Multi OBJECTIVE quadratic FRACTIONAL PROGRAMMING (MOQFP) problem involves optimization of several OBJECTIVE functions in the form of a ratio of numerator and denominator functions which involve both contains linear and quadratic forms with the assumption that the set of feasible solutions is a convex polyhedral with a finite number of extreme points and the denominator part of each of the OBJECTIVE functions is non-zero in the constraint set. In this paper, we extend the procedure as suggested by Lachhwani (Proc. Nat. Acad. Sci. India, 82 (4), 317-322) based on fuzzy goal PROGRAMMING approach for the solution of multi OBJECTIVE quadratic FRACTIONAL PROGRAMMING (MOQFP) problem.The proposed technique is simple, efficient and requires less computational work. In the proposed FGP model formulation, corresponding OBJECTIVEs of equivalent multi OBJECTIVE PROGRAMMING problem are transformed into fuzzy goals (membership functions) by means of assigning an aspiration level to each of them and suitable membership function is de fined for each OBJECTIVEs. Then achievement of the highest membership value of each of fuzzy goals is formulated by minimizing the sum of negative deviational variables. The proposed methodology is illustrated with numerical example in order to support the proposed methodology.

This paper deals with a MULTI-OBJECTIVE linear FRACTIONAL PROGRAMMING problem in fuzzy environment. The problem is considered by introducing all the parameters as piecewise quadratic fuzzy numbers. Through the use of the associated real number of the close interval approximation and the order relation of the piecewise quadratic fuzzy numbers, the problem is transformed into the corresponding crisp problem. A proposed method introduces to generate ideals and the set of all fuzzy efficient solutions. The advantage of it helps the decision maker to handle the real life problem. A numerical example is given illustrate the method.

In this paper a MULTI-OBJECTIVE linear FRACTIONAL PROGRAMMING problem with the fuzzy variables and vector of fuzzy resources is studied and an algorithm based on a parametric approach is proposed. The proposed solving procedure is based on the parametric approach to find the solution, which provides the decision maker with more complete information in line with reality. The simplicity of the proposed method is one of the advantages of the presented algorithm, which allows the decision maker to better understand the solving procedure. Moreover, a numerical example is presented to illustrate the proposed method.

Data envelopment analysis operates as a tool to appraise the relative efficiency of a set of homogenous decision making units. DEA allows each DMU to take its optimal weight in comparison to other DMUs while a similar condition is considered for other units. This feature threats the comparability of different units because different weighting schemes are used for different DMUs. In this paper, a model is presented to determine a common set of weights to calculate DMUs efficiency. This model is developed based on a multi OBJECTIVE FRACTIONAL linear PROGRAMMING model that considers the original DEA's results as ideal solution and seeks a set of common weights to evaluate DMUs and increases the model's discrimination power. A numerical example is solved and the proposed method's results are compared to some previous methods. This Comparison has shown the proposed method's advantages in ranking DMUs.

This paper presents a suitable solution procedure to solve the fully rough MULTI-OBJECTIVE MULTI-level linear FRACTIONAL PROGRAMMING (FRMMFP) problem. First, an extension of interval method is presented to deal with roughness of the stated problem. Then, an iterative technique is proposed for linearization of FRACTIONAL OBJECTIVEs. Finally, a modification of fuzzy approach is provided in the environment of the fully rough to solve the linear model. An example is provided for understanding the solution procedure of the proposed method.

In this paper, an attempt has been taken to develop a method to solve the neutrosophic multiOBJECTIVE linear FRACTIONAL PROGRAMMING (NMOLFPP) problem. In the first step of our method, the problem is linearized based on some transformations. Then, the linearized model is reduced to a crisp MULTI-OBJECTIVE PROGRAMMING problem with the help of the accuracy function for each OBJECTIVE. In the following, we extended Zimmerman’s approach to maximize the truth membership and minimize the indeterminacy and falsity membership functions in the solution procedure. Finally, to illustrate the proposed approach, a numerical example is included.

In this paper, we establish a proof for a necessary condition for multiple OBJECTIVE FRACTIONAL pro-gramming. In order to derive the set of necessary conditions, we employ an equivalent parametric problem. Also, we present the related semi parametric model.

In sciences and industries such as signal optimization, traffic assignment, economic market and etc, many problems have been modeled by bilevel PROGRAMMING (BLP) problems, where in each level one must optimize some OBJECTIVE functions. There are so many algorithms in order to find the global optimum of the linear version of BLP problems. This paper addresses MULTI-OBJECTIVE linear bilevel MULTI-follower PROGRAMMING (MOLBMFP) problems in which there is no sharing information among followers. It presents a new method for solving these problems.