Fuzzy Opt Dec Making (original) (raw)

A managerial decision-making approach to fuzzy linear programming problems

International Journal of Management Science and Engineering Management, 2014

In practice, there are many problems in which all decision parameters are fuzzy numbers, and such problems are usually solved by either probabilistic programming or multi-objective programming methods. In this paper, using the concept of fuzzy numbers comparison, we introduce a very effective method for solving these problems. Then we propose a new method for solving linear programming problems with fuzzy variables. This paper extends linear programming based problem into a fuzzy environment. With the problem assumptions, the optimal solution can still be theoretically solved using the simplex based method. To handle fuzzy decision variables can be generated initially, then solved and improved sequentially using the fuzzy decision approach by introducing a robust ranking technique. The proposed procedure was programmed. The model is illustrated with a numerical example and a sensitivity analysis is of the optimal solution is studied with respect changes in parameter which incorporates all concepts of a fuzzy arithmetic approach to draw managerial insights.

Linear programming with fuzzy parameters: An interactive method resolution

European Journal of Operational Research, 2007

This paper proposes a method for solving linear programming problems where all the coefficients are, in general, fuzzy numbers. We use a fuzzy ranking method to rank the fuzzy objective values and to deal with the inequality relation on constraints. It allows us to work with the concept of feasibility degree. The bigger the feasibility degree is, the worst the objective value will be. We offer the decision-maker (DM) the optimal solution for several different degrees of feasibility. With this information the DM is able to establish a fuzzy goal. We build a fuzzy subset in the decision space whose membership function represents the balance between feasibility degree of constraints and satisfaction degree of the goal. A reasonable solution is the one that has the biggest membership degree to this fuzzy subset. Finally, to illustrate our method, we solve a numerical example.

Decision Making in Fuzzy Environment

Fuzzy Logic is used in those type of problems in which the solution cannot be defined in rigid boundary either yes or no. In this environment the decision are not biased because the decisions are making on the basis of different criteria involved in that problem. Here membership functionis given to that criteria and using various fuzzy operation the calculation is done. In this thesis we have studied about fuzzy set and fuzzy logic and implement this in out ranking problem. We have also develop a code in C using DevC++ compiler by which out ranking can be done among any alternatives in different criteria.

Linear Programming Problems in Fuzzy Environment : The Post Optimal Analyses

2015

This paper proposes a new method of Robust ranking technique, which is used for defuzzifying the trapezoidal fuzzy number into a crisp number to represent the fuzzy set. In practice, there are many problems in which all decision parameters are fuzzy numbers, and such problems are usually solved by either probabilistic programming or multi objective programming methods. Unfortunately all these methods have shortcomings. In this paper, using the concept of comparison of fuzzy numbers, a very effective method is introduced for solving these problems. The model is illustrated with numerical application to generate a good solution and post optimal analyses are obtained. Investigation of the properties of an optimal solution allows developing a simplex algorithm in fuzzy environment. Furthermore, the proposed technique allows the significant ways to help the decision-maker for formulating their decisions and drawing managerial insights efficiently. © 2015 World Academic Press, UK. All rig...

Decision-Making in Fuzzy Environment: A Survey

Application of Decision Science in Business and Management [Working Title]

Multi-criteria decision-making (MCDM) is a crucial process in many business and management applications. The final decision is based upon the relative weights to the decision-making team. The analytic hierarchy process (AHP) has found to be one of the most successful approaches for evaluations of the weights and the importance of the criteria. However, most of the evaluated values are not so precise due to the fuzziness of the evaluating environment. This chapter surveys essentially the basic analytic hierarchy process and the fuzzy analytic hierarchy process (FAHP). It depicts through an example the steps for using the original analytic hierarchy process for two levels of criteria. Then, it uses the same example to explain the fuzzy approach in the evaluation. Finally, it compares both approaches.

Decision Making Approach to Fuzzy Linear Programming (FLP) Problems with Post Optimal Analysis

International Journal of Operations Research and Information Systems, 2015

This paper finds solutions to the fuzzy linear program where some parameters are fuzzy numbers. In practice, there are many problems in which all decision parameters are fuzzy numbers, and such problems are usually solved by either probabilistic programming or multi objective programming methods. Unfortunately all these methods have shortcomings. In this paper, using the concept of comparison of fuzzy numbers, the author introduces a very effective method for solving these problems. This paper extends linear programming based problem in fuzzy environment. With the problem assumptions, the optimal solution can still be theoretically solved using the simplex based method. To handle the fuzzy decision variables can be initially generated and then solved and improved sequentially using the fuzzy decision approach by introducing robust ranking technique. The model is illustrated with an application and a post optimal analysis approach is obtained. The proposed procedure was programmed wi...

New method for solving fuzzy linear programming problem

This study investigates possibilistic linear programming and offer a new method to achieve optimal value of the necessary degree of constraints for Decision Maker in fuzzy linear programming with fuzzy technological coefficients and solve problem by this value. In the proposed algorithm, fuzzy decision set algorithm have been used that is based on the definition of fuzzy decision. Yet in possibilistic programming problem there were not any method to establish optimum value of necessary degree. When possibilistic linear programming is used for solving fuzzy linear pro- gramming problem with fuzzy technological coefficients, the decision maker must establish necessary degree of constraints, there is a need for a method which is able to achieve optimal value of necessary degree and solve the problem.

Approach to decision making in fuzzy environment

Computers & Mathematics with Applications, 1999

A general approach to solving a wide class of optimization problems with fuzzy coefficients in objective functions and constraints is described. It is based on a modification of traditional mathematical programming methods and consists in formulating and solving one and the same problem within the framework of interrelated models with constructing equivalent analogs with fuzzy coefficients in objective function alone. This approach allows one to maximally cut off dominated alternatives from below as well as from above. The subsequent contraction of the decision uncertainty region is associated with reduction of the problem to multicriteria decision making in a fuzzy environment. The approach is applied within the context of fuzzy discrete optimization models, that is based on a modification of discrete optimization algorithms. The results of the paper are of a universal character and are already being used to solve problems of the design and control of power systems and subsystems. (~) 1999 Elsevier Science Ltd. All rights reserved. Keywords-Discrete optimization, Fuzzy coefficients, Nonfuzzy analog, Multicriteria selection of alternatives in fuzzy environment.