In this paper, a method is suggested to solve the nonlinear interval number programming problem with uncertain coefficients both in nonlinear objective function and nonlinear constraints. Based on an order relation of interval number, the uncertain objective function is transformed into two deterministic objective functions, in which the robustness of design is considered. Through a modified po...

Abstract In this paper, we use interval-valued fuzzy numbers to fuzzify the crisp linear programming to three cases. The first case, we use intervalvalued fuzzy numbers to fuzzify the coefficients in the objective function. We get a linear programming in the fuzzy sense. The second case, we use interval-valued fuzzy numbers to fuzzify the coefficients akj in the constraints about xj, j = 1, 2, ...

Helios is the first (to our knowledge) modeling language for global optimization using interval analysis. Helios makes it possible to state global optimization problems almost as in scientific papers and textbooks and is guaranteed to find all isolated solutions in constraint-solving problems and all global optima in optimization problems. Helios statements are compiled to Newton, a constraint ...

The interval linear programming (IvLP) 1 is a method for decision making under uncertainty. A weak feasible solution to IvLP is called weakly optimal if it is optimal for some scenario of the IvLP. One of the basic and difficult tasks in IvLP is to check whether a given point is weak optimal. In this paper, we investigate linear programming problems with interval right-hand side. Some necessary...

The equivalence between the interval-valued fuzzy set (IVFS) and the intuitionistic fuzzy set (IFS) is exploited to study linear programming problems involving interval uncertainty modeled using IFS. The non-membership of IFS is constructed with three different viewpoints viz., optimistic, pessimistic, and mixed. These constructions along with their indeterminacy factors result in S-shaped memb...

This paper discusses a class of linear programming problems with interval coefficients in both the objective functions and constraints. The noninferior solutions to such problems are defined based on two order relations between intervals, and can be found by solving a parametric linear programming problem. Considering the uncertain returns of assets in capital markets as intervals, we propose a...

The purpose of this paper is to analyze the convergence of interval-type algorithms for solving the generalized fractional program. They are characterized by an interval [LBk, UBk] including A*, and the length of the interval is reduced at each iteration. A closer analysis of the bounds LBk and UBk allows to modify slightly the best known interval-type algorithm NEWMODM accordingly to prove its...

This paper presents en algorithm for solving interval linear programming problems. The algorithm is a finite iterative method, which in each iteration solves a full row rank interval linear progranming problem, with only one additional constraint. The solution and/or problem chosen appears to be conputationally more efficient than that in the Ben-Israel and Robers algorithm.

8 This article investigates the consistency of interval fuzzy preference relations based on interval 9 arithmetic, and new definitions are introduced for additive consistent, multiplicative consistent 10 and weakly transitive interval fuzzy preference relations. Transformation functions are put 11 forward to convert normalized interval weights into consistent interval fuzzy preference relations...

A proper edge-coloring of a given undirected graph with natural numbers identified with colors is an interval (or consecutive) coloring if the colors of edges incident to each vertex form an interval of consecutive integers. Not all graphs admit such an edge-coloring and the problem of deciding whether a graph is interval colorable is NP-complete. For a graph that is not interval colorable, det...