This final project discusses the diagonalization of a matrix triangular fuzzy numbers in interval form. Negative positive triangular fuzzy number with the concept on geometrical area can be used to determine eigen values and eigen vector of matrix triangular fuzzy numbers in interval form matrix and needed arithmatic operation that have been modified which refers to eigenvalues and eigenve…
This final project discusses the inventory model with shortage in triangular fuzzy numbers. The inventory model used is the EOQ model. The optimal solution of the model is achieved by using the Kuhn-Tucker conditions. Furthermore, the obtained Kuhn-Tucker conditions are formed into nonlinear programming so that the best decision is obtained in solving the EOQ problem. Thus the average valu…
We discuss a the system of absolute value equations as a family of parameterized smooth equations and propose a smoothing Newton method to solve this class of problems. Proved that the method is globally and locally quadratically convergent under suitable assumptions. The preliminary numerical result demonstrate that the method is efective. This article is a review of the article Jiang [Ad…
ABSTRACT This nal project discusses a new iterative method for multiple roots of nonli- near equation which is free from second derivatives. Analytically it is shown that the method is of order three for a multiple roots and requires one function evaluation and two evaluations of rst derivative of function for each iteration. Numerical computations show that the new method gives the smal…
ABSTRACT This nal project discusses a transportation problem of the pentagonal fuzzy numbers using with the max-min method. This method is used to nd the initial base solution. Then to test the optimization and nd the optimal solution used the simplex transportation method. The solution is compared with the Vogel's approximation method. Based on the comparison of the two method, it is …
ABSTRACT This final project formulates the term life insurance premium with a uniform assumption for multiple decrement cases limited by two cases. Premium calculation is obtained by determining the life annuity first and the single premium value based on uniform assumptions. Life annuity and annual premiums are settled by first determining the insurance participant’s probability of exit…
ABSTRACT This final project discusses the premium of reserves of last survivor term life insurance based on premium sufficiency method for two persons. The calculation of this reserve is obtained by determining the single premium, annual premium, gross premium and life annuity with use at the constant force assumption. The premium is obtained by determining the life annuity and single prem…
ABSTRACT This nal project discusses the maximum ow using the Ford-Fulkerson al- gorithm and linear programming. Maximum ow problem solving using the Ford-Fulkerson algorithm is limited to capacity constraints, while solving using linear programming can be used for various kinds of constraints. At the end of the discussion, a maximum ow problem is given which is solved by using both …
ABSTRACT This nal project discusses some properties of decient perfect numbers, namely, every odd perfect numbers has a decient perfect numbers. Then there are odd perfect numbers and Descartes numbers from the decient perfect numbers. This is a review of article from Holdener dan Rachfal [The American Mathematical Monthly, 126 (2019), 541-546]. Keywords: Prime numbers, sigma function…
ABSTRACT This final projects discusses the trapezoidal fuzzy numbers transportation problem with mixed constraints. The cost coefficient is a fuzzy number that appears because there is uncertainty in costs that cannot be predicted due to several factors. The solution to the trapezoidal fuzzy number transportation problem uses the best candidate method (BCM) and the Vogel’s approximation …
ABSTRACT This final project discusses the mathematical modeling of a production planning using the preemptive goal programming method for priority based decision making. This problem aims to optimize the production planning by meeting the specified constraints and minimizing deviations from each goal to be achieved, based on the five types of best seller bread, production profits, producti…
ABSTRACT This nal project discusses the solution of assignment problem in the form of triangular fuzzy numbers that converted into crisp numbers, by using centroid method as ranking function. Then, the assignment problem in the form of crisp numbers is completed by using the Hungarian method, so that the solution that obtained from this method is used to properly place workers in order to…
ABSTRACT This nal project discusses the development of Japanese theorem for cyclic pentagon. The method is used to construct the diagonal from each point of the cyclic pentagon, so that three triangles are formed. Then it shows that the sum of incirle's radius of three triangles from the diagonal of cyclic pentagon is equal to the sum of incircle's radius of three triangles from diagonal …
ABSTRACT This final project discusses the existence of the perfect powers obtained by the result of the addition and subtraction of two Fibonacci numbers, namely and under the condition . In the case of , the addition or subtraction of and gives a product of and with and under the condition of or . Then the product of and is the perfect power in the form of with , a…
ABSTRACT This nal project discusses the properties of BN -algebra, the relationship BN - algebra with B -algebra, BF -algebra and Coxeter algebra. These properties are proved by using the binary operations contained in the group. This nal project is a review of article of Kim dan Kim [Kyungpook Mathematical Journal, 53 (2013), 175-184]. Keywords: BN-algebra, B-algebra, BF-algebra, Coxet…
This nal project discusses the development of high-order iteration methods with a weight function approach to nd solutions to systems of nonlinear sys- tems equations. Analytically it is proven that the resulting method have a convergance of six order. The computational test shows the obtained methods are comparable to the existing class methods. Keywords: Iterative method, order of conv…
ABSTRACT This nal project discusses the determination of the eigenvalues and eigenvectors of a triangular fuzzy number matrix. The negative-positive denition triangular fuzzy number is expressed based on its geometrical area. The goal is to determine the arithmetic operations constructed on the result of multiplication of the triangular fuzzy numbers. Then the negative-positive triangul…
ABSTRACT This final project discusses a modification of the Newton’s method with memory using the acceleration parameter to solve nonlinear equations. Modification is made by replacing the invariant parameter in the modified Newton method without memory with the acceleration parameter. The analysis of convergence shows that the convergene order of the proposed method is of 1+√2. Furthe…
ABSTRACT This final project discusses the optimal derivative-free iterative method based on inverse interpolation for solving nonlinear equations. The discussion begins with estimating the derivative of the function in the proposed method using the Cordero-Torregrosa conjecture, then it is continued by conducting a convergence analysis which shows that the proposed method is of order eight…
ABSTRACT This paper discusses Zillmer's reserve of last survivor endowment life insurance. Last survivor is life insurance of two person who are x years and y years old with a condition that premium is payed until the last death of insurance clients. Zillmer's reserve is modied prospective's reserve using the size of Zillmer's rate. The value of reserves is obtained by determining the sin…