The tolerance approach in multiobjective linear fractional programming

Arévalo, M T; Mármol, Amparo M.; Zapata, A.

doi:10.1007/bf02568552

Cited by 3 publications

(2 citation statements)

References 15 publications

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“…In the literature, for various types of fractional programming, there are many different sorts of studies; some of them deal with theory [3][4][5][6], and some of them concern with solution methods [2,[7][8][9][10][11][12][13][14][15][16][17][18] and applications [19]. Dinkelbach [7] presented the algorithm based on a theorem by Jagannathan [20] concerning the relationship between fractional and parametric programming and restated and proved this theorem in somewhat simpler way.…”

Section: Introductionmentioning

confidence: 99%

A Proposal to the Solution of Multiobjective Linear Fractional Programming Problem

Güzel

2013

Abstract and Applied Analysis

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We have proposed a new solution to the Multiobjective Linear Fractional Programming Problem (MOLFPP). The proposed solution is based on a theorem that deals with nonlinear fractional programming with single objective function and studied in the work by Dinkelbach, 1967. As a new contribution, we have proposed that is an efficient solution of MOLFPP if is an optimal solution of problem , where is for all . Hence, MOLFPP is simply reduced to linear programming problem (LPP). Some numerical examples are provided in order to illustrate the applications of the proposed method. The optimization software package, namely, WinQSB (Chang, 2001), has been employed in the computations.

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Section: Introductionmentioning

confidence: 99%

A Proposal to the Solution of Multiobjective Linear Fractional Programming Problem

Güzel

2013

Abstract and Applied Analysis

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“…In the literature, for various kinds of fractional programming, there are several different sorts of studies; some of them deal with theory (Jo and Lee, 1998;Liu and Yokoyama, 1999;Tigan and Stancu-Minasian, 2000;Patel, 2005), and some of them are concerned with solution methods (Stancu-Minasian and Pop, 2003;Dinkelbach, 1967;Arévalo et al, 1997;Calvete and Galé, 1999;Yadav and Mukherjee, 1990;Sakawa et al, 2000;Sakawa and Nishizaki, 2001;Gupta and Bhatia, 2001;Saad, 2005;Mohan and Nguyen, 2001;Güzel, 2013) and applications (Leber et al, 2005). Dinkelbach (1967) suggested the algorithm based on a theorem by Jagannathan (1966) concerning the relationship between fractions and parametric programming and restated and demonstrated this theorem in a somewhat simpler way.…”

Section: Introductionmentioning

confidence: 99%

Intuitionistic fuzzy optimization method for solving multi-objective linear fractional programming problems

Solomon¹,

Zaher²,

Saied³

2023

Int. j. adv. appl. sci.

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An iterative technique based on the use of parametric functions is proposed in this paper to obtain the best preferred optimal solution of a multi-objective linear fractional programming problem (MOLFPP). Each fractional objective is transformed into a non-fractional parametric function using certain initial values of parameters. The parametric values are iteratively calculated and the intuitionistic fuzzy optimization method is used to solve a multi-objective linear programming problem. Also, some basic properties and operations of an intuitionistic fuzzy set are considered. The development of the proposed algorithm is based on the principle of optimal decision set achieved by the intersection of various intuitionistic fuzzy decision sets which are obtained corresponding to each objective function. Additionally, as the intuitionistic fuzzy optimization method utilizes the degree of belonging and degree of non-belonging, we used the linear membership function for belonging and non-belonging to see its impact on optimization and to get insight into such an optimization process. The proposed approaches have been illustrated with numerical examples.

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A sixth bibliography of fractional programming

Stancu-Minasian

2006

Optimization

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The tolerance approach in multiobjective linear fractional programming

Cited by 3 publications

References 15 publications

A Proposal to the Solution of Multiobjective Linear Fractional Programming Problem

A Proposal to the Solution of Multiobjective Linear Fractional Programming Problem

Intuitionistic fuzzy optimization method for solving multi-objective linear fractional programming problems

A sixth bibliography of fractional programming

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