Portfolio selection can be regarded as a type of multi-objective decision problem. However, traditional solution methods rarely discussed the decision maker’s nonsatisfaction and hesitation degrees...

An Intuitionistic Fuzzy Multi-Objective Goal Programming Approach to Portfolio Selection

Recently, there is a growing attention by the researchers to solve and interpret the analysis of fully fuzzy linear programming problems in which all of the parameters as well as the decision variables are considered as fuzzy numbers. Under a fully uncertain environment where all of the data are stated as fuzzy, presenting the reasonable range of values for the decision variables may be comparatively better than the currently available crisp solutions so as to provide ranges of flexibility to decision makers. However, there is still a scarcity of solution methodologies on fuzzy mathematical programs with fuzzy decision variables. Based on this motivation, a new parametric method which is mainly based on α-cut representation of fuzzy intervals is proposed in this paper by incorporating the decision maker's attitude toward risk. In order to illustrate validity and practicality of the proposed method, it is applied to a generic reverse logistics network design model including fuzzy decision variables. To the best of our knowledge, this is the first study in the literature which presents fuzzy efficient solutions and analysis for a fully fuzzy reverse logistics network design problem with fuzzy decision variables. The provided solutions by the proposed method are also compared to the available solution methodologies from the literature in terms of computational efficiency, solution quality and ease of use. By using the proposed method, the decision makers can be supported by yielding fuzzy efficient solutions under different uncertainty levels and risk attitudes. The computational results have also shown that more reliable and necessarily precise solutions can be generated by the proposed method for a risk-averse decision maker.

An analysis of fully fuzzy linear programming with fuzzy decision variables through logistics network design problem

This paper focuses on Fully Fuzzy Multi-Objective Linear Programming (FFMOLP) problem in which all the coefficients and decision variables are LR flat fuzzy numbers, the more generalized version of fuzzy numbers and all the constraints are fuzzy inequalities. A new algorithm is proposed for solving FFMOLP problem which first converts it into the Multi-Objective Interval Linear Programming (MOILP) problem. Further, taking the help of fuzzy slack variable, fuzzy surplus variables, nearest interval approximation of fuzzy numbers and scalarization technique, MOILP is then converted into the Crisp Linear Programming (CLP) problem. It is shown that the optimal solution of CLP problem is the fuzzy Pareto optimal solution of FFMOLP problem. The main advantage of the proposed algorithm is that it transforms FFMOLP problem into Crisp Linear Programming problem.
 Moreover, to apply algorithm, only the knowledge of arithmetic operations of LR flat fuzzy numbers, centre and width of the closed intervals are required. At the end, to illustrate the proposed method and its effectiveness over the existing method, numerical examples are solved and compared.

Solving Fully Fuzzy Multi-objective Linear Programming Problem Using Nearest Interval Approximation of Fuzzy Number and Interval Programming

We investigate various types of fuzzy linear programming problems based on models and solution methods. First, we review fuzzy linear programming problems with fuzzy decision variables and fuzzy linear programming problems with fuzzy parameters (fuzzy numbers in the definition of the objective function or constraints) along with the associated duality results. Then, we review the fully fuzzy linear programming problems with all variables and parameters being allowed to be fuzzy. Most methods used for solving such problems are based on ranking functions, $$\alpha $$-cuts, using duality results or penalty functions. In these methods, authors deal with crisp formulations of the fuzzy problems. Recently, some heuristic algorithms have also been proposed. In these methods, some authors solve the fuzzy problem directly, while others solve the crisp problems approximately.

Fuzzy linear programming problems: models and solutions

A fuzzy approach for the reviewer assignment problem

A new method namely, decomposition method for solving integer linear programming problems with fuzzy variables by using classical integer linear programming has been proposed. In the decomposition method, ranking functions are not used. The proposed method can serve managers by providing the best solution to a variety of integer linear programming problems with fuzzy variables in a simple and effective manner. With the help of numerical examples, the decomposition method is illustrated. Mathematics Subject Classifications: 90C10, 90C70, 90C90, 65K05

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A New Method for Solving Integer Linear Programming Problems with Fuzzy Variables

http://theglobaljournals.com/ijsr/file.php?val=April_2014_1396529397_c3770_174.pdf

Solving Fully Fuzzy Multi-Objective Linear Programming Problems

A new posteriori method namely, moving optimal method is proposed for solving multiple objective linear programming problems. It provides efficient solution line segments to the problem with the percentage level of satisfaction of each of the objective at each point on it which is very much useful to decision makers for choosing an efficient solution according to their level of satisfaction on the objective functions. Illustrative example is presented to clarify the idea of the proposed approach. Mathematics Subject Classification : 90B06, 9050, 90C05, 90C29

Determining efficient solutions to multiple objective linear programming problems

A quick review on applications of fuzzy logic in waste water treatment.

A new method namely, objective separable method based on simplex method is proposed for finding an optimal solution to a quadratic programming problem in which the objective function can be factorized into two linear functions. The solution procedure of the proposed method is illustrated with the numerical example.

M. Jayalakshmi

Papers

A New Method for Solving Integer Linear Programming Problems with Fuzzy Variables

Solving Fully Fuzzy Multi-Objective Linear Programming Problems

Determining efficient solutions to multiple objective linear programming problems

A quick review on applications of fuzzy logic in waste water treatment.

A method for solving quadratic programming problems having linearly factorized objective function