Abstract

Linear Programming (LP) problem is one of optimization problem. Based on its limited resources and other restriction, we find the optimal solution for the problem. LP problems have very wide applications in our daily problems. They deal with situations where a number of resources, such as men materials, machines, and land are available, and are to be combined to yield one or more products. LP deals with that class of programming problems for which all relations among the variables are linear. The relation must be linear both in the constraints and in the function to be optimized. There are some types of fuzzy LP problems. One type is the right sides of the constraints are fuzzy numbers. The other type is the coefficients of the objective function are the fuzzy numbers. The most complicated type is the right side, the coefficients of the variables and the coefficients of the objective function are fuzzy numbers. There are many types of fuzzy numbers. Two of them are trapezoidal fuzzy number and triangular fuzzy number (TFN). They are easy to be counted and to be implemented. In this paper trapezoidal fuzzy number (TrNF) is defined, where the method of subtraction and division has been modified. These modified method is exactly inverse of the addition and multiplication operators. There are some techniques to solve the fuzzy LP problems. To slove this problem , we use trapezoidal fuzzy numbers. Here we propose a new operation on trapezodal fuzzy number to solve fuzzy LP problem using interval arithmetic based on Alpha-cut. We construct an assumptions to slove the trapezoidal fuzzy number linear programming problem.

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