Fuzzy Multiobjective Linear Fractional Programming Research Articles

An Application of Fully Intuitionistic Fuzzy Multi-objective Linear Fractional Programming Problem in E-education System

This article addresses a special class of non-linear programming problems, viz., linear fractional programming problems having multiple objectives. In solving the real-life linear fractional optimization problems, the ambiguity and hesitation in the decision are inherent and ever-present, therefore, it is perfectly viable to formulate and solve these optimization models using the intuitionistic fuzzy environment. The purpose of this study is to propose a simple and computationally efficient approach to obtain the solution of multiple objective linear fractional programming problems having all the decision variables and parameters expressed in terms of triangular intuitionistic fuzzy numbers. The proposed solution algorithm is primarily based on the goal programming approach, fuzzy-based linearization technique, and a membership function strategy. The original linear fractional programming problem is first converted to its equivalent deterministic/crisp multi-objective linear fractional optimization problem using the weighted goal programming methodology along with the linear membership technique to resolve the intuitionistic fuzzy constraints into the crisp one. Finally, the variable transformation technique for the under- and over-deviational variables of the goal programming model is employed to linearize all the fractions involved in the problem so as to convert the original problem to an equivalent linear optimization problem. Further, this linear programming problem can be solved using any available commercial packages. Moreover, a numerical illustration is provided to demonstrate the steps of the proposed technique followed by the analysis and solution of an E-education set-up problem. The discussion and comparisons of the practical case establish the relevancy and usefulness of the proposed model.

Scalarizing fuzzy multi-objective linear fractional programming with application

Scalarizing fuzzy multi-objective linear fractional programming with application

Extension principle-based solution approach to full fuzzy multi-objective linear fractional programming

Extension principle-based solution approach to full fuzzy multi-objective linear fractional programming

Fuzzy solution of fully fuzzy multi-objective linear fractional programming problems

In this study, we present a novel method for solving fully fuzzy multi-objective linear fractional programming problems without transforming to equivalent crisp problems. First, we calculate the fuzzy optimal value for each fractional objective function and then we convert the fully fuzzy multi-objective linear fractional programming problem to a single objective fuzzy linear fractional programming problem and find its fuzzy optimal solution which inturn yields a fuzzy Pareto optimal solution for the given fully fuzzy multi-objective linear fractional programming problem. To demonstrate the proposed strategy, a numerical example is provided.

A solving approach for fuzzy multi-objective linear fractional programming and application to an agricultural planting structure optimization problem

In this paper, an algorithm is presented to solve fuzzy multi-objective linear fractional programming (FMOLFP) problems through an approach based on superiority and inferiority measures method (SIMM). In the model for the proposed approach, each of fuzzy goals defined for the fractional objectives and some of constraints have fuzzy numbers. To achieve the highest membership value, SIMM is adopted to deal with fuzzy number in constraints, then a linear goal programming methodology is introduced to solve the problem in which the fractional objectives is fuzzy goals. A case of agricultural planting structures optimization problem is solved to illustrate the application of the algorithm. The results show that winter wheat and summer corn acreage should be 38,386.4 ha, and cotton acreage should be 20,669.6 ha. Because of high risk in cotton cultivation at present, the ratio of grain planted area to cotton planted area is unreasonable. An improved support in policy is necessary for the government to enhance the enthusiasm of farmers to plant cotton and sustain the development of cotton market in the long term.

Q-Taylor series method for solving fuzzy multiobjective linear fractional programming problem

In this work, we present a q -Taylor series method for fuzzy multiobjective linear fractional programming problems (FMOLFPPs). In q -calculus, q -Taylor series is a q -series expansion of a function with respect to q -derivatives. In the proposed approach, membership functions are defined to be piecewise linear. Membership functions associated with each objective of fuzy multiobjective linear fractional programming problem transformed by using q -Taylor series are unified. Thus, the problem is reduced to a single objective. To show the efficiency of the q -Taylor series method, we applied the method to some problems.

