents a fuzzy goal programming (FGP) procedure for solving bilevel multiobjective linear fractional programming (BL-MOLFP) problems. It makes an extension work of Moitra and Pal (2002) and Pal et al. (2003). In the proposed procedure, the membership functions for the defined fuzzy goals of the decision makers (DMs) objective functions at both levels as well as the membership functions 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. Then a fuzzy goal programming model to minimize the group regret of degree of satisfactions of both the decision makers is developed to achieve the highest degree (unity) of each of the defined membership function goals to the extent possible by minimizing their deviational variables and thereby obtaining the most satisfactory solution for both decision makers. 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. Illustrative numerical example is given to demonstrate the procedure.

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.

scholarly journals Fuzzy Goal Programming with an Imprecise Intuitionistic Fuzzy Preference Relations

Symmetry ◽  
2020 ◽  
Vol 12 (9) ◽  
pp. 1548
Author(s):  
Abdul Razzaq Abdul Ghaffar ◽  
Md. Gulzarul Hasan ◽  
Zubair Ashraf ◽  
Mohammad Faisal Khan
Keyword(s):  
Goal Programming ◽  
Distance Measure ◽  
Optimization Problems ◽  
Fuzzy Goal Programming ◽  
Preference Relations ◽  
Intuitionistic Fuzzy ◽  
Fuzzy Preference Relations ◽  
Fuzzy Goals ◽  
Fuzzy Goal ◽  
Fuzzy Preference

Fuzzy goal programming (FGP) is applied to solve fuzzy multi-objective optimization problems. In FGP, the weights are associated with fuzzy goals for the preference among them. However, the hierarchy within the fuzzy goals depends on several uncertain criteria, decided by experts, so the preference relations are not always easy to associate with weight. Therefore, the preference relations are provided by the decision-makers in terms of linguistic relationships, i.e., goal A is slightly or moderately or significantly more important than goal B. Due to the vagueness and ambiguity associated with the linguistic preference relations, intuitionistic fuzzy sets (IFSs) are most efficient and suitable to handle them. Thus, in this paper, a new fuzzy goal programming with intuitionistic fuzzy preference relations (FGP-IFPR) approach is proposed. In the proposed FGP-IFPR model, an achievement function has been developed via the convex combination of the sum of individual grades of fuzzy objectives and amount of the score function of IFPRs among the fuzzy goals. As an extension, we presented the linear and non-linear, namely, exponential and hyperbolic functions for the intuitionistic fuzzy preference relations (IFPRs). A study has been made to compare and analyze the three FGP-IFPR models with intuitionistic fuzzy linear, exponential, and hyperbolic membership and non-membership functions. For solving all three FGP-IFPR models, the solution approach is developed that established the corresponding crisp formulations, and the optimal solution are obtained. The validations of the proposed FGP-IFPR models have been presented with an experimental investigation of a numerical problem and a banking financial statement problem. A newly developed distance measure is applied to compare the efficiency of proposed models. The minimum value of the distance function represents a better and efficient model. Finally, it has been found that for the first illustrative problem considered, the exponential FGP-IFPR model performs best, whereas for the second problem, the hyperbolic FGP-IFPR model performs best and the linear FGP-IFPR model shows worst in both cases.

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.

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