A parametric approach to fuzzy multi-objective linear fractional program: An alpha cut based method

Borza, Mojtaba; Rambely, Azmin Sham

doi:10.3233/jifs-212105

Cited by 5 publications

(4 citation statements)

References 27 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…To obtain the pareto optimum solution, Stanojevic and Stanojevic [20] developed a technique for dealing with linear fractional programming problems with uncertain coefficients in the objective function. Borza and Rambely [21] discussed a method for solving linear fractional programming with fuzzy coefficients based on α-cuts and max-min. Ammar and Emsimir [22] solved triangular fuzzy rough integer linear programming (TFRILP) problems with α-level.…”

Section: Bulletin Of Electr Eng and Inf Issn: 2302-9285mentioning

confidence: 99%

A study on the solution of interval linear fractional programming problem

Murugan,

Thamaraiselvan

2024

Bulletin EEI

View full text Add to dashboard Cite

Interval linear fractional programming problem (ILFPP) approaches uncertain-ties in real-world systems such as business, manufacturing, finance, and eco-nomics. In this study, we propose solving the interval linear fractional pro-gramming (ILFP) problem using interval arithmetic. Further, to construct the problem, a suitable variable transformation is used to form an equivalent ILP problem, and a new algorithm is depicted to obtain the optimal solution with-out converting the problem into its conventional form. This paper compares the range, solutions, and approaches of ILFP with fuzzy linear fractional pro-gramming (FLFP) in solving real-world optimization problems. The illustrated numerical examples show a better range of interval solutions on practical appli-cations of ILFPs and uncertain parameters.

show abstract

Section: Bulletin Of Electr Eng and Inf Issn: 2302-9285mentioning

confidence: 99%

A study on the solution of interval linear fractional programming problem

Murugan,

Thamaraiselvan

2024

Bulletin EEI

View full text Add to dashboard Cite

show abstract

“…The (11) and its auxiliary problems are in the form of (5). Thus, by using variable transformations (6); the (7) is formulated as follows:…”

Section: Fuzzy Numbersmentioning

confidence: 99%

“…By using the notion of α−cuts and suitable variable changings, [5] developed a methods to LFPP with fuzzy coefficients. Based on the notion of α−cuts and using a parametric approach, Borza and Rambely [6,7] introduced two efficient methods dealing with MOLFPP including fuzzy coefficients.…”

mentioning

confidence: 99%

A new efficient approach to tackle multi objective linear fractional problem with flexible constraints

Borza

Rambely²

2023

JIMO

Self Cite

View full text Add to dashboard Cite

<p style='text-indent:20px;'>Finding efficient solutions for the multi-objective linear fractional programming problem (MOLFPP) is a challenging issue in optimization due to the fact that more than one objective must be taken into consideration by the decision maker. For this class of optimization problems, we deal with the concept of efficient solutions. The set of efficient solutions could be an infinite set especially when the objectives are in conflict. In this paper, we present a new methodology to address the MOLFPP with flexible constraints i.e. the constraints with fuzzy right hand sides. In the method, firstly, the concept of the <inline-formula><tex-math id="M1">\begin{document}$ \alpha- $\end{document}</tex-math></inline-formula>cuts and ranking of fuzzy numbers are utilized to transform the original problem into the MOLFPP with fixed right hand sides. Secondly, a new MOLFPP is constructed based on the membership functions of the objectives. Afterward this new problem is changed into a single objective programming problem using the weighted sum approach. Finally, the global optimal solution of this single objective programming is obtained by taking into account a finite number of linear programming problems (LPPs). It is proven that the obtained solution is efficient for the main problem. Numerical examples are given to illustrate the method and comparisons are made to show the accuracy.</p>

show abstract

“…Dutta et al [14,15] worked on the sensitivity of FLFPPs and also investigated the impact of tolerance on both LFPPs and FLFPPs. Recently, Borza and Rambely [16] solved the FLFPPs with crisp variables and coefficients as TFNs by using a combination of the max-min method and an α-cut-based approach.…”

Section: Introductionmentioning

confidence: 99%

On Fuzzy Linear Fractional Programming Problems via α-Cut-Based Method with Application in Transportation Sector

et al. 2023

View full text Add to dashboard Cite

The article provides an α-cut-based method that solves linear fractional programming problems with fuzzy variables and unrestricted parameters. The parameters and variables are considered as asymmetric triangular fuzzy numbers, which is a generalization of the symmetric case. The problem is solved by using α-cut of fuzzy numbers wherein the α- and r-cut are applied to the objective function and constraints, respectively. This reduces the problem into an equivalent biobjective model which leads to the upper and lower bounds of the given problem. Afterwards, the membership functions corresponding to various values of r∈(0,1] are obtained using the optimal values of the biobjective model. The proposed method is illustrated by taking an example from the literature to highlight the fallacy of an existing approach. Finally, a fuzzy linear fractional transportation problem is modelled and solved using the aforementioned technique.

show abstract

A parametric approach to fuzzy multi-objective linear fractional program: An alpha cut based method

Cited by 5 publications

References 27 publications

A study on the solution of interval linear fractional programming problem

A study on the solution of interval linear fractional programming problem

A new efficient approach to tackle multi objective linear fractional problem with flexible constraints

On Fuzzy Linear Fractional Programming Problems via α-Cut-Based Method with Application in Transportation Sector

Contact Info

Product

Resources

About