Program Linier Fuzzy Penuh Dengan Metode Kumar

Fully fuzzy linear programing is part of a crisp linear programming (linear programimg with a number of crisp) which the numbers used are fuzzy numbers. Solving a fully fuzzy linear programming problems by using Kumar method to fuzzy optimal solution and crisp optimal value.. Solving fuzzy optimal solution by Kumar method on triangular fuzzy number to divide into tree objective functions and defuzzification by using ranking function and α - cutting to get crisp optimal solution. This paper discusses about Kumar methods method for solving fully fuzzy linear programming in which fuzzy numbers used are triangular fuzzy numbers

Ranking Function Methods For Solving Fuzzy Linear Programming Problems

In this paper, we concentrate on linear programming problems in which the coefficients of objective function are fuzzy numbers, the right-hand side are fuzzy numbers too, and both the coefficients of objective function as well as right-hand side are fuzzy numbers. Then solving these fuzzy linear programming problems by using many linear ranking functions. After that develop six numerical examples to illustrates the steps of solutions for all these type of linear programming problems which studying in this paper. Keywords: Fuzzy set theory, fuzzy linear programming, linear ranking function, trapezoidal membership

Different strategies to solve fuzzy linear programming problems

Fuzzy linear programming problems have an essential role in fuzzy modeling, which can formulate uncertainty in actual environment In this paper we present methods to solve (i) the fuzzy linear programming problem in which the coefficients of objective function are trapezoidal fuzzy numbers, the coefficients of the constraints, right hand side of the constraints are triangular fuzzy numbers, and (ii) the fuzzy linear programming problem in which the variables are trapezoidal fuzzy variables, the coefficients of objective function and right hand side of the constraints are trapezoidal fuzzy numbers, (iii) the fuzzy linear programming problem in which the coefficients of objective function, the coefficients of the constraints, right hand side of the constraints are triangular fuzzy numbers. Here we use α –cut and ranking functions for ordering the triangular fuzzy numbers and trapezoidal fuzzy numbers. Finally numerical examples are provided to illustrate the various methods of the fuzzy linear programming problem and compared with the solution of the problem obtained after defuzzyfing in the beginning using ranking functions.&nbsp

A New Approach to Solve Intuitionistic Fuzzy Linear Programming Problems with Symmetric Trapezoidal Intuitionistic Fuzzy Numbers

Parvathi & Malathi (Intuitionistic fuzzy simplex method, International Journal of Computer Applications, 48, 39-48, 2012) proposed an intuitionistic fuzzy simplex algorithm to solve Intuitionistic Fuzzy Linear Programming Problems (IFLPPs) with Symmetric Trapezoidal Intuitionistic Fuzzy Numbers (STIFNs) by using a special ranking function and used the linearity property to obtain the desired results. In this paper, it is proved that the linearity property, used by authors, is not satisfied for given ranking function. So, to overcome this drawback, a new method is proposed to solve the same type of intuitionistic fuzzy linear programming problems. Keywords: Intuitionistic fuzzy linear programming problems, Symmetric trapezoidal intuitionistic fuzzy numbers, Ranking function

