The main purpose of this paper is to consider the t-best simultaneousapproximation in fuzzy normed spaces. We develop the theory of t-bestsimultaneous approximation in quotient spaces. Then, we discuss the relationshipin t-proximinality and t-Chebyshevity of a given space and its quotientspace.

The main purpose of this paper is to find t-best approximations in fuzzy normed spaces. We introduce the notions of t-proximinal sets and F-approximations and prove some interesting theorems. In particular, we investigate the set of all t-best approximations to an element from a set.

We study the interval subset sum problem (ISSP), a generalization of the classic subset-sum problem, where given a set of intervals, the goal is to choose a set of integers, at most one from each interval, whose sum best approximates a target integer T . For the cardinality constrained interval subset-sum problem (kISSP), at least kmin and at most kmax integers must be selected. Our main result...

Recall that the approximation ratio for an approximation algorithm is a measure to evaluate the approximation performance of the algorithm. The closer the ratio to 1 the better the approximation performance of the algorithm. It is notable that there is a class of NP-hard optimization problems, most originating from scheduling problems, for which there are polynomial time approximation algorithm...

We give a polynomial time approximation scheme (PTAS) for the recti-linear Steiner arborescence problem in the plane. The result is obtained by modifying Arora's PTAS for Euclidean TSP. The previously best known result was a 2-approximation algorithm.

For five single machine total tardiness problems a fully polynomial-time approximation scheme (FPTAS) based on a graphical algorithm is presented. The FPTAS has the best running time among the known approximation schemes for these problems.