An Approach for Solving Fuzzy Multi-Objective Linear Fractional Programming Problems

In this paper, an attempt has been taken to develop a method for solving fuzzy multi-objective linear fractional programming (FMOLFP) problem. Here, at first the FMOLFP problem is converted into (crisp) multi-objective linear fractional programming (MOLFP) problem using the graded mean integration representation (GMIR) method proposed by Chen and Hsieh. That is, all the fuzzy parameters of FMOLFP problem are converted into crisp values. Then the MOLFP problem is transformed into a single objective linear programming (LP) problem using a proposal given by Nuran Guzel. Finally the single objective LP problem is solved by regular simplex method which yields an efficient solution of the original FMOLFP problem. To show the efficiency of our proposed method, three numerical examples are illustrated and also for each example, a comparison is drawn between our proposed method and the respected existing method.

A goal programming procedure for solving fuzzy multiobjective fractional linear programming problems

This paper presents a modification of Pal, Moitra and Maulik's goal programming procedure for fuzzy multiobjective linear fractional programming problem solving. The proposed modification of the method allows simpler solving of economic multiple objective fractional linear programming (MOFLP) problems, enabling the obtained solutions to express the preferences of the decision maker defined by the objective function weights. The proposed method is tested on the production planning example.

Algorithm for Solving Fuzzy Multiobjective Linear Fractional Programming Problem by Additive Weighted Method

In this paper attention has been paid to the study of multiobjective linear fractional programming problem (MOLFPP) by using fuzzy set theoretic approach. In this approach, MOLFPP is transformed into multiobjective linear programming problem (MOLPP) by suitable transformation. In algorithm-I, MOLFPP is transformed into MOLPP by using fuzzy set theory and the pareto optimal solution of the transformed MOLPP is obtained by applying Zimmermann’s min-operator model and simplex method. Further we have used additive weighted method to modify the above approach. Algorithm-II has been presented to find the pareto optimal solution of MOLFPP by applying additive weighted method. To demonstrate the applicability of the proposed approach, one numerical example is solved to find the pareto optimal solution by applying this two algorithms.

Taylor series approach to fuzzy multiobjective linear fractional programming

This paper presents the use of a Taylor series for fuzzy multiobjective linear fractional programming problems (FMOLFP). The Taylor series is a series expansion that a representation of a function. In the proposed approach, membership functions associated with each objective of fuzzy multiobjective linear fractional programming problem transformed by using a Taylor series are unified. Thus, the problem is reduced to a single objective. Practical applications and numerical examples are used in order to show the efficiency and superiority of the proposed approach.

A goal programming procedure for fuzzy multiobjective linear fractional programming problem

This paper presents a goal programming (GP) procedure for fuzzy multiobjective linear fractional programming (FMOLFP) problems. In the proposed approach, which is motivated by Mohamed (Fuzzy Sets and Systems 89 (1997) 215), GP model for achievement of the highest membership value of each of fuzzy goals defined for the fractional objectives is formulated. In the solution process, 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. The approach is illustrated by two numerical examples.

Sensitivity analysis in fuzzy multiobjective linear fractional programming problem

In this paper, we study measurement of sensitivity for changes of violations in the aspiration level for the fuzzy multiobjective linear fractional programming problem.

A parallel algorithm and duality for a fuzzy multiobjective lienar fractional programming problem

This paper deals with the duality and the associated results in a special type of nonconvex fuzzy programming with linear fractional objectives. Extending the results on the generalized linear fractional program by Jagannathan and Schaible, the associated dual is derived via Farkas' lemma. An algorithm in a dual-parallel-processor environment is developed based on the duality relations established. The effectiveness of the algorithm is illustrated by the computational experiments conducted with five test problems in fuzzy multiobjective linear fractional programming. Sensitivity analysis results for the FMOLFP with respect to fuzzy parameters are also presented.