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 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.

scholarly journals Portfolio selection problem: a comparison of fuzzy goal programming and linear physical programming

2016 ◽  
Vol 6 (2) ◽  
pp. 121-128 ◽  
Author(s):  
Fusun Kucukbay ◽  
Ceyhun Araz
Keyword(s):  
Portfolio Selection ◽  
Goal Programming ◽  
Optimal Solution ◽  
Good Alternative ◽  
Fuzzy Goal Programming ◽  
Selection Problem ◽  
Physical Programming ◽  
Portfolio Selection Problem ◽  
Linear Physical Programming ◽  
Fuzzy Goal

Investors have limited budget and they try to maximize their return with minimum risk. Therefore this study aims to deal with the portfolio selection problem. In the study two criteria are considered which are expected return, and risk. In this respect, linear physical programming (LPP) technique is applied on Bist 100 stocks to be able to find out the optimum portfolio. The analysis covers the period April 2009- March 2015. This period is divided into two; April 2009-March 2014 and April 2014 – March 2015. April 2009-March 2014 period is used as data to find an optimal solution. April 2014-March 2015 period is used to test the real performance of portfolios. The performance of the obtained portfolio is compared with that obtained from fuzzy goal programming (FGP). Then the performances of both method, LPP and FGP are compared with BIST 100 in terms of their Sharpe Indexes. The findings reveal that LPP for portfolio selection problem is a good alternative to FGP.

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