in this paper, the notions of $(t,s)$-composition matrix and$(t,s)$-interval-valued intuitionistic fuzzy equivalence matrix areintroduced where $(t,s)$ is a dual pair of triangular module. theyare the generalization of composition matrix and interval-valuedintuitionistic fuzzy equivalence matrix. furthermore, theirproperties and characterizations are presented. then a new methodbased on $tilde{...

A major issue in Lagrangian relaxation for integer programming problems is to maximize the dual function which is piece-wise linear, and consists of many facets. Available methods include the subgradient method, the bundle method, and the recently developed surrogate subgradient method. Each of the above methods, however, has its own limitations. Based on the insights obtained from these method...

In this paper, a new approach to determine the numerical solution of two-dimensional fuzzy Fredholm integral equation of the second kind (2DFFIE2) is proposed. This method is based on the fuzzy bivariate Bernstein polynomials. By using fuzzy bivariate Bernstein polynomials, a 2DFFIE2 can be transformed to a dual fuzzy linear system. The error estimate of this method is presented in terms of the...

The dual simplex algorithm is an attractive alternative as a solution method for linear programming problems. Since the addition of new constraints to a problem typically breaks primal feasibility but not dual feasibility, the dual simplex can be deployed for rapid reoptimization, without the need of finding new primal basic feasible solutions. This is especially useful in integer programming, ...

Recently, the primal–dual simplex method has been used to solve linear programs with a large number of columns. We present a parallel primal–dual simplex algorithm that is capable of solving linear programs with at least an order of magnitude more columns than the previous work. The algorithm repeatedly solves several linear programs in parallel and combines the dual solutions to obtain a new d...

Twenty-four algorithmic variants of the path-generation approach were investigated, based on the formulated LP model (MMP, MMD), the LP solution method (primal, dual), the pricing mechanism (single, multiple, partial), and the selection of dual variables (extreme-point, interior-point). Table I summarizes the codings used to specify these 24 algorithms. In option C, the master problem was solve...

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 m...

the purpose of this paper is to develop a methodology for solving a new type of matrix games in which payoffs are expressed with triangular intuitionistic fuzzy numbers (tifns). in this methodology, the concept of solutions for matrix games with payoffs of tifns is introduced. a pair of auxiliary intuitionistic fuzzy programming models for players are established to determine optimal strategies...

This paper deals with ridge estimation of fuzzy nonparametric regression models using triangular fuzzy numbers. This estimation method is obtained by implementing ridge regression learning algorithm in the La- grangian dual space. The distance measure for fuzzy numbers that suggested by Diamond is used and the local linear smoothing technique with the cross- validation procedure for selecting t...