Numerical Solution of NTH - Order Fuzzy Initial Value Problems by Fourth Order Runge-Kutta Method Basesd On Contrahamonic Mean

In this paper, a numerical method for Nth - order fuzzy initial value problems (FIVP) based on Seikkala derivative of fuzzy process is studied. The fourth order Runge-Kutta method based on Contra-harmonic Mean (RKCoM4) is used to find the numerical solution of this problem and the convergence and stability of the method is proved. This method is illustrated by solving second and third order FIVPs. The results show that the proposed method suits well to find the numerical solution of Nth - order FIVPs

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 for Solving Deterministic Multi-Item Fuzzy Inventory Model Three Constraints

ABSTRACT: This paper discusses an Economic Order Quantity (EOQ) model in which fuzzy multi-item inventory model together with three constraints. The setup costs, the holding costs, demands, storage area, investment amount and the maximum average number of units are considered as triangular fuzzy numbers. The fuzzy parameters in the constraints are then transformed into crisp using GMIR technique. The fuzzy parameters in the objective function are then transformed into corresponding interval numbers. Minimization of the interval objective function (obtained by using interval parameters) has been transformed into a classical multi-objective EOQ problem. The order relation that represents the decision maker's preference among the interval objective function has been defined by the right limit, left limit, and center which is the half -width of an interval. This concept is used to minimize the interval objective function. The problem has been solved by fuzzy programming technique. Finally, the proposed method is illustrated with a numerical example. KEYWORDS: Inventory, space constraint, investment constraint, maximum average number of units constraint, EOQ, Interval number, Fuzzy sets, triangular fuzzy number, GMIR technique, Fuzzy optimization technique, Multi-objective Programming I.INTRODUCTION In traditional mathematical problems, the parameters are always treated as deterministic in nature. However, in practical problem, uncertainty always exists. In order to deal with such uncertain situations fuzzy model is used. In such cases, fuzzy set theory, introduced by Zadeh [15] is acceptable. There are several studies on fuzzy EOQ model. Lin et al. The parameters in any inventory model are normally variable uncertain, imprecise and adoptable to the optimum decision making process and the determination of optimum order quality becomes a vague decision making process. The vagueness pertained in the above parameters analyze the inventory problem in a fuzzy environment. On the basis of this idea the GMIR technique The article is organized as follows: In section 1 preliminary definition of fuzzy set, interval number, and triangular fuzzy number, α-cut of a fuzzy number, basic arithmetic optimization in interval, GMIR technique and nearest interval approximation is briefly described. Section 2 contains model formulation. The fuzzy optimization technique is section 3. In section 4 the process is illustrated by a numerical example and in the last section the entire work is concluded