Computational studies of some fuzzy mathematical problems

In modelling and optimizing real world systems and processes, one usually ends up with a linear or nonlinear programming problem, namely maximizing one or more objective functions subject to a set of constraint equations or inequalities. For many cases, the constraints do not need to be satisfied exactly, and the coefficients involved in the model are imprecise in nature and have to be described by fuzzy numbers to reflect the real world nature. The resulting mathematical programming problem is referred to as a fuzzy mathematical programming problem.Over the past decades, a great deal of work has been conducted to study fuzzy mathematical programming problems and a large volume of results have been obtained. However, many issues have not been resolved. This research is thus undertaken to study two types of fuzzy mathematical programming problems. The first type of problems is fuzzy linear programming in which the objective function contains fuzzy numbers. To solve this type of problems, we firstly introduce the concept of fuzzy max order and non-dominated optimal solution to fuzzy mathematical programming problems within the framework of fuzzy mathematics. Then, based on the new concept introduced, various theorems are developed, which involve converting the fuzzy linear programming problem to a four objective linear programming problem of non-fuzzy members. The theoretical results and methods developed are then validated and their applications for solving fuzzy linear problems are demonstrated through examples.The second type of problems which we tackle in this research is fuzzy linear programming in which the constraint equations or inequalities contain fuzzy numbers. For this work, we first introduce a new concept, the α-fuzzy max order. Based on this concept, the general framework of an α-fuzzy max order method is developed for solving fuzzy linear programming problems with fuzzy parameters in the constraints. For the special cases in which the constraints consist of inequalities containing fuzzy numbers with isosceles triangle or trapezoidal membership functions, we prove that the feasible solution space can be determined by the respective 3n or 4n non-fuzzy inequalities. For the general cases in which the constraints contain fuzzy numbers with any other form of membership functions, robust numerical algorithms have been developed for the determination of the feasible solution space and the optimal solution to the fuzzy linear programming problem in which the constraints contain fuzzy parameters. Further, by using the results for both the first and second types of problems, general algorithms have also been developed for the general fuzzy linear programming problems in which both the objective function and the constraint inequalities contain fuzzy numbers with any forms of membership functions. Some examples are then presented to validate the theoretical results and the algorithms developed, and to demonstrate their applications

A Novel Technique for Solving Multiobjective Fuzzy Linear Programming Problems

This study considers multiobjective fuzzy linear programming (MFLP) problems in which the coefficients in the objective functions are triangular fuzzy numbers. The study proposing a new technique to transform MFLP problems into the equivalent single fuzzy linear programming problem and then solving it via linear ranking function using the simplex method, supported by numerical example

Fuzzy linear programming problems : models and solutions

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

A Novel Method for Solving the Fully Fuzzy Bilevel Linear Programming Problem

We address a fully fuzzy bilevel linear programming problem in which all the coefficients and variables of both objective functions and constraints are expressed as fuzzy numbers. This paper is to develop a new method to deal with the fully fuzzy bilevel linear programming problem by applying interval programming method. To this end, we first discretize membership grade of fuzzy coefficients and fuzzy decision variables of the problem into a finite number of α-level sets. By using α-level sets of fuzzy numbers, the fully fuzzy bilevel linear programming problem is transformed into an interval bilevel linear programming problem for each α-level set. The main idea to solve the obtained interval bilevel linear programming problem is to convert the problem into two deterministic subproblems which correspond to the lower and upper bounds of the upper level objective function. Based on the Kth-best algorithm, the two subproblems can be solved sequentially. Based on a series of α-level sets, we introduce a linear piecewise trapezoidal fuzzy number to approximate the optimal value of the upper level objective function of the fully fuzzy bilevel linear programming problem. Finally, a numerical example is provided to demonstrate the feasibility of the proposed approach

Metode Mehar Untuk Solusi Optimal Fuzzy Dan Analisa Sensitivitas Program Linier Dengan Variabel Fuzzy Bilangan Triangular

. Fuzzy linear programming problems containing closely with uncertainty about the parameters. Changes in the value of the parameters without changing the optimal solution or change the optimal solution is called sensitivity analysis. Sensitivity analysis is a basic for studying the effect of the changes that occur to the optimal solution. Linear programming with fuzzy variable is a form of fuzzy linear program is not fully because there are objective function coefficients and coefficients of constraints that are crisp numbers. Resolving the problem of linear programming with fuzzy variables by using mehar method will get solutions and optimal fuzzy value and solutions and optimal crisp value. To solve the problem of linear program with fuzzy variable is using mehar, must be converted beforehand in the form of crisp linear programming. This thesis explores mehar method to solve linear programming problems with fuzzy variables with triangular number and a sensitivity analysis on the optimum solution FVLP so that when there is a change of data of the problem, new solution will remain optimal

Evaluating fuzzy inequalities and solving fully fuzzified linear fractional programs

In our earlier articles, we proposed two methods for solving the fully fuzzified linear fractional programming (FFLFP) problems. In this paper, we introduce a different approach of evaluating fuzzy inequalities between two triangular fuzzy numbers and solving FFLFP problems. First, using the Charnes-Cooper method, we transform the linear fractional programming problem into a linear one. Second, the problem of maximizing a function with triangular fuzzy value is transformed into a problem of deterministic multiple objective linear programming. Illustrative numerical examples are given to clarify the developed theory and the proposed algorithm